Artykuły w czasopismach: „Double Gaussian Distribution”

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Khatoon, Rukaiya, Zahir Shah, Ranjeev Misra, and Rupjyoti Gogoi. "Study of long-term flux and photon index distributions of blazars using RXTE observations." Monthly Notices of the Royal Astronomical Society 491, no. 2 (2019): 1934–40. http://dx.doi.org/10.1093/mnras/stz3108.

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ABSTRACT We present a detailed study of flux and index distributions of three blazars [one flat-spectrum radio quasar (FSRQ) and two BL Lacertae objects (BL Lacs)] by using 16 yr of Rossi X-ray Timing Explorer (RXTE) archival data. The three blazars were chosen such that their flux and index distributions have sufficient number of data points (≥90) with relatively less uncertainty $\left(\overline{\sigma _{\rm err}^{2}}/\sigma ^{2} &lt; 0.2\right)$ in light curves. Anderson–Darling (AD) test and histogram fitting show that flux distribution of FSRQ 3C 273 is lognormal, while its photon index distribution is Gaussian. This result is consistent with linear Gaussian perturbation in the particle acceleration time-scale, which produces lognormal distribution in flux. However, for two BL Lacs, viz. Mrk 501 and Mrk 421, AD test shows that their flux distributions are neither Gaussian nor lognormal, and their index distributions are non-normal. The histogram fitting of Mrk 501 and Mrk 421 suggests that their flux distributions are more likely to be a bimodal, and their index distributions are double Gaussian. Since, Sinha et al. had shown that Gaussian distribution of index produces a lognormal distribution in flux, double Gaussian distribution of index in Mrk 501 and Mrk 421 indicates that their flux distributions are probably double lognormal. Observation of double lognormal flux distribution with double Gaussian distribution in index reaffirms two flux states hypothesis. Further, the difference observed in the flux distribution of FSRQ (3C 273) and BL Lacs (Mrk 501 and Mrk 421) at X-rays suggests that the low-energy emitting electrons have a single lognormal flux distribution, while the high-energy ones have a double lognormal flux distribution.

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Schreiber, Johannes, Amr Balbaa, and Carlo L. Bottasso. "Brief communication: A double-Gaussian wake model." Wind Energy Science 5, no. 1 (2020): 237–44. http://dx.doi.org/10.5194/wes-5-237-2020.

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Abstract. In this paper, an analytical wake model with a double-Gaussian velocity distribution is presented, improving on a similar formulation by Keane et al. (2016). The choice of a double-Gaussian shape function is motivated by the behavior of the near-wake region that is observed in numerical simulations and experimental measurements. The method is based on the conservation of momentum principle, while stream-tube theory is used to determine the wake expansion at the tube outlet. The model is calibrated and validated using large eddy simulations replicating scaled wind turbine experiments. Results show that the tuned double-Gaussian model is superior to a single-Gaussian formulation in the near-wake region.

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Crandall, Sara, Stephen Houston, and Bharat Ratra. "Non-Gaussian error distribution of 7Li abundance measurements." Modern Physics Letters A 30, no. 25 (2015): 1550123. http://dx.doi.org/10.1142/s0217732315501230.

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We construct the error distribution of [Formula: see text] abundance measurements for 66 observations (with error bars) used by Spite et al. (2012) that give [Formula: see text] (median and [Formula: see text] symmetrized error). This error distribution is somewhat non-Gaussian, with larger probability in the tails than is predicted by a Gaussian distribution. The 95.4% confidence limits are [Formula: see text] in terms of the quoted errors. We fit the data to four commonly used distributions: Gaussian, Cauchy, Student’s t and double exponential with the center of the distribution found with both weighted mean and median statistics. It is reasonably well described by a widened [Formula: see text] Student’s t distribution. Assuming Gaussianity, the observed A(Li) is [Formula: see text] away from that expected from standard Big Bang Nucleosynthesis (BBN) given the Planck observations. Accounting for the non-Gaussianity of the observed A(Li) error distribution reduces the discrepancy to [Formula: see text], which is still significant.

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Jung, Hak-Kee. "Subthreshold Characteristics of Double Gate MOSFET for Gaussian Function Distribution." Journal of the Korean Institute of Information and Communication Engineering 16, no. 6 (2012): 1260–65. http://dx.doi.org/10.6109/jkiice.2012.16.6.1260.

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Tang, Heng-Song, Wei-Lie Meng, and Neng-Hui Zhang. "Mechanical properties of double-stranded DNA biofilm with Gaussian distribution." Acta Mechanica Sinica 30, no. 1 (2014): 15–19. http://dx.doi.org/10.1007/s10409-014-0023-z.

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Fitch, A. C. "An Improved Double-Gaussian Closure for the Subgrid Vertical Velocity Probability Distribution Function." Journal of the Atmospheric Sciences 76, no. 1 (2019): 285–304. http://dx.doi.org/10.1175/jas-d-18-0149.1.

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Abstract The vertical velocity probability distribution function (PDF) is analyzed throughout the depth of the lower atmosphere, including the subcloud and cloud layers, in four large-eddy simulation (LES) cases of shallow cumulus and stratocumulus. Double-Gaussian PDF closures are examined to test their ability to represent a wide range of turbulence statistics, from stratocumulus cloud layers characterized by Gaussian turbulence to shallow cumulus cloud layers displaying strongly non-Gaussian turbulence statistics. While the majority of the model closures are found to perform well in the former case, the latter presents a considerable challenge. A new model closure is suggested that accounts for high skewness and kurtosis seen in shallow cumulus cloud layers. The well-established parabolic relationship between skewness and kurtosis is examined, with results in agreement with previous studies for the subcloud layer. In cumulus cloud layers, however, a modified relationship is necessary to improve performance. The new closure significantly improves the estimation of the vertical velocity PDF for shallow cumulus cloud layers, in addition to performing well for stratocumulus. In particular, the long updraft tail representing the bulk of cloudy points is much better represented and higher-order moments diagnosed from the PDF are also greatly improved. However, some deficiencies remain owing to fundamental limitations of representing highly non-Gaussian turbulence statistics with a double-Gaussian PDF.

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Jung, Hak Kee. "Projected Range Dependent Tunneling Current of Asymmetric Double Gate MOSFET." International Journal of Electrical and Computer Engineering (IJECE) 6, no. 1 (2016): 113. http://dx.doi.org/10.11591/ijece.v6i1.9342.

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This study is to analyze the changes of tunneling current according to projected range, a variable of Gaussian function of channel doping function of Asymmetric Double Gate; ADG MOSFET. In MOSFET with channel length below 10 nm, tunneling current occupies a large percentage among off-currents. The increase of tunneling current has a large effect on the characteristics of subthreshold such as threshold voltage movement and the decline of subthreshold swing value, so the accurate analysis of this is being required. To analyze this, potential distribution of series form was obtained using Gaussian distribution function, and using this hermeneutic potential distribution, thermionic emission current and tunneling current making up off-current were obtained. At this point, the effect that the changes of projected range, a variable of Gaussian distribution function, have on the ratio of tunneling current among off-currents was analyzed. As a result, the smaller projected range was, the lower the ratio of tunneling current was. When projected range increased, tunneling current increased largely. Also, it was observed that the value of projected range which the ratio of tunneling current increased changed according to maximum channel doping value, channel length, and channel width.

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Jung, Hak Kee. "Projected Range Dependent Tunneling Current of Asymmetric Double Gate MOSFET." International Journal of Electrical and Computer Engineering (IJECE) 6, no. 1 (2016): 113. http://dx.doi.org/10.11591/ijece.v6i1.pp113-119.

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This study is to analyze the changes of tunneling current according to projected range, a variable of Gaussian function of channel doping function of Asymmetric Double Gate; ADG MOSFET. In MOSFET with channel length below 10 nm, tunneling current occupies a large percentage among off-currents. The increase of tunneling current has a large effect on the characteristics of subthreshold such as threshold voltage movement and the decline of subthreshold swing value, so the accurate analysis of this is being required. To analyze this, potential distribution of series form was obtained using Gaussian distribution function, and using this hermeneutic potential distribution, thermionic emission current and tunneling current making up off-current were obtained. At this point, the effect that the changes of projected range, a variable of Gaussian distribution function, have on the ratio of tunneling current among off-currents was analyzed. As a result, the smaller projected range was, the lower the ratio of tunneling current was. When projected range increased, tunneling current increased largely. Also, it was observed that the value of projected range which the ratio of tunneling current increased changed according to maximum channel doping value, channel length, and channel width.

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Ohmasa, Yoshinori, and Ayano Chiba. "Intensity distribution profile of double Bragg scattering in the small-angle region from highly oriented pyrolytic graphite." Acta Crystallographica Section A Foundations and Advances 74, no. 6 (2018): 681–98. http://dx.doi.org/10.1107/s2053273318012469.

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It is observed that radial streak patterns of double Bragg scattering appear in the small-angle X-ray scattering from highly oriented pyrolytic graphite (HOPG). The intensity profile of double Bragg scattering from an HOPG sample is calculated theoretically. Assuming that the c axes of the graphite crystallites in the HOPG sample are distributed around an orientation vector and their distribution function has a Gaussian form, it is found that the intensity profile of double Bragg scattering is expressed by a double Gaussian function of the scattering angle and the azimuthal angle of the streak. The calculated intensity profile is compared with the experimental one. The method developed in this article can be used to estimate the orientational distribution of crystallites in uniaxial polycrystalline materials.

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Bobby, A., S. Verma, K. Asokan, P. M. Sarun, and B. K. Antony. "Phase transition induced double-Gaussian barrier height distribution in Schottky diode." Physica B: Condensed Matter 431 (December 2013): 6–10. http://dx.doi.org/10.1016/j.physb.2013.08.037.

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Jiang, J. Z., Q. A. Pankhurst, and M. R. J. Gibbs. "A double-Gaussian approach to the moment distribution in amorphous metals." Hyperfine Interactions 94, no. 1 (1994): 2137–43. http://dx.doi.org/10.1007/bf02063752.

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Akter, Suraiya, and Simon P. Goodwin. "Finding binary star fractions in any distribution." Monthly Notices of the Royal Astronomical Society 488, no. 3 (2019): 3446–51. http://dx.doi.org/10.1093/mnras/stz1939.

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Abstract Candidate visual binary systems are often found by identifying two stars that are closer together than would be expected by chance. However, in regions with non-trivial density distributions, the ‘random’ distances between stars varies because of the background distribution, as well as the presence of binaries. We show that when no binaries are present, the distribution of the ratios of the distances to the nearest and tenth nearest neighbours, d1/d10, is always well approximated by a Gaussian with mean 0.2–0.3 and variance 0.16–0.19 for any underlying density distribution. The introduction of binaries causes some (or all) nearest neighbours to become closer than expected by random chance, introducing a component to the distribution where d1/d10 is much lower than expected. We show how a simple single or double Gaussian fit to the distribution of d1/d10 can be used to find the binary fraction in any underlying density distribution quickly and simply.

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Lairez, Didier, Alexis Chennevière, and Frédéric Ott. "Exact resolution function for double-disk chopper neutron time-of-flight spectrometers: application to reflectivity." Journal of Applied Crystallography 53, no. 2 (2020): 464–76. http://dx.doi.org/10.1107/s1600576720001764.

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The exact resolution function of the transfer vector for the HERMÈS reflectometer at the Laboratoire Léon Brillouin is calculated as an example of a neutron time-of-flight spectrometer with a double-disk chopper. The calculation accounts for the wavelength distribution of the incident beam, the tilt of the chopper axis, collimation and gravity, without an assumption of Gaussian distributions or the independence of these different contributions. A numerical implementation is provided. It is shown that data fitting using this exact resolution function allows much better results to be reached than with the usual approximation by a Gaussian profile.

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Ge, Shurong, and Junhua Wu. "The Analysis of WJ Distribution as an Extended Gaussian Function: Case Study." Applied Sciences 12, no. 15 (2022): 7773. http://dx.doi.org/10.3390/app12157773.

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The double exponential WJ distribution has been shown to competently describe extreme events and critical phenomena, while the Gaussian function has celebrated rich applications in many other fields. Here we present the analysis that the WJ distribution may be properly treated as an extended Gaussian function. Based on the Taylor expansion, we propose three methods to formulate the WJ distribution in the form of Gaussian functions, with Method I and Method III being accurate and self-consistent, and elaborate the relationship among the parameters of the functions. Moreover, we derive the parameter scaling formula of the WJ distribution to express a general Gaussian function, with the work illustrated by a classical case of extreme events and critical phenomena and application to topical medical image processing to prove the effectiveness of the WJ distribution rather than the Gaussian function. Our results sturdily advocate that the WJ distribution can elegantly represent a Gaussian function of arbitrary parameters, whereas the latter usually is not able to satisfactorily describe the former except for specific parameter sets. Thus, it is conclusive that the WJ distribution offers applicability in extreme events and critical phenomena as well as processes describable by the Gaussian function, namely, implying plausibly a unifying approach to the pertinent data processing of those quite distinct areas and establishing a link between relevant extreme value theories and Gaussian processes.

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Sybingco, Edwin, and Elmer P. Dadios. "Blind Image Quality Assessment Based on Natural Statistics of Double-Opponency." Journal of Advanced Computational Intelligence and Intelligent Informatics 22, no. 5 (2018): 725–30. http://dx.doi.org/10.20965/jaciii.2018.p0725.

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One of the challenges in image quality assessment (IQA) is to determine the quality score without the presence of the reference image. In this paper, the authors proposed a no-reference image quality assessment method based on the natural statistics of double-opponent (DO) cells. It utilizes the statistical modeling of the three opponency channels using the generalized Gaussian distribution (GGD) and asymmetric generalized Gaussian distribution (AGGD). The parameters of GGD and AGGD are then applied to feedforward neural network to predict the image quality. Result shows that for any opposing channels, its natural statistics parameters when applied to feedforward neural network can achieve satisfactory prediction of image quality.

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Angus, John E. "Some Asymptotic Analysis of Resistant Rules For Outlier Labeling." Probability in the Engineering and Informational Sciences 3, no. 1 (1989): 157–64. http://dx.doi.org/10.1017/s0269964800001042.

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Previous studies have examined the behavior of outlier detection rules for symmetric distributions that label as “outside” any observations that fall outside the interval [FL – k(Fu – FL), Fu + k(Fu – FL)], where FL and FU are functions of the order statistics estimating the 0.25 and 0.75 quantiles of the distribution underlying the i.i.d. sample. A measure of the performance of this type of rule is the “some-outside rate” per sample computed with respect to a given (usually Gaussian) null distribution. The “some-outside rate” (SOR) per sample is the probability that the sample will contain one or more observations labeled as “outside,” given that the null distribution is the true distribution. In this paper, asymptotic expansions of k = kn as a function of n that guarantee an asymptotically constant, prespecified SOR are given for a variety of symmetric null distributions including the Gaussian, double exponential, logistic, and Cauchy distributions. The main theorem also applies to the case of a nonsymmetric null distribution by slightly modifying the labeling rule.

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Huang, Wayne Cheng-Wei, and Herman Batelaan. "Dynamics Underlying the Gaussian Distribution of the Classical Harmonic Oscillator in Zero-Point Radiation." Journal of Computational Methods in Physics 2013 (October 7, 2013): 1–19. http://dx.doi.org/10.1155/2013/308538.

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Stochastic electrodynamics (SED) predicts a Gaussian probability distribution for a classical harmonic oscillator in the vacuum field. This probability distribution is identical to that of the ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and the Gaussian probability distribution, we perform a numerical simulation and follow the motion of the oscillator. The dynamical information obtained through the simulation provides insight to the connection between the classic double-peak probability distribution and the Gaussian probability distribution. A main objective for SED research is to establish to what extent the results of quantum mechanics can be obtained. The present simulation method can be applied to other physical systems, and it may assist in evaluating the validity range of SED.

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Li, Yin-Jie, Shao-Peng Tang, Yuan-Zhu Wang, et al. "Population Properties of Neutron Stars in the Coalescing Compact Binaries." Astrophysical Journal 923, no. 1 (2021): 97. http://dx.doi.org/10.3847/1538-4357/ac34f0.

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Abstract We perform a hierarchical Bayesian inference to investigate the population properties of the coalescing compact binaries involving at least one neutron star (NS). With the current gravitational-wave (GW) observation data, we can rule out none of the double Gaussian, single Gaussian, and uniform NS mass distribution models, though a specific double Gaussian model inferred from the Galactic NSs is found to be slightly more preferred. The mass distribution of black holes (BHs) in the neutron star–black hole (NSBH) population is found to be similar to that in the Galactic X-ray binaries. Additionally, the ratio of the merger rate densities between NSBHs and BNSs is estimated to be ∼3:7. The spin properties of the binaries, though constrained relatively poorly, play a nontrivial role in reconstructing the mass distribution of NSs and BHs. We find that a perfectly aligned spin distribution can be ruled out, while a purely isotropic distribution of spin orientation is still allowed. To evaluate the feasibility of reliably determining the population properties of NSs in the coalescing compact binaries with upcoming GW observations, we perform simulations with a mock population. We find that with 100 detections (including BNSs and NSBHs) the mass distribution of NSs can be well determined, and the fraction of BNSs can also be accurately estimated.

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Clerk, Luke De, and Sergey Savel’ev. "Nonstationary Generalised Autoregressive Conditional Heteroskedasticity Modelling for Fitting Higher Order Moments of Financial Series within Moving Time Windows." Journal of Probability and Statistics 2022 (May 20, 2022): 1–19. http://dx.doi.org/10.1155/2022/4170866.

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Here, we present a method for a simple GARCH (1,1) model to fit higher order moments for different companies’ stock prices. When we assume a Gaussian conditional distribution, we fail to capture any empirical data when fitting the first three even moments of financial time series. We show instead that a mixture of normal distributions is needed to better capture the higher order moments of the data. To demonstrate this point, we construct regions (parameter diagrams), in the fourth- and sixth-order standardised moment space, where a GARCH (1,1) model can be used to fit moment values and compare them with the corresponding moments from empirical data for different sectors of the economy. We found that the ability of the GARCH model with a double normal conditional distribution to fit higher order moments is dictated by the time window our data spans. We can only fit data collected within specific time window lengths and only with certain parameters of the conditional double Gaussian distribution. In order to incorporate the nonstationarity of financial series, we assume that the parameters of the GARCH model can have time dependence. Furthermore, using the method developed here, we investigate the effect of the COVID-19 pandemic has upon stock’s stability and how this compares with the 2008 financial crash.

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Ghosh, Aniruddha, and Somnath Chattopadhyaya. "Prediction of Temperature Distribution on Submerged Arc Welded Plates through Gaussian Heat Distribution Technique." Advanced Materials Research 284-286 (July 2011): 2477–80. http://dx.doi.org/10.4028/www.scientific.net/amr.284-286.2477.

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Submerged Arc Welding process (SAW) is a high quality, very high deposition rate welding process. It has lot of social and economical implecations.This paper makes an attempt to uncover an important area on studies of temperature distribution during submerged arc welding because this may pave the way for application of microstructure modeling, thermal stress analysis, residual stress/distribution and welding process simulation. Prediction of temperature variation of entire plates during welding through an analytical solution is derived from the transient multi dimensional heat conduction of semi infinite plate. The heat input that is applied on the plate is exactly same amount of heat lost for electric arc, which is assumed to be a moving double conical heat source with Gaussian distribution for Submerged Arc Welding process. Good agreement between predicted and experimental results has been achieved.

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Jung, Hak-Kee. "Analysis of Drain Induced Barrier Lowering for Double Gate MOSFET Using Gaussian Distribution." Journal of the Korean Institute of Information and Communication Engineering 16, no. 2 (2012): 325–30. http://dx.doi.org/10.6109/jkiice.2012.16.2.325.

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Janardhanam, V., I. Jyothi, P. R. Sekhar Reddy, et al. "Double Gaussian barrier distribution of permalloy (Ni0.8Fe0.2) Schottky contacts to n-type GaN." Superlattices and Microstructures 120 (August 2018): 508–16. http://dx.doi.org/10.1016/j.spmi.2018.06.019.

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Wallis, Kenneth F. "The Two-Piece Normal, Binormal, or Double Gaussian Distribution: Its Origin and Rediscoveries." Statistical Science 29, no. 1 (2014): 106–12. http://dx.doi.org/10.1214/13-sts417.

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Shibib, Khalid, Mohammed Minshid, and Nebras Alattar. "Thermal and stress analysis in Nd: YAG laser rod with different double end pumping methods." Thermal Science 15, suppl. 2 (2011): 399–407. http://dx.doi.org/10.2298/tsci101201004s.

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In this work, the finite element analysis has been used to predict the temperature distribution in Nd: YAG laser rod; double end-pumped by two methods Gaussian or top hat beam. The rod is cooled by water passing through annular, which surrounds the active media. The temperature distribution has been used to predict numerically, the nodal displacements, strain and stress based on the principle of virtual work. The main task is to determine the temperature distribution in Nd: YAG laser rod, the subsequent value and location of maximum tensile hoop stress associated with the two types of the double end pumping for different absorption power. Some conclusions are obtained; as the radius pumping ratio increases the location of maximum hoop stress will move toward the periphery and vice-versa. Small reduction is observed in the location of maximum hoop stress when pumping method change from the top-hat beam to Gaussian beam, especially at low radius pumping ratio and high absorption power. Top hat beam end pumping will cause more intense tension hoop stress at the facets of the rod than that of Gaussian beam even the later may produce high center temperature. This work may be important for designer while choosing the type of pumping, maximum produced tensile hoop stress and its location, especially when hoop stress is ultimate.

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Hu, Baoyu, Yulong Pei, Jinjun Tang, and Wei Gao. "Common network characteristics of four bus transport networks in Northeast China based on a perfect space P." International Journal of Modern Physics B 32, no. 21 (2018): 1850228. http://dx.doi.org/10.1142/s0217979218502284.

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The space P and space L representation models are often adopted together in the empirical analysis of bus transport networks (BTNs). In this paper, we develop a new representation model for BTNs using double edge weights and node weights, namely perfect space P. The model incorporates the number and lengths of directed routes between the two stations and the number of routes that connect to each station. Based on the model, we develop an empirical study on four large BTNs in Northeast China. Some common network characteristics of the BTNs are revealed and discussed in detail. The results show that several empirical distributions follow an exponential law. Moreover, the unweighted path length distributions can be fitted by a Gaussian function, while the weighted path length distributions can be fitted by a composite Gaussian function. Specifically, we introduce the weighted-degree distribution with different lengths and the special edge weight distribution, given the new evidence for the random behavior during the expansion of BTNs, including new stations and routes.

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Abdul Razzaq, Mohammed Jalal, and Kadhim A. Hubeatir. "Analysis of Thermal Effects within Cylindrical Shape Solid-State Laser Rod." Materials Science Forum 1002 (July 2020): 264–72. http://dx.doi.org/10.4028/www.scientific.net/msf.1002.264.

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In this work, a temperature-dependent analytical model was modified to predict the thermal effects of diode laser double–end-pumped cylindrical laser rod under Gaussian pump beam distribution. Heat load and temperature distribution were analyzed using the Kirchhoff integral transform method. Results show that a maximum temperature difference of approximately 69.61 K was obtained on each side face of the laser rod at a maximum power of 40 W (equally divided on each face). The total thermal focal length of approximately 34.64 mm was calculated under the Gaussian pumping profile. The finite element method code incorporated with well-verified software was used to numerically verify the obtained results, where the analytical and numerical results are highly matched. The results reveal that the total thermal focal length produced in a double–end-pumped geometry is two times less than that obtained from a single-end-pumped geometry.

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Aljohani, Hassan M. "Stationary Wavelet with Double Generalised Rayleigh Distribution." Mathematical Problems in Engineering 2021 (May 3, 2021): 1–14. http://dx.doi.org/10.1155/2021/6646287.

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Statistics are mathematical tools applying scientific investigations, such as engineering and medical and biological analyses. However, statistical methods are often improved. Nowadays, statisticians try to find an accurate way to solve a problem. One of these problems is estimation parameters, which can be expressed as an inverse problem when independent variables are highly correlated. This paper’s significant goal is to interpret the parameter estimates of double generalized Rayleigh distribution in a regression model using a wavelet basis. It is difficult to use the standard version of the regression methods in practical terms, which is obtained using the likelihood. Since a noise level usually makes the result of estimation unstable, multicollinearity leads to various estimates. This kind of problem estimates that features of the truth are complicated. So it is reasonable to use a mixed method that combines a fully Bayesian approach and a wavelet basis. The usual rule for wavelet approaches is to choose a wavelet basis, where it helps to compute the wavelet coefficients, and then, these coefficients are used to remove Gaussian noise. Recovering data is typically calculated by inverting the wavelet coefficients. Some wavelet bases have been considered, which provide a shift-invariant wavelet transform, simultaneously providing improvements in smoothness, in recovering, and in squared-error performance. The proposed method uses combining a penalized maximum likelihood approach, a penalty term, and wavelet tools. In this paper, real data are involved and modeled using double generalized Rayleigh distributions, as they are used to estimate the wavelet coefficients of the sample using numerical tools. In practical applications, wavelet approaches are recommended. They reduce noise levels. This process may be useful since the noise level is often corrupted in real data, as a significant cause of most numerical estimation problems. A simulation investigation is studied using the MCMC tool to estimate the underlying features as an essential task statistics.

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Moldovan, Dumitrița, and Radu Fechete. "Bimodal 1H Double Quantum Build-Up Curves by Fourier and Laplace-like Transforms on Aged Cross-Linked Natural Rubber." Polymers 13, no. 20 (2021): 3523. http://dx.doi.org/10.3390/polym13203523.

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The 1H DQ Fourier and Laplace-like spectra for a series of cross-linked natural rubber (NR) samples naturally aged during six years are presented and characterized. The DQ build-up curves of these samples present two peaks which cannot be described by classical functions. The DQ Fourier spectra can be obtained after a numeric procedure which introduces a correction time which depends less on the chosen approximation, spin-½ and isolated CH2 and CH3 functional groups. The DQ Fourier spectra are well described by the distributions of the residual dipolar coupling correlated with the distribution of the end-to-end vector of the polymer network, and with the second and fourth van Vleck moments. The deconvolution of DQ Fourier spectra with a sum of four Gaussian variates show that the center and the width of Gaussian functions increase linearly with the increase in the cross-link density. The Laplace-like spectra for the natural aged NR DQ build-up curves are presented. The centers of four Gaussian distributions obtained via both methods are consistent. The differences between the Fourier and Laplace-like spectra consist mainly of the spectral resolution in the favor of Laplace-like spectra. The last one was used to discuss the effect of natural aging for cross-linked NR.

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Grana, Dario. "Multivariate probabilistic rock-physics models using Kumaraswamy distributions." GEOPHYSICS 86, no. 5 (2021): MR261—MR270. http://dx.doi.org/10.1190/geo2021-0124.1.

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Rock-physics models are physical equations that map petrophysical properties into geophysical variables, such as elastic properties and density. These equations are generally used in quantitative log and seismic interpretation to estimate the properties of interest from measured well logs and seismic data. Such models are generally calibrated using core samples and well-log data and result in accurate predictions of the unknown properties. Because the input data are often affected by measurement errors, the model predictions are often uncertain. Instead of applying rock-physics models to deterministic measurements, I have applied the models to the probability density function (PDF) of the measurements. This approach has been previously adopted in the literature using Gaussian distributions, but for petrophysical properties of porous rocks, such as volumetric fractions of solid and fluid components, the standard probabilistic formulation based on Gaussian assumptions is not applicable due to the bounded nature of the properties, the multimodality, and the nonsymmetric behavior. The proposed approach is based on the Kumaraswamy PDF for continuous random variables, which allows modeling double-bounded nonsymmetric distributions and is analytically tractable, unlike beta or Dirichlet distributions. I have developed a probabilistic rock-physics model applied to double-bounded continuous random variables distributed according to a Kumaraswamy distribution and derived the analytical solution of the probability distribution of the rock-physics model predictions. The method is evaluated for three rock-physics models: Raymer’s equation, Dvorkin’s stiff sand model, and Kuster-Toksöz’s inclusion model.

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Doh, Guentae, Holak Kim, Dongho Lee, Sanghoo Park, Stéphane Mazouffre, and Wonho Choe. "Structure of the ion acceleration region in cylindrical Hall thruster plasmas." Journal of Physics D: Applied Physics 55, no. 22 (2022): 225204. http://dx.doi.org/10.1088/1361-6463/ac5773.

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Abstract We investigated the structure of the ion acceleration region and the shape of the ion velocity distribution function (IVDF) in cylindrical Hall thruster plasmas, using laser-induced fluorescence spectroscopy on Xe II metastable ions. On the thruster axis, the acceleration front is located deeper than a half-length of the discharge channel length, and the acceleration region reaches up to 3 times the discharge channel length (several centimeters) away from the channel exit, regardless of the discharge condition. It is noteworthy that ion acceleration mostly (more than 70%) takes place outside the discharge channel. The IVDF is close to a single Gaussian inside the discharge channel. It however becomes substantially asymmetric when moving downstream. Double Gaussian distributions including cold and hot ion groups was in good agreement with the measured ion velocity distributions downstream with an R-squared greater than 0.995.

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Grana, Dario. "Bayesian rock-physics inversion with Kumaraswamy prior models." GEOPHYSICS 87, no. 3 (2022): M87—M97. http://dx.doi.org/10.1190/geo2021-0469.1.

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The prediction of rock and fluid volumetric fractions from elastic attributes often is referred to as petrophysical or rock-physics inversion because it requires rock-physics models to map petrophysical properties into geophysical variables, such as velocities and density. Bayesian approaches are suitable for rock-physics inverse problems because the solution, expressed in the form of a probability distribution, can represent the uncertainty of the model predictions due to the errors in the measured data. Bayesian inverse methods often rely on Gaussian prior distributions for their analytical tractability. However, Gaussian distributions are theoretically not applicable to rock and fluid volumetric fractions because, by definition, they are nonzero on the entire set of real numbers, whereas rock and fluid volumetric fractions are bounded between zero and one. The proposed rock physics inversion is based on a Bayesian approach that assumes Kumaraswamy probability density functions for the prior distribution to model double-bounded nonsymmetric continuous random variables between zero and one. The results of the Bayesian inverse problem are the pointwise probability distributions of the rock and fluid volumetric fractions conditioned on the seismic attributes. In the first application, the method is validated using synthetic well-log data for the soft sand and stiff rock-physics models with comparisons with several prior models. In the second application, the method is applied to a 2D real data set to obtain the posterior distribution, the maximum a posteriori, and the confidence intervals of porosity, mineral volumes, and fluid saturations. The most likely model of rock and fluid properties estimated from the posterior distribution assuming a Kumaraswamy prior model finds higher accuracies compared to the corresponding results obtained with a Gaussian prior model.

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32

Yang, Hai-Feng, Yao-Hua Hu, and Yong-Gang Tan. "Transfer of a wave packet in double-well potential." International Journal of Modern Physics B 32, no. 11 (2018): 1850131. http://dx.doi.org/10.1142/s021797921850131x.

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Energy potentials with double-well structures are typical in atoms and molecules systems. A manipulation scheme using Half Cycles Pulses (HCPs) is proposed to transfer a Gaussian wave packet between the two wells. On the basis of quantum mechanical simulations, the time evolution and the energy distribution of the wave packet are evaluated. The effect of time parameters, amplitude, and number of HCPs on spatial and energy distribution of the final state and transfer efficiency are investigated. After a carefully tailored HCPs sequence is applied to the initial wave packet localized in one well, the final state is a wave packet localized in the other well and populated at the lower energy levels with narrower distribution. The present scheme could be used to control molecular reactions and to prepare atoms with large dipole moments.

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Ruzgas, Tomas, and Indrė Drulytė. "Kernel Density Estimators for Gaussian Mixture Models." Lietuvos statistikos darbai 52, no. 1 (2013): 14–21. http://dx.doi.org/10.15388/ljs.2013.13919.

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The problem of nonparametric estimation of probability density function is considered. The performance of kernel estimators based on various common kernels and a new kernel K (see (14)) with both fixed and adaptive smoothing bandwidth is compared in terms of the symmetric mean absolute percentage error using the Monte Carlo method. The kernel K is everywhere positive but has lighter tails than the Gaussian density. Gaussian mixture models from a collection introduced by Marron and Wand (1992) are taken for Monte Carlo simulations. The adaptive kernel method outperforms the smoothing with a fixed bandwidth in the majority of models. The kernel K shows better performance for Gaussian mixtures with considerably overlapping components and multiple peaks (double claw distribution).

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Zhang, Jianwei, Yiyan Yang, Chengmin Zhang, et al. "The mass distribution of Galactic double neutron stars: constraints on the gravitational-wave sources like GW170817." Monthly Notices of the Royal Astronomical Society 488, no. 4 (2019): 5020–28. http://dx.doi.org/10.1093/mnras/stz2020.

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ABSTRACT The merger event of double neutron star (DNS) system (GW170817) was detected by the gravitational-wave (GW) detectors (Advanced LIGO and Advanced Virgo) in 2017 for the first time, so their mass distribution has become a significant topic with the new round GW hunting (O3) in 2019. A few models (e.g. Gaussian, two-Gaussian, or mixture-Gaussian) were adopted to draw the mass distribution of observed Galactic DNS systems, however, there is no a confirmed model now due to the small size of DNS samples (N < 20). Here we focus on determining the most probable distribution ranges of DNS masses without model selection by assuming the neutron star masses to be uniformly distributed between the lower and upper bounds. We apply a Bayesian analysis and Markov chain Monte Carlo simulation to 15 Galactic DNS systems, and obtain that the component masses of DNS systems should mainly fall in the range of 1.165–1.590 M⊙, and the predominant ranges for the total mass, mass ratio, and chirp mass lie in 2.535–2.867 M⊙, 0.741–0.995, and 1.115–1.237 M⊙, respectively. Our results are in agreement with the properties of DNS in GW170817, whose 90 per cent credible intervals for the component masses, total masses, mass ratio, and chirp masses are 1.16–1.60 M⊙, $2.73_{-0.01}^{+0.04}\, \mathrm{ M}_\odot$, 0.73–1.00, and $1.186_{-0.001}^{+0.001}\, \mathrm{ M}_\odot$, respectively. The above similarity is an important indicator that reveals the source of GW170817 to be a DNS system from the galaxy NGC 4993, and our results can be tested by the forthcoming GW hunting O3.

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Lu, Yong-Feng, and Yoshinobu Aoyagi. "Temperature Rise and Heat Flux Induced by Laser Beam with Double-Gaussian Intensity Distribution." Japanese Journal of Applied Physics 34, Part 1, No. 7A (1995): 3759–63. http://dx.doi.org/10.1143/jjap.34.3759.

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Chiani, Marco, and Alberto Zanella. "On the distribution of an arbitrary subset of the eigenvalues for some finite dimensional random matrices." Random Matrices: Theory and Applications 09, no. 01 (2019): 2040004. http://dx.doi.org/10.1142/s2010326320400043.

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We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant operator. Specifically, we derive compact expressions for the joint probability distribution function of the eigenvalues and the expectation of functions of the eigenvalues, including joint moments, for the case of both ordered and unordered eigenvalues.

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Konygin, G. N., and O. M. Nemtsova. "USING A DOUBLE CONVOLUTION OF LORENTZ AND GAUSS FUNCTIONS FOR PROCESSING THE MÖSSBAUER SPECTRA OF THE SUPERSATURATED DISORDERED SOLID SOLUTIONS." Journal of Applied Spectroscopy 88, no. 6 (2021): 907–13. http://dx.doi.org/10.47612/0514-7506-2021-88-6-907-913.

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An algorithm for mathematical processing of the Mössbauer spectra of supersaturated disordered solid solutions by the Tikhonov regularization method using a double convolution of the Lorentz function and two Gaussians is proposed. By the examples of spectra of supersaturated disordered solid solutions Fe100–xGex (x = 10—25 at.%) and Fe75Si15Al10, it is shown that the algorithm allows more correct processing, which provides a reliable distribution function of the hyperfine magnetic field. It is shown that to take into account the statistical ensemble of nonequivalent local atomic configurations of Fe atoms in disordered supersaturated solid solutions, it is necessary to use not only the convolution of two Gaussian functions, but also the projection scaling factor of the hyperfine magnetic field onto the velocity scale.

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Zacchei, Enrico, and José Luis Molina. "Estimation of optimal area and volume for double arch-dams." MATEC Web of Conferences 211 (2018): 14002. http://dx.doi.org/10.1051/matecconf/201821114002.

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This research is focused on the optimum area and volume estimation of double arch dams. The first stage of the methodology refers to defining issues about Bayesian estimators to obtain the value for designing the optimum dam shape. After that, the shape equations are iterated step-bystep to obtain the optimal solution. From the inventory of existing dams, it is possible to extract many important values although they are not sufficient. To obtain the non-available data, the Gaussian distribution under the Bayesian theorem hypotheses has been employed. This theorem converts the prior distribution using unknown parameters into the posterior distribution which provides expected estimators. The choice of the dam shape is strongly based on the experience, therefore by knowing and applying real information of existing dams it is possible to carry out a more precise analysis.

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Rusakov, Oleg V., and Roman A. Ragozin. "On extremes of PSI-processes and gaussian limits of their normalized independent identical distributed sums." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 9, no. 2 (2022): 269–77. http://dx.doi.org/10.21638/spbu01.2022.208.

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We define PSI-process — Poisson Stochastic Index process, as a continuous time random process which is obtained by a manner of a randomization for the discrete time of a random sequence. We consider the case when a double stochastic Poisson process generates this randomization, i. e. such Poisson process has a random intensity. Under condition of existence of the second moment the stationary PSI-processes possess a covariance which coincides with the Laplace transform of the random intensity. In our paper we derive distributions of extremes for a one PSI-process, and these extremes are expressed in terms of Laplace transform of the random intensity. The second task that we solve is a convergence of the maximum of Gaussian limit for normalized sums of i. i. d. stationary PSI-processes. We obtain necessary and sufficient conditions for the intensity under which, after proper centering and normalization, this Gaussian limit converges in distribution to the double Exponential Law. For solution this task we essentially base on the monograph: M.R.Leadbetter, Georg Lindgren, Holder Rootzen (1986) “Extremes and Relative Properties of Random Sequences and Processes”, end essentially use the Tauberian theorem in W. Feller form.

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40

Naumann, A. K., A. Seifert, and J. P. Mellado. "A refined statistical cloud closure using double-Gaussian probability density functions." Geoscientific Model Development 6, no. 5 (2013): 1641–57. http://dx.doi.org/10.5194/gmd-6-1641-2013.

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Abstract. We introduce a probability density function (PDF)-based scheme to parameterize cloud fraction, average liquid water and liquid water flux in large-scale models, that is developed from and tested against large-eddy simulations and observational data. Because the tails of the PDFs are crucial for an appropriate parameterization of cloud properties, we use a double-Gaussian distribution that is able to represent the observed, skewed PDFs properly. Introducing two closure equations, the resulting parameterization relies on the first three moments of the subgrid variability of temperature and moisture as input parameters. The parameterization is found to be superior to a single-Gaussian approach in diagnosing the cloud fraction and average liquid water profiles. A priori testing also suggests improved accuracy compared to existing double-Gaussian closures. Furthermore, we find that the error of the new parameterization is smallest for a horizontal resolution of about 5–20 km and also depends on the appearance of mesoscale structures that are accompanied by higher rain rates. In combination with simple autoconversion schemes that only depend on the liquid water, the error introduced by the new parameterization is orders of magnitude smaller than the difference between various autoconversion schemes. For the liquid water flux, we introduce a parameterization that is depending on the skewness of the subgrid variability of temperature and moisture and that reproduces the profiles of the liquid water flux well.

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41

Naumann, A. K., A. Seifert, and J. P. Mellado. "A refined statistical cloud closure using double-Gaussian probability density functions." Geoscientific Model Development Discussions 6, no. 1 (2013): 1085–125. http://dx.doi.org/10.5194/gmdd-6-1085-2013.

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Abstract. We introduce a probability density function (PDF) based scheme to parameterize cloud fraction, average liquid water and liquid water flux in large-scale models, that is developed from and tested against large-eddy simulations and observational data. Because the tails of the PDFs are crucial for an appropriate parameterization of cloud properties, we use a double-Gaussian distribution that is able to represent the observed, skewed PDFs properly. Introducing two closure equations, the resulting parameterization relies on the first three moments of the subgrid variability of temperature and moisture as input parameters. The parameterization is shown to be clearly superior to a single-Gaussian approach in diagnosing the cloud fraction and average liquid water profiles and improves existing double-Gaussian closures. We find that the error of the new parameterization is smallest for a horizontal resolution of about 5–20 km and also depends on the appearance of mesoscale structures that are accompanied by higher rain rates. In combination with simple autoconversion schemes that only depend on the liquid water, the error introduced by the new parameterization is orders of magnitude smaller than the difference between various autoconversion schemes. For the liquid water flux, we introduce a parameterization that is depending on the skewness of the subgrid variability of temperature and moisture and that reproduces the profiles of the liquid water flux well.

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42

Sondergaard, Thomas, and Pierre F. J. Lermusiaux. "Data Assimilation with Gaussian Mixture Models Using the Dynamically Orthogonal Field Equations. Part II: Applications." Monthly Weather Review 141, no. 6 (2013): 1761–85. http://dx.doi.org/10.1175/mwr-d-11-00296.1.

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Abstract The properties and capabilities of the Gaussian Mixture Model–Dynamically Orthogonal filter (GMM-DO) are assessed and exemplified by applications to two dynamical systems: 1) the double well diffusion and 2) sudden expansion flows; both of which admit far-from-Gaussian statistics. The former test case, or twin experiment, validates the use of the Expectation-Maximization (EM) algorithm and Bayesian Information Criterion with GMMs in a filtering context; the latter further exemplifies its ability to efficiently handle state vectors of nontrivial dimensionality and dynamics with jets and eddies. For each test case, qualitative and quantitative comparisons are made with contemporary filters. The sensitivity to input parameters is illustrated and discussed. Properties of the filter are examined and its estimates are described, including the equation-based and adaptive prediction of the probability densities; the evolution of the mean field, stochastic subspace modes, and stochastic coefficients; the fitting of GMMs; and the efficient and analytical Bayesian updates at assimilation times and the corresponding data impacts. The advantages of respecting nonlinear dynamics and preserving non-Gaussian statistics are brought to light. For realistic test cases admitting complex distributions and with sparse or noisy measurements, the GMM-DO filter is shown to fundamentally improve the filtering skill, outperforming simpler schemes invoking the Gaussian parametric distribution.

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Jung, Hak-Kee. "The Analysis of Breakdown Voltage for the Double-gate MOSFET Using the Gaussian Doping Distribution." Journal of information and communication convergence engineering 10, no. 2 (2012): 200–204. http://dx.doi.org/10.6109/jicce.2012.10.2.200.

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Yıldırım, Nezir, Abdulmecit Turut, and Veyis Turut. "The theoretical and experimental study on double-Gaussian distribution in inhomogeneous barrier-height Schottky contacts." Microelectronic Engineering 87, no. 11 (2010): 2225–29. http://dx.doi.org/10.1016/j.mee.2010.02.007.

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Beştaş, A. N., S. Yazıcı, F. Aktaş, and B. Abay. "Double Gaussian distribution of barrier height for FeCrNiC alloy Schottky contacts on p-Si substrates." Applied Surface Science 318 (November 2014): 280–84. http://dx.doi.org/10.1016/j.apsusc.2014.05.126.

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Tuğluoğlu, Nihat, Ö. Faruk Yüksel, Haluk Şafak, and Serdar Karadeniz. "The double Gaussian distribution of inhomogeneous barrier heights in the organic-on-inorganic Schottky devices." physica status solidi (a) 209, no. 11 (2012): 2313–16. http://dx.doi.org/10.1002/pssa.201228163.

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Shan, Chenghao, Weidong Zhou, Yefeng Yang, and Hanyu Shan. "A new robust Kalman filter with measurement loss based on mixing distribution." Transactions of the Institute of Measurement and Control 44, no. 8 (2021): 1699–707. http://dx.doi.org/10.1177/01423312211054942.

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A new robust Kalman filter (KF) based on mixing distribution is presented to address the filtering issue for a linear system with measurement loss (ML) and heavy-tailed measurement noise (HTMN) in this paper. A new Student’s t-inverse-Wishart-Gamma mixing distribution is derived to more rationally model the HTMN. By employing a discrete Bernoulli random variable (DBRV), the form of measurement likelihood function of double mixing distributions is converted from a weighted sum to an exponential product, and a hierarchical Gaussian state-space model (HGSSM) is therefore established. Finally, the system state, the intermediate random variables (IRVs) of the new STIWG distribution, and the DBRV are simultaneously estimated by utilizing the variational Bayesian (VB) method. Numerical example simulation experiment indicates that the proposed filter in this paper has superior performance than current algorithms in processing ML and HTMN.

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Bottani, E. J., J. R. Zarate, and L. E. Torre Cascarini De. "Argon and Nitrogen Physical Adsorption on Boron Nitride." Adsorption Science & Technology 4, no. 1-2 (1987): 121–30. http://dx.doi.org/10.1177/0263617487004001-211.

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Physical adsorption isotherms of N2 and Ar on boron nitride are analysed and the behaviour of the adsorbed phase is discussed. Different models are used to interpret the adsorbed states. The behaviour of the BET C parameter suggests that a phase-transition occurs in Ar adsorption which is not showed in its isotherm. Adsorption energies distribution functins are calculated using a double Gaussian as distribution function. Nitrogen cross-sectional areas, under experimental conditions are estimated respect to those of the Ar.

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N. Veerabagu Suresh, R.C. Sarasvathi, Haresh M. Pandya, and K.B. Rajesh. "Generation of multiple focal hole segment by tight focusing of azimuthally polarized double ring shaped beam." Journal of Environmental Nanotechnology 2, (Special Issue) (2022): 37–41. http://dx.doi.org/10.13074/jent.2013.02.nciset36.

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Based on the vector diffraction theory, the effect of phase modulation on the intensity distribution of TEM11 mode azimuthally polarized Laguerre-Gaussian beam in the focal region of high NA lens is investigated theoretically. It is observed that a properly designed complex phase filter can generate multiple focal hole segment and it is useful for the manipulation of optical traps.

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Gullu, H. H., D. Seme Sirin, and D. E. Yıldız. "Analysis of Double Gaussian Distribution on Barrier Inhomogeneity in a Au/n-4H SiC Schottky Diode." Journal of Electronic Materials 50, no. 12 (2021): 7044–56. http://dx.doi.org/10.1007/s11664-021-09254-3.

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