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Journal articles on the topic 'Probability mass functions'

Author: Grafiati

Published: 6 September 2023

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1

Gilbert, L., G. de Cooman, and E. E. Kerre. "Practical implementation of possibilistic probability mass functions." Soft Computing - A Fusion of Foundations, Methodologies and Applications 7, no. 5 (April 1, 2003): 304–9. http://dx.doi.org/10.1007/s00500-002-0217-3.

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2

Racine, Jeffrey S., Qi Li, and Karen X. Yan. "Kernel smoothed probability mass functions for ordered datatypes." Journal of Nonparametric Statistics 32, no. 3 (May 12, 2020): 563–86. http://dx.doi.org/10.1080/10485252.2020.1759595.

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3

Drane, J. Wanzer, Suhua Cao, Lixia Wang, and T. Postelnicu. "Limiting Forms of Probability Mass Functions via Recurrence Formulas." American Statistician 47, no. 4 (November 1993): 269. http://dx.doi.org/10.2307/2685285.

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4

Drane, J. Wanzer, Suhua Cao, Lixia Wang, and T. Postelnicu. "Limiting forms of Probability Mass Functions via Recurrence Formulas." American Statistician 47, no. 4 (November 1993): 269–74. http://dx.doi.org/10.1080/00031305.1993.10475996.

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5

Bergbusch, Peter A. "Isochrone Probability Functions for Old Stellar Systems." Symposium - International Astronomical Union 190 (1999): 345–46. http://dx.doi.org/10.1017/s0074180900118170.

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The isochrone probability function (IPF) is derived from the slope of the mass–distance relation on an isochrone in where the distance along the isochrone is computed with respect to some arbitrary, well-defined point. IPFs contain the information needed to calculate both luminosity functions and color functions, and they provide a straightforward way of generating synthetic stellar populations.

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6

Provost, Serge B., Min Jiang, and Hyung-Tae Ha. "Moment-Based Approximations of Probability Mass Functions with Applications Involving Order Statistics." Communications in Statistics - Theory and Methods 38, no. 12 (June 3, 2009): 1969–81. http://dx.doi.org/10.1080/03610920902835052.

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7

Warr, Richard L. "Numerical Approximation of Probability Mass Functions via the Inverse Discrete Fourier Transform." Methodology and Computing in Applied Probability 16, no. 4 (August 24, 2013): 1025–38. http://dx.doi.org/10.1007/s11009-013-9366-3.

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8

Rachev, S. T., and I. Olkin. "Mass transportation problems with capacity constraints." Journal of Applied Probability 36, no. 2 (June 1999): 433–45. http://dx.doi.org/10.1239/jap/1032374463.

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We exhibit solutions of Monge–Kantorovich mass transportation problems with constraints on the support of the feasible transportation plans and additional capacity restrictions. The Hoeffding–Fréchet inequalities are extended for bivariate distribution functions having fixed marginal distributions and satisfying additional constraints. Sharp bounds for different probabilistic functionals (e.g. Lp-distances, covariances, etc.) are given when the family of joint distribution functions has prescribed marginal distributions, satisfies restrictions on the support, and is bounded from above, or below, by other distributions.

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9

Wang, Jiandong, Zhen Wang, Xuan Zhou, and Fan Yang. "Design of delay timers based on estimated probability mass functions of alarm durations." Journal of Process Control 110 (February 2022): 154–65. http://dx.doi.org/10.1016/j.jprocont.2022.01.002.

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10

Belaid, Nawal, Smail Adjabi, Nabil Zougab, and Célestin C. Kokonendji. "Bayesian bandwidth selection in discrete multivariate associated kernel estimators for probability mass functions." Journal of the Korean Statistical Society 45, no. 4 (December 2016): 557–67. http://dx.doi.org/10.1016/j.jkss.2016.04.001.

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11

Belaid, Nawal, Smail Adjabi, Célestin C. Kokonendji, and Nabil Zougab. "Bayesian local bandwidth selector in multivariate associated kernel estimator for joint probability mass functions." Journal of Statistical Computation and Simulation 86, no. 18 (May 5, 2016): 3667–81. http://dx.doi.org/10.1080/00949655.2016.1181178.

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12

Urbán, András, and Viktor Józsa. "Investigation of Fuel Atomization with Density Functions." Periodica Polytechnica Mechanical Engineering 62, no. 1 (November 7, 2017): 33. http://dx.doi.org/10.3311/ppme.11312.

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Atomization involves mass, energy, and impulse transfer, in such a complex way that the overall process can only be described by empirical and semi-empirical correlations to date. The phenomenon of atomization is used in numerous applications, e.g., in combustion technology and metallurgy. However, many formulae are available in the literature to derive mean diameters of the spray, size distribution functions are barely discussed. Based on the measurement results performed earlier by a Phase Doppler Anemometer, twenty probability density functions were evaluated and seven are discussed in detail over the course of the present paper. The atomization pressure was varied, and characteristic regimes of the spray were measured. Interestingly, the analysis showed that not only the three most commonly used probability density functions (Nukiyama-Tanasawa, Rosin-Rammler, and Gamma) are eligible for describing the size distribution of the spray.

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13

YOUSSEF, SAUL. "QUANTUM MECHANICS AS BAYESIAN COMPLEX PROBABILITY THEORY." Modern Physics Letters A 09, no. 28 (September 14, 1994): 2571–86. http://dx.doi.org/10.1142/s0217732394002422.

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As a possible alternative to conventional quantum mechanics, the Bayesian version of probability theory is extended to include complex probabilities. An additional assumption of realism restores a frequency interpretation while coexisting with Bell’s theorem. Such complex probabilities are shown to have a superposition principle, to include wave functions which are expansions in eigenfunctions of Hermitian operators, to have a path-integral representation and to describe both pure and mixed systems. A scalar particle in Rd is shown to obey the Schrödinger equation with mass, vector potential and metric appearing as moments of a fundamental probability. Illustrative examples are given. The quantum version of Bayesian inference is discussed.

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14

Zhang, Xu-Hong, and Fu-Hu Liu. "Statistical Behavior of Lepton Pair Spectrum in the Drell-Yan Process and Signal from Quark-Gluon Plasma in High-Energy Collisions." Advances in High Energy Physics 2021 (June 1, 2021): 1–21. http://dx.doi.org/10.1155/2021/9548737.

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We analyze the transverse momentum ( p T ) spectra of lepton pairs ( ℓ ℓ ¯ ) generated in the Drell-Yan process, as detected in proton-nucleus (pion-nucleus) and proton-(anti)proton collisions by ten collaborations over a center-of-mass energy s N N or s if in a simplified form) range from ~ 20 GeV to above 10 TeV. Three types of probability density functions (the convolution of two Lévy-Tsallis functions, the two-component Erlang distribution, and the convolution of two Hagedorn functions) are utilized to fit and analyze the p T spectra. The fit results are approximately in agreement with the collected experimental data. Consecutively, we obtained the variation law of related parameters as a function of s and invariant mass Q . In the fit procedure, a given Lévy-Tsallis (or Hagedorn) function can be regarded as the probability density function of transverse momenta contributed by a single quark ( q ) or anti-quark ( q ¯ ). The Drell-Yan process is then described by the statistical method.

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15

Nadarajah, Saralees, and Jiahang Lyu. "New discrete heavy tailed distributions as models for insurance data." PLOS ONE 18, no. 5 (May 5, 2023): e0285183. http://dx.doi.org/10.1371/journal.pone.0285183.

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Although many data sets are discrete and heavy tailed (for example, number of claims and claim amounts if recorded as rounded values), not many discrete heavy tailed distributions are available in the literature. In this paper, we discuss thirteen known discrete heavy tailed distributions, propose nine new discrete heavy tailed distributions and give expressions for their probability mass functions, cumulative distribution functions, hazard rate functions, reversed hazard rate functions, means, variances, moment generating functions, entropies and quantile functions. Tail behaviour and a measure of asymmetry are used to compare the known and new discrete heavy tailed distributions. The better fits of the discrete heavy tailed distributions over their continuous counterparts as assessed by probability plots are illustrated using three data sets. Finally, a simulated study is performed to assess the finite sample performance of the maximum likelihood estimators used in the data application section.

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16

Jaafari, Abolfazl, Davood Mafi-Gholami, Binh Thai Pham, and Dieu Tien Bui. "Wildfire Probability Mapping: Bivariate vs. Multivariate Statistics." Remote Sensing 11, no. 6 (March 13, 2019): 618. http://dx.doi.org/10.3390/rs11060618.

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Wildfires are one of the most common natural hazards worldwide. Here, we compared the capability of bivariate and multivariate models for the prediction of spatially explicit wildfire probability across a fire-prone landscape in the Zagros ecoregion, Iran. Dempster–Shafer-based evidential belief function (EBF) and the multivariate logistic regression (LR) were applied to a spatial dataset that represents 132 fire events from the period of 2007–2014 and twelve explanatory variables (altitude, aspect, slope degree, topographic wetness index (TWI), annual temperature, and rainfall, wind effect, land use, normalized difference vegetation index (NDVI), and distance to roads, rivers, and residential areas). While the EBF model successfully characterized each variable class by four probability mass functions in terms of wildfire probabilities, the LR model identified the variables that have a major impact on the probability of fire occurrence. Two distribution maps of wildfire probability were developed based upon the results of each model. In an ensemble modeling perspective, we combined the two probability maps. The results were verified and compared by the receiver operating characteristic (ROC) and the Wilcoxon Signed-Rank Test. The results showed that although an improved predictive accuracy (AUC = 0.864) can be achieved via an ensemble modeling of bivariate and multivariate statistics, the models fail to individually provide a satisfactory prediction of wildfire probability (EBFAUC = 0.701; LRAUC = 0.728). From these results, we recommend the employment of ensemble modeling approaches for different wildfire-prone landscapes.

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17

Younus, Muhammad, Sabah Usman, and Samia Jawed. "Effects of Obesity on Lung Functions in Young Adults." Annals of King Edward Medical University 24, no. 1 (April 28, 2018): 672–78. http://dx.doi.org/10.21649/akemu.v24i1.2363.

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Obesity is a global health problem and its prevalence is increasing continuously. It is the fifth leading cause of death worldwide and is associated with decreased lung functions. Objective: This study was designed to compare the pulmonary functions in obese and non-obese subjects. Additionally, we aimed to correlate the body mass index (BMI), waist circumference (WC), and waist-to-hip ratio (WHR) with pulmonary function tests (PFT’s). Material and Methods: This cross sectional comparative study was conducted at the Institute of Chest Medicine, King Edward Medical University, Lahore, Pakistan. One hundred and twenty individuals consisting of 60 obese (30 males, 30 females) and 60 non-obese (30 males, 30 females), fulfilling the inclusion criteria, were enrolled through non-probability purposive sampling. Informed written consent was taken from all subjects. The demographic information of these subjects such as name, age, sex, height, weight, body mass index, waist circumference, and waist-to-hip ratio were recorded. Spirometry of all the subjects was performed on Spirolab iii. Correlation between FVC, FEV1, FEV1/ FVC ratio and body mass index, waist circumference, and waist to hip ratio was measured by Pearson coefficient. A p value

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18

BANNUR, V. M., L. S. CELENZA, HUANG-HE CHEN, SHUN-FU GAO, and C. M. SHAKIN. "MEAN-FIELD THEORY OF CONFINED PARTICLES: OFF-MASS-SHELL ASPECTS OF RELATIVISTIC WAVE FUNCTIONS." International Journal of Modern Physics A 05, no. 08 (April 20, 1990): 1479–507. http://dx.doi.org/10.1142/s0217751x90000660.

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We study nonlinear equations in two variables which arise in a theory of nontopological solitons. For simplicity, we limit our considerations to a relativistic mean-field description of two scalar particles which form a bound state. We present results for a model in which the constituents have a momentum-dependent mass whose form is motivated by nonperturbative QCD studies. We discuss the probability distribution of the squared four-momentum, k2, of a particle of momentum kμ. We also introduce a definition of the “constituent mass” of our particles and comment on the relation of our model to the constituent quark model of hadron structure. The wave functions obtained have an interesting structure and are free of the on-mass-shell singularities which are present in solutions of conventional Bethe-Salpeter equations.

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19

Skoog, Gary R., and James E. Ciecka. "Probability Mass Functions for Years to Final Separation from the Labor Force Induced by the Markov Model." Journal of Forensic Economics 16, no. 1 (December 1, 2003): 51–86. http://dx.doi.org/10.5085/0898-5510-16.1.51.

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20

Skoog, Gary, and James Ciecka. "Probability mass functions for additional years of labor market activity induced by the Markov (increment–decrement) model." Economics Letters 77, no. 3 (November 2002): 425–31. http://dx.doi.org/10.1016/s0165-1765(02)00159-3.

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21

Dilworth, S. J., and S. R. Mane. "Applications of Fuss-Catalan Numbers to Success Runs of Bernoulli Trials." Journal of Probability and Statistics 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/2071582.

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In a recent paper, the authors derived the exact solution for the probability mass function of the geometric distribution of orderk, expressing the roots of the associated auxiliary equation in terms of generating functions for Fuss-Catalan numbers. This paper applies the above formalism for the Fuss-Catalan numbers to treat additional problems pertaining to occurrences of success runs. New exact analytical expressions for the probability mass function and probability generating function and so forth are derived. First, we treat sequences of Bernoulli trials withr≥1occurrences of success runs of lengthkwithl-overlapping. The casel<0, where there must be a gap of at leastltrials between success runs, is also studied. Next we treat the distribution of the waiting time for therthnonoverlapping appearance of a pair of successes separated by at mostk-2failures (k≥2).

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22

Iyengar, R. N., and C. S. Manohar. "Probability Distribution of the Eigenvalues of the Random String Equation." Journal of Applied Mechanics 56, no. 1 (March 1, 1989): 202–7. http://dx.doi.org/10.1115/1.3176047.

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The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.

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23

Kolomiitseva, T. A. "On the asymptotic behavior of subharmonic functions with a regular mass distribution." Journal of Soviet Mathematics 49, no. 2 (April 1990): 906–12. http://dx.doi.org/10.1007/bf02205638.

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24

Dandekar, Rahul, and Anupam Kundu. "Mass fluctuations in random average transfer process in open set-up." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 1 (January 1, 2023): 013205. http://dx.doi.org/10.1088/1742-5468/acac70.

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Abstract We define a new mass transport model on a one-dimensional lattice of size N with continuous masses at each site. The lattice is connected to mass reservoirs of different ‘chemical potentials’ at the two ends. The mass transfer dynamics in the bulk is equivalent to the dynamics of the gaps between particles in the random average process. In the non-equilibrium steady state, we find that the multi-site arbitrary order cumulants of the masses can be expressed as an expansion in powers of 1 / N where at each order the cumulants have a scaling form. We introduce a novel operator approach which allows us to compute these scaling functions at different orders of 1 / N . Moreover, this approach reveals that, to express the scaling functions for higher order cumulants completely one requires all lower order multi-site cumulants. This is in contrast to the Wick’s theorem in which all higher order cumulants are expressed solely in terms of two-site cumulants. We support our results with evidence from Monte Carlo simulations.

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25

Cressie, Noel, and Subhash Lele. "New models for Markov random fields." Journal of Applied Probability 29, no. 4 (December 1992): 877–84. http://dx.doi.org/10.2307/3214720.

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The Hammersley–Clifford theorem gives the form that the joint probability density (or mass) function of a Markov random field must take. Its exponent must be a sum of functions of variables, where each function in the summand involves only those variables whose sites form a clique. From a statistical modeling point of view, it is important to establish the converse result, namely, to give the conditional probability specifications that yield a Markov random field. Besag (1974) addressed this question by developing a one-parameter exponential family of conditional probability models. In this article, we develop new models for Markov random fields by establishing sufficient conditions for the conditional probability specifications to yield a Markov random field.

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26

Cressie, Noel, and Subhash Lele. "New models for Markov random fields." Journal of Applied Probability 29, no. 04 (December 1992): 877–84. http://dx.doi.org/10.1017/s0021900200043758.

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The Hammersley–Clifford theorem gives the form that the joint probability density (or mass) function of a Markov random field must take. Its exponent must be a sum of functions of variables, where each function in the summand involves only those variables whose sites form a clique. From a statistical modeling point of view, it is important to establish the converse result, namely, to give the conditional probability specifications that yield a Markov random field. Besag (1974) addressed this question by developing a one-parameter exponential family of conditional probability models. In this article, we develop new models for Markov random fields by establishing sufficient conditions for the conditional probability specifications to yield a Markov random field.

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27

Senga Kiessé, Tristan, Nabil Zougab, and Célestin C. Kokonendji. "Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data." Computational Statistics 31, no. 1 (October 20, 2015): 189–206. http://dx.doi.org/10.1007/s00180-015-0627-1.

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28

Guo, Shannon, and Samir E. Chidiac. "Probability Characteristics of a Crack Hitting Spherical Healing Agent Particles: Application to a Self-Healing Cementitious System." Materials 15, no. 20 (October 20, 2022): 7355. http://dx.doi.org/10.3390/ma15207355.

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A geometric model is developed to statistically study the probability characteristics of crack intersecting self-healing capsules with a structured random distribution in a cement paste mix. To evaluate the probability of a crack intersecting encapsulated particles, the fill ratio of the crack, and the depth of the first-hit capsule, Monte Carlo simulations are performed. The variables are the crack geometry, i.e., width, length, depth, orientation, skewness, and so on; the size and mass fraction of healing capsules; and the agglomeration of capsules. Models based on statistical analyses for hit probability , crack fill ratio at 95% confidence level, and first hit depth at 95% confidence level are expressed as functions of capsule size and mass fraction, as well as crack geometry. The model assumptions and results are evaluated using data reported in the literature. The data include results from experimental and theoretical studies.

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29

Scollnik, David Peter Michael. "Bayesian Inference for Three Bivariate Beta Binomial Models." Open Statistics & Probability Journal 08, no. 1 (October 16, 2017): 27–38. http://dx.doi.org/10.2174/1876527001708010027.

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Background:This paper considers three two-dimensional beta binomial models previously introduced in the literature. These were proposed as candidate models for modelling forms of correlated and overdispersed bivariate count data. However, the first model has a complicated form of bivariate probability mass function involving a generalized hypergeometric function and the remaining two do not have closed forms of probability mass functions and are not amenable to analysis using maximum likelihood. This limited their applicability.Objective:In this paper, we will discuss how the Bayesian analyses of these models may go forward using Markov chain Monte Carlo and data augmentation.Results:An illustrative example having to do with student achievement in two related university courses is included. Posterior and posterior predictive inferences and predictive information criteria are discussed.

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30

Kinugawa, Tomoya, Takashi Nakamura, and Hiroyuki Nakano. "Gravitational waves from Population III binary black holes are consistent with LIGO/Virgo O3a data for the chirp mass larger than ∼20 M⊙." Monthly Notices of the Royal Astronomical Society: Letters 504, no. 1 (April 5, 2021): L28—L33. http://dx.doi.org/10.1093/mnrasl/slab032.

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ABSTRACT The probability number distribution function of binary black hole mergers observed by LIGO/Virgo O3a has double peaks as a function of chirp mass Mchirp, total mass Mtotal, primary black hole mass M1, and secondary one M2, respectively. The larger chirp mass peak is at Mchirp≅ 30 M⊙. The distribution of M2 versus M1 follows the relation of M2≅ 0.7M1. For initial mass functions of Population III stars in the form of f(M) ∝ M−α, population synthesis numerical simulations with 0 ≤ α ≤ 1.5 are consistent with O3a data for Mchirp ≳ 20 M⊙. The distribution of M2 versus M1 for simulation data also agrees with M2 ≅ 0.7M1 relation of O3a data.

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31

Brandolin, Adriana, and Mariano Asteasuain. "Mathematical Modeling of Bivariate Distributions of Polymer Properties Using 2D Probability Generating Functions. Part II: Transformation of Population Mass Balances of Polymer Processes." Macromolecular Theory and Simulations 22, no. 5 (June 2013): 273–308. http://dx.doi.org/10.1002/mats.201200089.

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32

Larson, Vincent E., and Jean-Christophe Golaz. "Using Probability Density Functions to Derive Consistent Closure Relationships among Higher-Order Moments." Monthly Weather Review 133, no. 4 (April 2005): 1023–42. http://dx.doi.org/10.1175/mwr2902.1.

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Parameterizations of turbulence often predict several lower-order moments and make closure assumptions for higher-order moments. In principle, the low- and high-order moments share the same probability density function (PDF). One closure assumption, then, is the shape of this family of PDFs. When the higher-order moments involve both velocity and thermodynamic scalars, often the PDF shape has been assumed to be a double or triple delta function. This is equivalent to assuming a mass-flux model with no subplume variability. However, PDF families other than delta functions can be assumed. This is because the assumed PDF methodology is fairly general. This paper proposes closures for several third- and fourth-order moments. To derive the closures, the moments are assumed to be consistent with a particular PDF family, namely, a mixture of two trivariate Gaussians. (This PDF is also called a double Gaussian or binormal PDF by some authors.) Separately from the PDF assumption, the paper also proposes a simplified relationship between scalar and velocity skewnesses. This PDF family and skewness relationship are simple enough to yield simple, analytic closure formulas relating the moments. If certain conditions hold, this set of moments is specifically realizable. By this it is meant that the set of moments corresponds to a real Gaussian-mixture PDF, one that is normalized and nonnegative everywhere. This paper compares the new closure formulas with both large eddy simulations (LESs) and closures based on double and triple delta PDFs. This paper does not implement the closures in a single-column model and test them interactively. Rather, the comparisons are diagnostic; that is, low-order moments are extracted from the LES and treated as givens that are input into the closures. This isolates errors in the closures from errors in a single-column model. The test cases are three atmospheric boundary layers: a trade wind cumulus layer, a stratocumulus layer, and a clear convective case. The new closures have shortcomings, but nevertheless are superior to the double or triple delta closures in most of the cases tested.

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33

Kim, Taekyun, Dae Kim, L. LeeaHyunseok, and Seong-Ho Park. "Dimorphic properties of Bernoulli random variable." Filomat 36, no. 5 (2022): 1711–17. http://dx.doi.org/10.2298/fil2205711k.

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The aim of this paper is to study a dimorphic property associated with two different sums of identically independent Bernoulli random variables having two different families of probability mass functions. In addition, we give two expressions on sums of products of degenerate Stirling numbers of the second kind and Stirling numbers of the first kind connected with those two different sums of identically independent Bernoulli random variables.

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34

Berger, Uwe, Gerd Baumgarten, Jens Fiedler, and Franz-Josef Lübken. "A new description of probability density distributions of polar mesospheric clouds." Atmospheric Chemistry and Physics 19, no. 7 (April 8, 2019): 4685–702. http://dx.doi.org/10.5194/acp-19-4685-2019.

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Abstract. In this paper we present a new description of statistical probability density functions (pdfs) of polar mesospheric clouds (PMCs). The analysis is based on observations of maximum backscatter, ice mass density, ice particle radius, and number density of ice particles measured by the ALOMAR Rayleigh–Mie–Raman lidar for all PMC seasons from 2002 to 2016. From this data set we derive a new class of pdfs that describe the statistics of PMC events that is different from previous statistical methods using the approach of an exponential distribution commonly named the g distribution. The new analysis describes successfully the probability distributions of ALOMAR lidar data. It turns out that the former g-function description is a special case of our new approach. In general the new statistical function can be applied to many kinds of different PMC parameters, e.g., maximum backscatter, integrated backscatter, ice mass density, ice water content, ice particle radius, ice particle number density, or albedo measured by satellites. As a main advantage the new method allows us to connect different observational PMC distributions of lidar and satellite data, and also to compare with distributions from ice model studies. In particular, the statistical distributions of different ice parameters can be compared with each other on the basis of a common assessment that facilitates, for example, trend analysis of PMC.

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GABETTA, ESTER, and EUGENIO REGAZZINI. "ABOUT THE GENE FAMILIES SIZE DISTRIBUTION IN A RECENT MODEL OF GENOME EVOLUTION." Mathematical Models and Methods in Applied Sciences 20, no. 06 (June 2010): 1005–20. http://dx.doi.org/10.1142/s0218202510004519.

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We analyze a class of probability distributions for family sizes in a duplication, loss and change (DLC) model of genome evolution, recently introduced by Tiuryn, Wójtowicz and Rudnicki. After providing expressions for the generating functions of the density p and of the right-tail Q of the above distributions, we obtain closed forms for p and Q in terms of Gauss hypergeometric functions. Then, by resorting to the literature about special functions and their approximations, we provide an asymptotic expression for Q, which depends on parameters connected with the strengths of duplication and change. This shows that the DLC model yields a rich statistical model for the size distribution, whose elements are characterized by a composition of a power component with a negative exponential one. We also study the limiting distributions, as the parameters are made arbitrarily close to points of the boundary of their natural domain. In addition to the geometric distribution and to the unit mass at 1, the limiting class contains the distributions with the "longest" tails in the DLC model. A characterization of these probability laws is given.

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36

Sigtermans, David. "A Path-Based Partial Information Decomposition." Entropy 22, no. 9 (August 29, 2020): 952. http://dx.doi.org/10.3390/e22090952.

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Based on the conceptual basis of information theory, we propose a novel mutual information measure—‘path-based mutual information’. This information measure results from the representation of a set of random variables as a probabilistic graphical model. The edges in this graph are modeled as discrete memoryless communication channels, that is, the underlying data is ergodic, stationary, and the Markov condition is assumed to be applicable. The associated multilinear stochastic maps, tensors, transform source probability mass functions into destination probability mass functions. This allows for an exact expression of the resulting tensor of a cascade of discrete memoryless communication channels in terms of the tensors of the constituting communication channels in the paths. The resulting path-based information measure gives rise to intuitive, non-negative, and additive path-based information components—redundant, unique, and synergistic information—as proposed by Williams and Beer. The path-based redundancy satisfies the axioms postulated by Williams and Beer, the identity axiom postulated by Harder, and the left monotonicity axiom postulated Bertschinger. The ordering relations between redundancies of different joint collections of sources, as captured in the redundancy lattices of Williams and Beer, follow from the data processing inequality. Although negative information components can arise, we speculate that these either result from unobserved variables, or from adding additional sources that are statistically independent from all other sources to a system containing only non-negative information components. This path-based approach illustrates that information theory provides the concepts and measures for a partial information decomposition.

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37

Shirasaki, Masato, Kana Moriwaki, Taira Oogi, Naoki Yoshida, Shiro Ikeda, and Takahiro Nishimichi. "Noise reduction for weak lensing mass mapping: an application of generative adversarial networks to Subaru Hyper Suprime-Cam first-year data." Monthly Notices of the Royal Astronomical Society 504, no. 2 (April 9, 2021): 1825–39. http://dx.doi.org/10.1093/mnras/stab982.

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ABSTRACT We propose a deep-learning approach based on generative adversarial networks (GANs) to reduce noise in weak lensing mass maps under realistic conditions. We apply image-to-image translation using conditional GANs to the mass map obtained from the first-year data of Subaru Hyper Suprime-Cam (HSC) Survey. We train the conditional GANs by using 25 000 mock HSC catalogues that directly incorporate a variety of observational effects. We study the non-Gaussian information in denoised maps using one-point probability distribution functions (PDFs) and also perform matching analysis for positive peaks and massive clusters. An ensemble learning technique with our GANs is successfully applied to reproduce the PDFs of the lensing convergence. About $60{{\ \rm per\ cent}}$ of the peaks in the denoised maps with height greater than 5σ have counterparts of massive clusters within a separation of 6 arcmin. We show that PDFs in the denoised maps are not compromised by details of multiplicative biases and photometric redshift distributions, nor by shape measurement errors, and that the PDFs show stronger cosmological dependence compared to the noisy counterpart. We apply our denoising method to a part of the first-year HSC data to show that the observed mass distribution is statistically consistent with the prediction from the standard ΛCDM model.

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38

Beghin, Luisa, and Claudio Macci. "Fractional Discrete Processes: Compound and Mixed Poisson Representations." Journal of Applied Probability 51, no. 01 (March 2014): 19–36. http://dx.doi.org/10.1017/s0021900200010056.

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We consider two fractional versions of a family of nonnegative integer-valued processes. We prove that their probability mass functions solve fractional Kolmogorov forward equations, and we show the overdispersion of these processes. As particular examples in this family, we can define fractional versions of some processes in the literature as the Pólya-Aeppli process, the Poisson inverse Gaussian process, and the negative binomial process. We also define and study some more general fractional versions with two fractional parameters.

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39

Sun, Xiaoying, Hangzi Wu, and Yue Wu. "Probability mass functions forecasting of occupants’ sensation votes under the effects of temperature, illuminance, and sound level based on ANN." Journal of Building Engineering 43 (November 2021): 102882. http://dx.doi.org/10.1016/j.jobe.2021.102882.

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40

Du, Yuan-Wei, Yu-Kun Shan, Chang-Xing Li, and Rui Wang. "Mass Collaboration-Driven Method for Recommending Product Ideas Based on Dempster-Shafer Theory of Evidence." Mathematical Problems in Engineering 2018 (September 27, 2018): 1–10. http://dx.doi.org/10.1155/2018/1980152.

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In the mass collaboration mode, there exist a large number of product ideas with low value density and thousands of participants who are differed on their professional backgrounds, knowledge structures, and value orientations. It is impossible for each participant to give a comprehensive evaluation of each idea as that in traditional methods for the reasons as mentioned above. In order to solve this problem, a mass collaboration-driven method for recommending product ideas is proposed based on Dempster-Shafer theory of evidence (DST). Firstly, the method for computing basic probability assignment (BPA) function, which can effectively reflect the facticity of experts’ evaluations, is introduced by discounting belief degrees with weights to extract the evaluation information of product ideas. Then, Dempster’s combination rule is used to combine the derived BPA functions for two times: the first one is to combine the discounted BPA functions on all criteria with respect to a specified expert and the other is to combine the combined BPA functions for all experts with respect to a specified alternative. Finally, the steps of mass collaboration-driven method for recommending product ideas based on the DST are proposed. An illustrative example is provided to demonstrate the applicability of the proposed method.

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41

Nejad, S. Mohammad Moosavi, and Mahdi Delpasand. "Spin-dependent fragmentation functions of gluon splitting into heavy quarkonia considering three different scenarios." International Journal of Modern Physics A 30, no. 32 (November 17, 2015): 1550179. http://dx.doi.org/10.1142/s0217751x15501791.

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Heavy quarkonium production is a powerful implement to study the strong interaction dynamics and QCD theory. Fragmentation is the dominant production mechanism for heavy quarkonia with large transverse momentum. With the large heavy quark mass, the relative motion of the heavy quark pair inside a heavy quarkonium is effectively nonrelativistic and it is also well known that their fragmentation functions can be calculated in the perturbative QCD framework. Here, we analytically calculate the process-independent fragmentation functions for a gluon to split into the spin-singlet and spin-triplet [Formula: see text]-wave heavy quarkonia using three different scenarios. We will show that the fragmentation probability of the gluon into the spin-triplet bound-state is the biggest one.

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42

Mucesh, S., W. G. Hartley, A. Palmese, O. Lahav, L. Whiteway, A. F. L. Bluck, A. Alarcon, et al. "A machine learning approach to galaxy properties: joint redshift–stellar mass probability distributions with Random Forest." Monthly Notices of the Royal Astronomical Society 502, no. 2 (January 21, 2021): 2770–86. http://dx.doi.org/10.1093/mnras/stab164.

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ABSTRACT We demonstrate that highly accurate joint redshift–stellar mass probability distribution functions (PDFs) can be obtained using the Random Forest (RF) machine learning (ML) algorithm, even with few photometric bands available. As an example, we use the Dark Energy Survey (DES), combined with the COSMOS2015 catalogue for redshifts and stellar masses. We build two ML models: one containing deep photometry in the griz bands, and the second reflecting the photometric scatter present in the main DES survey, with carefully constructed representative training data in each case. We validate our joint PDFs for 10 699 test galaxies by utilizing the copula probability integral transform and the Kendall distribution function, and their univariate counterparts to validate the marginals. Benchmarked against a basic set-up of the template-fitting code bagpipes, our ML-based method outperforms template fitting on all of our predefined performance metrics. In addition to accuracy, the RF is extremely fast, able to compute joint PDFs for a million galaxies in just under 6 min with consumer computer hardware. Such speed enables PDFs to be derived in real time within analysis codes, solving potential storage issues. As part of this work we have developed galpro1, a highly intuitive and efficient python package to rapidly generate multivariate PDFs on-the-fly. galpro is documented and available for researchers to use in their cosmology and galaxy evolution studies.

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43

Beghin, Luisa, and Claudio Macci. "Fractional Discrete Processes: Compound and Mixed Poisson Representations." Journal of Applied Probability 51, no. 1 (March 2014): 19–36. http://dx.doi.org/10.1239/jap/1395771411.

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We consider two fractional versions of a family of nonnegative integer-valued processes. We prove that their probability mass functions solve fractional Kolmogorov forward equations, and we show the overdispersion of these processes. As particular examples in this family, we can define fractional versions of some processes in the literature as the Pólya-Aeppli process, the Poisson inverse Gaussian process, and the negative binomial process. We also define and study some more general fractional versions with two fractional parameters.

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44

Morvan, Daniel, Jean-Louis Golmard, Michel Komajda, and Gérard Drobinski. "Model-based determination of cut-off values for left ventricular hypertrophy from echocardiographic myocardial mass data." Clinical Science 82, no. 1 (January 1, 1992): 25–32. http://dx.doi.org/10.1042/cs0820025.

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1. The left ventricular myocardial mass is a measurement that is easy to obtain by echocardiography. It is currently used for the definition of left ventricular hypertrophy, but cut-off values are often critical, since they depend on covariates of left ventricular myocardial mass such as sex, age, body surface area, physical training, blood pressure, etc. As it is very difficult in any laboratory to obtain a sufficient number of normal subjects for the establishment of left ventricular myocardial mass experimental distributions, we propose a non-linear model for the calculation of echocardiographic left ventricular myocardial mass distribution in normal subjects, from personal and literature data. Left ventricular myocardial mass probability density function was computed from the following two assumptions: the joint distribution of the internal and external left ventricular diameters is assumed to be bivariate normal, and the relation between left ventricular myocardial mass and ventricular diameters is given by the formula of Devereux & Reicheck (Devereux, R. B. & Reicheck, N. Circulation 1977; 55, 613-8). 2. The Gaussian assumption was tested by using skewness tests. The model was further developed for the myocardial mass index distribution. The calculated probability density functions were compared with experimental data and showed very good agreement. Furthermore, they were used to define cut-off values of left ventricular hypertrophy at selected false-positive ratios. Finally, since left ventricular myocardial mass may vary under normal conditions with co-variates, the model may provide co-variate-matched cut-off values for any, even small, series of non-diseased control subjects.

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45

Sharma, Anurag, Thiyam Tamphasana Devi, and Bimlesh Kumar. "Turbulence in continuous flow surface aeration systems." Water Science and Technology 75, no. 5 (December 23, 2016): 1148–57. http://dx.doi.org/10.2166/wst.2016.607.

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Turbulence characteristics in an optimal continuous surface aeration system were investigated in this study. The experimental system consists of a rectangular tank, where flow is driven by equally spaced aerators placed on the liquid surface. The mass-transfer coefficient and turbulent parameters at the tank's inlet and outlet were measured to enable analysis of their interdependent relationships. The turbulence parameters are linked closely to the system's mass-transfer process. Turbulent bursting analysis has shown that ejection and sweep events govern the hydrodynamics of the systems. Turbulent intensity increases with increasing speed of rotation, and consequently the mass-transfer coefficient also increases. The universal probability distribution functions of the velocity fluctuations in continuous flow surface aeration systems follow the Gram-Charlier series, based on exponential distribution, and the theoretical and experimental curves match.

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GOGBERASHVILI, MERAB. "OCTONIONIC VERSION OF DIRAC EQUATIONS." International Journal of Modern Physics A 21, no. 17 (July 10, 2006): 3513–23. http://dx.doi.org/10.1142/s0217751x06028436.

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It is shown that a simple continuity condition in the algebra of split octonions suffices to formulate a system of differential equations that are equivalent to the standard Dirac equations. In our approach the particle mass and electromagnetic potentials are part of an octonionic gradient function together with the space–time derivatives. As distinct from previous attempts to translate the Dirac equations into different number systems here the wave functions are real split octonions and not bi-spinors. To formulate positively defined probability amplitudes four different split octonions (transforming into each other by discrete transformations) are necessary, rather then two complex wave functions which correspond to particles and antiparticles in usual Dirac theory.

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47

Terek, Milan. "Regional Incomes Structure Analysis in Slovak Republic On the Basis of EU-SILC Data." Scientific Annals of Economics and Business 64, no. 2 (June 27, 2017): 171–85. http://dx.doi.org/10.1515/saeb-2017-0011.

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Abstract The paper deals with the regional incomes structure analysis in Slovak republic on the basis of European Union statistics on income and living conditions in Slovak republic data. The empirical probability mass function and empirical cumulative distribution function is constructed with aid of given sampling weights. On the basis of these functions the median, medial, standard deviation and population histogram of the whole gross household incomes for the whole Slovak republic and separately for eight Slovak regions are estimated and compared.

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48

Wood, Norman B., Tristan S. L’Ecuyer, Andrew J. Heymsfield, and Graeme L. Stephens. "Microphysical Constraints on Millimeter-Wavelength Scattering Properties of Snow Particles." Journal of Applied Meteorology and Climatology 54, no. 4 (April 2015): 909–31. http://dx.doi.org/10.1175/jamc-d-14-0137.1.

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AbstractA Bayesian optimal estimation retrieval is used to determine probability density functions of snow microphysical parameters from ground-based observations taken during four snowfall events in southern Ontario, Canada. The retrieved variables include the parameters of power laws describing particle mass and horizontally projected area. The results reveal nontrivial correlations between mass and area parameters that were not apparent in prior studies. The observations provide information mainly about the mass coefficient , somewhat less information about the mass exponent and the projected area coefficient , and minimal information about the projected area exponent . The expected values for retrieved mass power-law parameters = 0.003 28 and = 2.25 are consistent with those from several prior studies that looked at the mass of aggregate-like particles and precipitating ice aloft as functions of maximum particle dimension. Differences from other studies appear related to differences in the dimensions used to define particle size. The retrieval allows the analysis of relatively large volumes of continuous observations, greatly enhancing sampling relative to single-particle analyses. The retrieved properties are used to constrain 94-GHz (W band) radar scattering properties for a variety of snow particle shapes. Synthetic reflectivities calculated using these scattering properties and observed particle size distributions show that a branched, spatial aggregate-like particle produces good agreement with coincident observed W-band reflectivities. Uncertainties in the synthetic reflectivities, estimated by applying a simple error-propagation model, are substantial and are dominated by the uncertainties in and .

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49

Mohammed, B. I., Nicholas Makumi, Ramy Aldallal, Taysir E. Dyhoum, and Hassan M. Aljohani. "A New Model of Discrete-Continuous Bivariate Distribution with Applications to Medical Data." Computational and Mathematical Methods in Medicine 2022 (May 21, 2022): 1–7. http://dx.doi.org/10.1155/2022/1883491.

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The bivariate Poisson exponential-exponential distribution is an important lifetime distribution in medical data analysis. In this article, the conditionals, probability mass function (pmf), Poisson exponential and probability density function (pdf), and exponential distribution are used for creating bivariate distribution which is called bivariate Poisson exponential-exponential conditional (BPEEC) distribution. Some properties of the BPEEC model are obtained such as the normalized constant, conditional densities, regression functions, and product moment. Moreover, the maximum likelihood and pseudolikelihood methods are used to estimate the BPEEC parameters based on complete data. Finally, two data sets of real bivariate data are analyzed to compare the methods of estimation. In addition, a comparison between the BPEEC model with the bivariate exponential conditionals (BEC) and bivariate Poisson exponential conditionals (BPEC) is considered.

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50

Irish, Jennifer L., Donald T. Resio, Taylor G. Asher, and Yi Liu. "CHARACTERIZATION OF SPATIAL VARIATION IN HURRICANE SURGE." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 51. http://dx.doi.org/10.9753/icce.v36.currents.51.

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Planning, engineering, and development along surgeprone coasts rely on probabilistic surge hazard assessments. Over the last decade, U.S. agencies have implemented the joint probability method with optimal sampling (JPM-OS) (e.g., Resio et al. 2009) to overcome shortcomings in probabilistic estimates developed from the limited set of observed surges alone. Here, optimal sampling is used to reduce the number of high-fidelity surge simulations needed, given computational resource limitations. In current practice, hazard assessments with the JPM-OS use discrete storm simulations (order of 200 to 1000 storms), where each is assigned a probability mass (e.g., Toro et al. 2010), rather than defining surges for the continuum of probability densities. Such an approach introduces uncertainty because it does not fully capture the natural structure inherent in surge response (meteorological and larger-scale bathymetric effects) (Resio et al. 2017). On the other hand, physically based surge response functions (SRFs) that capture natural structure in the surge response provide an accurateâ€”0.2 to 0.5 m rootmean- square error depending on topographic and geographic complexityâ€”and efficient means for continuously defining probability densities (e.g., Taylor et al. 2015). But, application of SRFs in JPM-OS (JPMOS- SRF) has not been widely used in practice due a lack of systematic methods for spatial interpolation along complex shorelines and throughout the floodplain. Herein, we explore the use of spatially derived empirical orthogonal functions (EOFs) to overcome this spatial interpolation challenge.

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