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Journal articles on the topic 'Gamma mixture'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Guardone, Alberto, Piero Colonna, Emiliano Casati, and Enrico Rinaldi. "Non-classical gas dynamics of vapour mixtures." Journal of Fluid Mechanics 741 (February 13, 2014): 681–701. http://dx.doi.org/10.1017/jfm.2013.13.

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AbstractThe non-classical gas dynamics of binary mixtures of organic fluids in the vapour phase is investigated for the first time. A predictive thermodynamic model is used to compute the relevant mixture properties, including its critical point coordinates and the local value of the fundamental derivative of gas dynamics $\Gamma $. The considered model is the improved Peng–Robinson Stryjek–Vera cubic equation of state, complemented by the Wong–Sandler mixing rules. A finite thermodynamic region is found where the nonlinearity parameter $\Gamma $ is negative and therefore non-classical gas dynamics phenomena are admissible. A non-monotone dependence of $\Gamma $ on the mixture composition is observed in the case of binary mixtures of siloxane and perfluorocarbon fluids, with the minimum value of $\Gamma $ in the mixture being always larger than that of its more complex component. The observed dependence indicates that non-ideal mixing has a strong influence on the gas dynamics behaviour, either classical or non-classical, of the mixture. Numerical experiments of the supersonic expansion of a mixture flow around a sharp corner show the transition from the classical configuration, exhibiting an isentropic rarefaction fan centred at the expansion corner, to non-classical ones, including mixed expansion waves and rarefaction shock waves, if the mixture composition is changed.

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2

Jones, G., C. D. Lai, and J. C. W. Rayner. "A bivariate gamma mixture distribution." Communications in Statistics - Theory and Methods 29, no. 12 (January 2000): 2775–90. http://dx.doi.org/10.1080/03610920008832636.

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3

Block, Henry W., Naftali A. Langberg, Thomas H. Savits, and Jie Wang. "Continuous Mixtures of Exponentials and IFR Gammas Having Bathtub-Shaped Failure Rates." Journal of Applied Probability 47, no. 04 (December 2010): 899–907. http://dx.doi.org/10.1017/s0021900200007245.

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It can be seen that a mixture of an exponential distribution and a gamma distribution with increasing failure rate for the right choice of parameters can yield a distribution with a bathtub-shaped failure rate. In this paper we consider a continuous mixture of exponentials and a continuous mixture of gammas with increasing failure rates and show that the resulting mixture has a bathtub-shaped failure rate.

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4

Block, Henry W., Naftali A. Langberg, Thomas H. Savits, and Jie Wang. "Continuous Mixtures of Exponentials and IFR Gammas Having Bathtub-Shaped Failure Rates." Journal of Applied Probability 47, no. 4 (December 2010): 899–907. http://dx.doi.org/10.1239/jap/1294170507.

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It can be seen that a mixture of an exponential distribution and a gamma distribution with increasing failure rate for the right choice of parameters can yield a distribution with a bathtub-shaped failure rate. In this paper we consider a continuous mixture of exponentials and a continuous mixture of gammas with increasing failure rates and show that the resulting mixture has a bathtub-shaped failure rate.

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5

Zaman, M. R., M. K. Roy ., and N. Akhter . "Chi-square Mixture of Gamma Distribution." Journal of Applied Sciences 5, no. 9 (August 15, 2005): 1632–35. http://dx.doi.org/10.3923/jas.2005.1632.1635.

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6

Webb, Andrew R. "Gamma mixture models for target recognition." Pattern Recognition 33, no. 12 (December 2000): 2045–54. http://dx.doi.org/10.1016/s0031-3203(99)00195-8.

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7

LIU, XIN, CRISTIAN PASARICA, and YONGZHAO SHAO. "Testing Homogeneity in Gamma Mixture Models." Scandinavian Journal of Statistics 30, no. 1 (March 2003): 227–39. http://dx.doi.org/10.1111/1467-9469.00328.

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8

Hamed, M. S. "THE MIXTURE WEIBULL-GENERALIZED GAMMA DISTRIBUTION." Advances and Applications in Statistics 62, no. 2 (June 20, 2020): 139–71. http://dx.doi.org/10.17654/as062020139.

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9

Wei, Zhengyuan, Suping Li, Qiao Li, Yucan Yu, and Xiaoyang Zheng. "Gamma mixture of generalized error distribution." Communications in Statistics - Theory and Methods 49, no. 19 (May 3, 2019): 4819–33. http://dx.doi.org/10.1080/03610926.2019.1609037.

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10

Viziananda, S., K. Srinivasa, and P. Srinivasa. "Truncated Compound Normal with Gamma Mixture Model for Mixture Density Estimation." International Journal of Computer Applications 157, no. 3 (January 17, 2017): 6–12. http://dx.doi.org/10.5120/ijca2017912643.

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11

Boland, Philip J., Frank Proschan, and Y. L. Tong. "Crossing Properties of Mixture Distributions." Probability in the Engineering and Informational Sciences 3, no. 3 (July 1989): 355–66. http://dx.doi.org/10.1017/s0269964800001224.

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Mixture distributions are a frequently used tool in modelling random phenomena. We consider mixtures of densities from a one-parameter exponenvial family of distributions. Using the tools of totally positive functions and the variation-diminishing property of such, we study the effect of sign-crossing properties of two mixing densities μ1 and μ2 on the resulting mixture distributions f1 and f2. The results enable us to make stochastic and variability cornparisons for binomial-beta, mixed Weibull, and mixed gamma distributions.

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12

EKHOSUEHI, Nosakhare, Lawrence NZEI, and Festus OPONE. "A New Mixture of Exponential-Gamma Distribution." GAZI UNIVERSITY JOURNAL OF SCIENCE 33, no. 2 (June 1, 2020): 548–64. http://dx.doi.org/10.35378/gujs.475102.

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13

Gharib, M. "Two characterisations of a gamma mixture distribution." Bulletin of the Australian Mathematical Society 52, no. 3 (December 1995): 353–58. http://dx.doi.org/10.1017/s0004972700014842.

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Two characterisations are obtained for a gamma mixture distribution. The first is a generalisation of a result of Engel, Zijlstra and Philips [4] and the second based on Gumbel's bivariate exponential distribution. The two characterisatio are of direct relevance to some practical problems.

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14

Ahmed, S. E., M. N. Goria, and A. Hussein. "Gamma Mixture: Bimodality, Inflexions and L-Moments." Communications in Statistics - Theory and Methods 37, no. 8 (February 22, 2008): 1147–61. http://dx.doi.org/10.1080/03610920701713286.

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15

Cowell, R. G., S. L. Lauritzen, and J. Mortera. "A gamma model for {DNA} mixture analyses." Bayesian Analysis 2, no. 2 (June 2007): 333–48. http://dx.doi.org/10.1214/07-ba214.

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16

Adnan, Mian Arif Shams, Humayun Kiser, Asif Shams Adnan, and Silvey Shamsi. "A CLASS OF FOLDED GAMMA MIXTURE DISTRIBUTIONS." Far East Journal of Theoretical Statistics 60, no. 1-2 (October 20, 2020): 1–23. http://dx.doi.org/10.17654/ts060020001.

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17

K.J., John. "Characterization of a Mixture of Gamma Density." Calcutta Statistical Association Bulletin 41, no. 1-4 (March 1991): 169–72. http://dx.doi.org/10.1177/0008068319910115.

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18

Mallya, Ganeshchandra, Shivam Tripathi, and Rao S. Govindaraju. "Probabilistic drought classification using gamma mixture models." Journal of Hydrology 526 (July 2015): 116–26. http://dx.doi.org/10.1016/j.jhydrol.2014.11.008.

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19

Usman, Aliyu, Muslich Hartadi Sutanto, Madzlan Napiah, Salah E. Zoorob, Nura Shehu Aliyu Yaro, and Muhammad Imran Khan. "Comparison of Performance Properties and Prediction of Regular and Gamma-Irradiated Granular Waste Polyethylene Terephthalate Modified Asphalt Mixtures." Polymers 13, no. 16 (August 6, 2021): 2610. http://dx.doi.org/10.3390/polym13162610.

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The utilization of waste polyethylene terephthalate (WPET) as aggregate substitutes in pavement has been extensively promoted because of its environmental advantages. However, previous studies have shown that a high percentage of WPET reduces the performance of the pavement. To increase the durability of pavement and mitigate the environmental issues caused by WPET, WPET is treated with gamma-irradiation as a component in asphalt mixtures. The study objectives were to investigate the feasibility of using WPET granules as a sustainable aggregate on asphalt mixture stiffness and rutting and predict the asphalt mixture performance containing irradiated WPET via an RSM-ANN-framework. To achieve the objectives, stiffness and rutting tests were conducted to evaluate the WPET modified mixtures’ performance. The result indicated that samples containing 40% irradiated WPET provided a better performance compared to mixtures containing 20% non-irradiated WPET, increasing the stiffness by 27% and 21% at 25 °C and 40 °C, respectively, and rutting resistance by 11% at 45 °C. Furthermore, both predictive models developed demonstrated excellent reliability. The ANN exhibited superior performance than the RSM. The utilization of WPET as aggregate in asphalt mixtures represents a way to addressing related recycling issues while also improving performance. With gamma-irradiation treatment, the utilization of WPET can be increased with improved asphalt mixture performance.

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20

Sallay, Hassen, Sami Bourouis, and Nizar Bouguila. "Online Learning of Finite and Infinite Gamma Mixture Models for COVID-19 Detection in Medical Images." Computers 10, no. 1 (December 27, 2020): 6. http://dx.doi.org/10.3390/computers10010006.

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The accurate detection of abnormalities in medical images (like X-ray and CT scans) is a challenging problem due to images’ blurred boundary contours, different sizes, variable shapes, and uneven density. In this paper, we tackle this problem via a new effective online variational learning model for both mixtures of finite and infinite Gamma distributions. The proposed approach takes advantage of the Gamma distribution flexibility, the online learning scalability, and the variational inference efficiency. Three different batch and online learning methods based on robust texture-based feature extraction are proposed. Our work is evaluated and validated on several real challenging data sets for different kinds of pneumonia infection detection. The obtained results are very promising given that we approach the classification problem in an unsupervised manner. They also confirm the superiority of the Gamma mixture model compared to the Gaussian mixture model for medical images’ classification.

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21

Sarabia, José María, Emilio Gómez-Déniz, Faustino Prieto, and Vanesa Jordá. "AGGREGATION OF DEPENDENT RISKS IN MIXTURES OF EXPONENTIAL DISTRIBUTIONS AND EXTENSIONS." ASTIN Bulletin 48, no. 3 (April 25, 2018): 1079–107. http://dx.doi.org/10.1017/asb.2018.13.

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AbstractThe distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf) and the cumulative distribution function (cdf) of aggregated risks, modelled according to a mixture of exponential distributions. We first review the properties of the multivariate mixture of exponential distributions, to then obtain the analytical formulation for the pdf and the cdf for the aggregated distribution. We study in detail some specific families with Pareto (Sarabia et al., 2016), gamma, Weibull and inverse Gaussian mixture of exponentials (Whitmore and Lee, 1991) claims. We also discuss briefly the computation of risk measures, formulas for the ruin probability (Albrecher et al., 2011) and the collective risk model. An extension of the basic model based on mixtures of gamma distributions is proposed, which is one of the suggested directions for future research.

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22

Bentoumi, Ahmed, Amar Mezache, and Houcine Oudira. "Parameter Estimation of Rayleigh-Generalized Gamma Mixture Model." Instrumentation Mesure Métrologie 19, no. 1 (March 20, 2020): 59–64. http://dx.doi.org/10.18280/i2m.190108.

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23

Zhang, Zhi-Bin, En-Bo Yang, Chul-Sung Choi, and Heon-Young Chang. "Classifying gamma-ray bursts with Gaussian Mixture Model." Monthly Notices of the Royal Astronomical Society 462, no. 3 (July 28, 2016): 3243–54. http://dx.doi.org/10.1093/mnras/stw1835.

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24

Oikonomou, K. N. "Prediction with the dynamic Bayesian gamma mixture model." IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 27, no. 4 (July 1997): 529–42. http://dx.doi.org/10.1109/3468.594918.

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25

Kong, Long, and Georges Kaddoum. "Secrecy Characteristics With Assistance of Mixture Gamma Distribution." IEEE Wireless Communications Letters 8, no. 4 (August 2019): 1086–89. http://dx.doi.org/10.1109/lwc.2019.2907083.

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26

Al-Saleh, Jamal A., and Satish K. Agarwal. "Finite mixture of gamma distributions: A conjugate prior." Computational Statistics & Data Analysis 51, no. 9 (May 2007): 4369–78. http://dx.doi.org/10.1016/j.csda.2006.06.005.

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27

Aljohani, Hassan M., and Nada M. Alfaer. "Hybrid Censoring Schemes with Mixture Gamma Failure Distribution." Journal of Mathematics 2021 (April 3, 2021): 1–11. http://dx.doi.org/10.1155/2021/6641078.

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Censoring schemes have received much attention over the past decades. Hybrid censoring schemes are censoring schemes mixed of type-I (T-1) and type-II (T-2) censoring schemes, a most popular area of study in life-testing or reliability experiments. More precisely, hybrid censoring can be described as a mixture of T-I and T-2 schemes. Gamma distribution is widely used, and its connection has more distributions. Mixture and single gamma distribution will be studied to estimate parameters, based on type-II hybrid censoring schemes (T-2HCS). We will apply algorithms to compute the maximum likelihood (ML) estimators and Bayesian approaches, using statistics, such as Markov chain Monte Carlo methods. Bayes estimators and corresponding highest posterior density confidence intervals will be tabled. Also, Markov chain Monte Carlo simulation is implemented to compare the performances of the different methods and the real dataset is analyzed for illustrative purposes.

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28

Mazarura, Jocelyn, Alta de Waal, and Pieter de Villiers. "A Gamma-Poisson Mixture Topic Model for Short Text." Mathematical Problems in Engineering 2020 (April 29, 2020): 1–17. http://dx.doi.org/10.1155/2020/4728095.

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Most topic models are constructed under the assumption that documents follow a multinomial distribution. The Poisson distribution is an alternative distribution to describe the probability of count data. For topic modelling, the Poisson distribution describes the number of occurrences of a word in documents of fixed length. The Poisson distribution has been successfully applied in text classification, but its application to topic modelling is not well documented, specifically in the context of a generative probabilistic model. Furthermore, the few Poisson topic models in the literature are admixture models, making the assumption that a document is generated from a mixture of topics. In this study, we focus on short text. Many studies have shown that the simpler assumption of a mixture model fits short text better. With mixture models, as opposed to admixture models, the generative assumption is that a document is generated from a single topic. One topic model, which makes this one-topic-per-document assumption, is the Dirichlet-multinomial mixture model. The main contributions of this work are a new Gamma-Poisson mixture model, as well as a collapsed Gibbs sampler for the model. The benefit of the collapsed Gibbs sampler derivation is that the model is able to automatically select the number of topics contained in the corpus. The results show that the Gamma-Poisson mixture model performs better than the Dirichlet-multinomial mixture model at selecting the number of topics in labelled corpora. Furthermore, the Gamma-Poisson mixture produces better topic coherence scores than the Dirichlet-multinomial mixture model, thus making it a viable option for the challenging task of topic modelling of short text.

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29

Yu, Yaming. "Stochastic Ordering of Exponential Family Distributions and Their Mixturesxk." Journal of Applied Probability 46, no. 01 (March 2009): 244–54. http://dx.doi.org/10.1017/s0021900200005337.

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We investigate stochastic comparisons between exponential family distributions and their mixtures with respect to the usual stochastic order, the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. A general theorem based on the notion of relative log-concavity is shown to unify various specific results for the Poisson, binomial, negative binomial, and gamma distributions in recent literature. By expressing a convolution of gamma distributions with arbitrary scale and shape parameters as a scale mixture of gamma distributions, we obtain comparison theorems concerning such convolutions that generalize some known results. Analogous results on convolutions of negative binomial distributions are also discussed.

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30

Yu, Yaming. "Stochastic Ordering of Exponential Family Distributions and Their Mixturesxk." Journal of Applied Probability 46, no. 1 (March 2009): 244–54. http://dx.doi.org/10.1239/jap/1238592127.

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We investigate stochastic comparisons between exponential family distributions and their mixtures with respect to the usual stochastic order, the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. A general theorem based on the notion of relative log-concavity is shown to unify various specific results for the Poisson, binomial, negative binomial, and gamma distributions in recent literature. By expressing a convolution of gamma distributions with arbitrary scale and shape parameters as a scale mixture of gamma distributions, we obtain comparison theorems concerning such convolutions that generalize some known results. Analogous results on convolutions of negative binomial distributions are also discussed.

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31

Adachi, K., J. Kim, T. Asakura, and E. Schwartz. "Characterization of two types of fetal hemoglobin: alpha 2G gamma 2 and alpha 2A gamma 2." Blood 75, no. 10 (May 15, 1990): 2070–75. http://dx.doi.org/10.1182/blood.v75.10.2070.2070.

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Abstract The effect of differences in G gamma and A gamma fractions of fetal hemoglobin (HbF) on the kinetics of polymerization of HbS-HbF mixtures was studied. We also examined their effect on oxygen affinity, surface hydrophobicity, mechanical stability, and solubility of HbF. Differences in G gamma:A gamma ratio did not affect the polymerization of mixtures of HbF and HbS, suggesting that the inhibitory effect of HbF on the polymerization of HbS is independent of the G gamma:A gamma ratio of HbF and is totally dependent on the fraction of HbF in the mixture. The oxygen equilibrium curve of HbF was not affected by differences in the ratios of G gamma and A gamma in HbF. In contrast, surface hydrophobicity, mechanical stability, and solubility of HbF were affected by differences in the G gamma:A gamma ratio. The higher the G gamma:A gamma ratio, the smaller the elution volume on a TSK Gel SW hydrophobic column in high phosphate buffer. The mechanical stability of HbF was also dependent on the ratio of G gamma:A gamma; stability was greater at higher fractions of A gamma. Differences in the G gamma:A gamma ratio also affected solubility of HbF: HbF containing the higher fraction of G gamma was the more soluble. These data indicate that although alanine at the 136th position of the gamma chains has a stronger surface hydrophobicity than does glycine, this difference does not affect either the polymerization of HbS or the oxygen affinity of HbF.

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32

Adachi, K., J. Kim, T. Asakura, and E. Schwartz. "Characterization of two types of fetal hemoglobin: alpha 2G gamma 2 and alpha 2A gamma 2." Blood 75, no. 10 (May 15, 1990): 2070–75. http://dx.doi.org/10.1182/blood.v75.10.2070.bloodjournal75102070.

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The effect of differences in G gamma and A gamma fractions of fetal hemoglobin (HbF) on the kinetics of polymerization of HbS-HbF mixtures was studied. We also examined their effect on oxygen affinity, surface hydrophobicity, mechanical stability, and solubility of HbF. Differences in G gamma:A gamma ratio did not affect the polymerization of mixtures of HbF and HbS, suggesting that the inhibitory effect of HbF on the polymerization of HbS is independent of the G gamma:A gamma ratio of HbF and is totally dependent on the fraction of HbF in the mixture. The oxygen equilibrium curve of HbF was not affected by differences in the ratios of G gamma and A gamma in HbF. In contrast, surface hydrophobicity, mechanical stability, and solubility of HbF were affected by differences in the G gamma:A gamma ratio. The higher the G gamma:A gamma ratio, the smaller the elution volume on a TSK Gel SW hydrophobic column in high phosphate buffer. The mechanical stability of HbF was also dependent on the ratio of G gamma:A gamma; stability was greater at higher fractions of A gamma. Differences in the G gamma:A gamma ratio also affected solubility of HbF: HbF containing the higher fraction of G gamma was the more soluble. These data indicate that although alanine at the 136th position of the gamma chains has a stronger surface hydrophobicity than does glycine, this difference does not affect either the polymerization of HbS or the oxygen affinity of HbF.

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33

Rafiei, Maryam, Anis Iranmanesh, and Daya k. Nagar. "A Bivariate Gamma Distribution Whose Marginals are Finite Mixtures of Gamma Distributions." Statistics, Optimization & Information Computing 8, no. 4 (August 25, 2020): 950–71. http://dx.doi.org/10.19139/soic-2310-5070-1001.

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In this article a new bivariate distribution, whose both the marginals are finite mixture of gamma distribution has been defined. Several of its properties such moments, correlation coefficients, measure of skewness, moment generating function, Renyi and Shannon entropies have been derived. Simulation study have been conducted to evaluate the performance of maximum likelihood method.

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34

Amrani, DL, PJ Newman, D. Meh, and MW Mosesson. "The role of fibrinogen A alpha chains in ADP-induced platelet aggregation in the presence of fibrinogen molecules containing gamma' chains." Blood 72, no. 3 (September 1, 1988): 919–24. http://dx.doi.org/10.1182/blood.v72.3.919.919.

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Abstract Human plasma fibrinogen (Fgn) is heterogenous with respect to the size of its gamma chains, which differ in that residues 408 to 411 of gammaA chains (93% of total) are replaced in gamma' chains by a unique 20 amino acid sequence (gamma408 to gamma427). In this study, we compared the contribution to adenosine diphosphate (ADP)-induced platelet aggregation of the A alpha chains in Fgn molecules containing predominantly (fraction 1–2) or exclusively (peak 1 Fgn) gammaA chains with that of molecules containing approximately 50% gamma' chains (peak 2 Fgn). Using washed human platelets, we confirmed that the number of peak 2 Fgn molecules binding to platelets in the presence of ADP was about half the number of peak 1 Fgn molecules (18,962 +/- 2,298 v 44,366 +/- 16,096 molecules per platelet), and that isolated S- carboxymethylated (SCM) gammaA chains supported ADP-induced platelet aggregation nearly as well as peak 1 Fgn. In contrast, SCM-gamma' chains alone supported aggregation poorly, whereas a mixture of SCM- gammaA and gamma' chains (1:1 ratio) gave intermediate results. Despite the findings with isolated SCM-gamma' chains, we found that peak 2 Fgn supported platelet aggregation nearly as well as peak 1 Fgn. However, peak 2 Fgn from which carboxy (COOH)-terminal A alpha chain segments had been removed by digestion with plasmin showed a markedly decreased platelet aggregation potential. Peak 1 Fgn core fraction from an 88% to 90% coagulable plasmin digest, or Fgn fraction 1–9, which has a high gammaA/gamma' chain ratio (93:7), but lacks COOH-terminal regions of A alpha chains, supported platelet aggregation to the same extent as did intact peak 2 Fgn. These findings indicate that Fgn molecules containing gamma' chains can approach the aggregation potential of Fgn molecules containing predominantly or exclusively gammaA chains only if intact A alpha chains are also present.

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Amrani, DL, PJ Newman, D. Meh, and MW Mosesson. "The role of fibrinogen A alpha chains in ADP-induced platelet aggregation in the presence of fibrinogen molecules containing gamma' chains." Blood 72, no. 3 (September 1, 1988): 919–24. http://dx.doi.org/10.1182/blood.v72.3.919.bloodjournal723919.

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Human plasma fibrinogen (Fgn) is heterogenous with respect to the size of its gamma chains, which differ in that residues 408 to 411 of gammaA chains (93% of total) are replaced in gamma' chains by a unique 20 amino acid sequence (gamma408 to gamma427). In this study, we compared the contribution to adenosine diphosphate (ADP)-induced platelet aggregation of the A alpha chains in Fgn molecules containing predominantly (fraction 1–2) or exclusively (peak 1 Fgn) gammaA chains with that of molecules containing approximately 50% gamma' chains (peak 2 Fgn). Using washed human platelets, we confirmed that the number of peak 2 Fgn molecules binding to platelets in the presence of ADP was about half the number of peak 1 Fgn molecules (18,962 +/- 2,298 v 44,366 +/- 16,096 molecules per platelet), and that isolated S- carboxymethylated (SCM) gammaA chains supported ADP-induced platelet aggregation nearly as well as peak 1 Fgn. In contrast, SCM-gamma' chains alone supported aggregation poorly, whereas a mixture of SCM- gammaA and gamma' chains (1:1 ratio) gave intermediate results. Despite the findings with isolated SCM-gamma' chains, we found that peak 2 Fgn supported platelet aggregation nearly as well as peak 1 Fgn. However, peak 2 Fgn from which carboxy (COOH)-terminal A alpha chain segments had been removed by digestion with plasmin showed a markedly decreased platelet aggregation potential. Peak 1 Fgn core fraction from an 88% to 90% coagulable plasmin digest, or Fgn fraction 1–9, which has a high gammaA/gamma' chain ratio (93:7), but lacks COOH-terminal regions of A alpha chains, supported platelet aggregation to the same extent as did intact peak 2 Fgn. These findings indicate that Fgn molecules containing gamma' chains can approach the aggregation potential of Fgn molecules containing predominantly or exclusively gammaA chains only if intact A alpha chains are also present.

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36

Block, Henry W., Naftali A. Langberg, and Thomas H. Savits. "A MIXTURE OF EXPONENTIAL AND IFR GAMMA DISTRIBUTIONS HAVING AN UPSIDEDOWN BATHTUB-SHAPED FAILURE RATE." Probability in the Engineering and Informational Sciences 26, no. 4 (July 30, 2012): 573–80. http://dx.doi.org/10.1017/s0269964812000204.

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We consider a mixture of one exponential distribution and one gamma distribution with increasing failure rate. For the right choice of parameters, it is shown that its failure rate has an upsidedown bathtub shape failure rate. We also consider a mixture of a family of exponentials and a family of gamma distributions and obtain a similar result.

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37

Tzougas, George, Spyridon Vrontos, and Nicholas Frangos. "OPTIMAL BONUS-MALUS SYSTEMS USING FINITE MIXTURE MODELS." ASTIN Bulletin 44, no. 2 (January 10, 2014): 417–44. http://dx.doi.org/10.1017/asb.2013.31.

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AbstractThis paper presents the design of optimal Bonus-Malus Systems using finite mixture models, extending the work of Lemaire (1995; Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance. Norwell, MA: Kluwer) and Frangos and Vrontos (2001; Frangos, N. and Vrontos, S. (2001) Design of optimal bonus-malus systems with a frequency and a severity component on an individual basis in automobile insurance. ASTIN Bulletin, 31(1), 1–22). Specifically, for the frequency component we employ finite Poisson, Delaporte and Negative Binomial mixtures, while for the severity component we employ finite Exponential, Gamma, Weibull and Generalized Beta Type II mixtures, updating the posterior probability. We also consider the case of a finite Negative Binomial mixture and a finite Pareto mixture updating the posterior mean. The generalized Bonus-Malus Systems we propose, integrate risk classification and experience rating by taking into account both the a priori and a posteriori characteristics of each policyholder.

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38

Waheed, M. EL-Sayed, Osama Abdo Mohamed, and M. E. Abd El-aziz. "Mixture of Generalized Gamma Density-Based Score Function for Fastica." Mathematical Problems in Engineering 2011 (2011): 1–14. http://dx.doi.org/10.1155/2011/150294.

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We propose an entirely novel family of score functions for blind signal separation (BSS), based on the family of mixture generalized gamma density which includes generalized gamma, Weilbull, gamma, and Laplace and Gaussian probability density functions. To blindly extract the independent source signals, we resort to the FastICA approach, whilst to adaptively estimate the parameters of such score functions, we use Nelder-Mead for optimizing the maximum likelihood (ML) objective function without relaying on any derivative information. Our experimental results with source employing a wide range of statistics distribution show that Nelder-Mead technique produce a good estimation for the parameters of score functions.

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K. Zenner, Eric, and Mahdi Teimouri. "Modeling in Forestry Using Mixture Models Fitted to Grouped and Ungrouped Data." Forests 12, no. 9 (September 3, 2021): 1196. http://dx.doi.org/10.3390/f12091196.

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The creation and maintenance of complex forest structures has become an important forestry objective. Complex forest structures, often expressed in multimodal shapes of tree size/diameter (DBH) distributions, are challenging to model. Mixture probability density functions of two- or three-component gamma, log-normal, and Weibull mixture models offer a solution and can additionally provide insights into forest dynamics. Model parameters can be efficiently estimated with the maximum likelihood (ML) approach using iterative methods such as the Newton-Raphson (NR) algorithm. However, the NR algorithm is sensitive to the choice of initial values and does not always converge. As an alternative, we explored the use of the iterative expectation-maximization (EM) algorithm for estimating parameters of the aforementioned mixture models because it always converges to ML estimators. Since forestry data frequently occur both in grouped (classified) and ungrouped (raw) forms, the EM algorithm was applied to explore the goodness-of-fit of the gamma, log-normal, and Weibull mixture distributions in three sample plots that exhibited irregular, multimodal, highly skewed, and heavy-tailed DBH distributions where some size classes were empty. The EM-based goodness-of-fit was further compared against a nonparametric kernel-based density estimation (NK) model and the recently popularized gamma-shaped mixture (GSM) models using the ungrouped data. In this example application, the EM algorithm provided well-fitting two- or three-component mixture models for all three model families. The number of components of the best-fitting models differed among the three sample plots (but not among model families) and the mixture models of the log-normal and gamma families provided a better fit than the Weibull distribution for grouped and ungrouped data. For ungrouped data, both log-normal and gamma mixture distributions outperformed the GSM model and, with the exception of the multimodal diameter distribution, also the NK model. The EM algorithm appears to be a promising tool for modeling complex forest structures.

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Arahmane, Hanane, El-Mehdi Hamzaoui, and Rajaa Cherkaoui El Moursli. "Improving Neutron-Gamma Discrimination with Stilbene Organic Scintillation Detector Using Blind Nonnegative Matrix and Tensor Factorization Methods." Journal of Spectroscopy 2019 (May 30, 2019): 1–9. http://dx.doi.org/10.1155/2019/8360395.

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In order to perform highly qualified neutron-gamma discrimination in mixed radiation field, we investigate the application of blind source separation methods based on nonnegative matrix and tensor factorization algorithms as new and robust neutron-gamma discrimination software-based approaches. These signal processing tools have allowed to recover original source components from real-world mixture signals which have been recorded at the output of the stilbene scintillation detector. The computation of the performance index of separability of each tested nonnegative algorithm has allowed to select Second-Order NMF algorithm and NTF-2 model as the most efficient techniques for discriminating neutrons and gammas. Furthermore, the neutron-gamma discrimination is highlighted through the computation of the cross-correlation function. The performance of the blind source separation methods has been quantified through the obtained results that prove a good neutron-gamma separation.

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Adachi, K., J. Pang, P. Konitzer, and S. Surrey. "Polymerization of recombinant hemoglobin F gamma E6V and hemoglobin F gamma E6V, gamma Q87T alone, and in mixtures with hemoglobin S." Blood 87, no. 4 (February 15, 1996): 1617–24. http://dx.doi.org/10.1182/blood.v87.4.1617.bloodjournal8741617.

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To further understand determinants for Hemoglobin (Hb) S polymerization, as well as the inhibitory mechanism of Hb F on Hb S polymerization, Hb F variants containing Val-gamma 6 (Hb F gamma E6V) or Val-gamma 6, Thr-gamma 87 (Hb F gamma E6V, gamma Q87T) were expressed in yeast. The oxy form of Hb F gamma E6V was about 10-fold less stable to mechanical agitation than native oxy Hb F, which is similar to stability differences comparing oxy Hb S and oxy Hb A. Deoxy Hb F gamma E6V showed approximately 20-fold decreased solubility compared with native deoxy Hb F in high phosphate buffer and formed gels like deoxy Hb S in low phosphate buffer, indicating that the Val- gamma 6 substitution decreases solubility of Hb F like Val-beta 6 in deoxy Hb S. Oversaturated deoxy Hb F gamma E6V polymerized without a delay time in low and high phosphate buffers, in contrast to deoxy Hb S, which is accompanied by a distinct delay time before polymerization. Deoxy Hb F gamma E6V, gamma Q87T also polymerized without a delay time like deoxy Hb F gamma E6V. These results suggest that deoxy Hb F gamma E6V gamma Q87T polymers are different from those of deoxy Hb S, and that contact sites differ from those of deoxy Hb S, even though both have the same primary donor (A3) and acceptor sites in the EF helix. These results also suggest that other amino acids in addition to beta 6 Val and amino acids in the F helix are critical for nucleation- controlled polymerization of deoxy Hb S. 1:1 mixtures of deoxy Hb S and either Hb F variant polymerized with a delay time when the concentrations for the Hb S/Hb F gamma E6V and Hb S/Hb F gamma E6V, gamma Q87T mixtures were about 2- and 1.5-fold, respectively, higher than that for Hb S. Logarithmic plots of delay time versus concentration for Hb S/Hb F gamma E6V mixtures showed the same straight line as the line for Hb S/Hb S beta T87Q mixtures, but values for Hb S/Hb F gamma E6V, gamma Q87T mixtures were intermediate between those for Hb S and Hb S/Hb F gamma E6V mixtures. A 1:1 mixture of deoxy Hb A and Hb F gamma E6V, gamma Q87T also polymerized, but exhibited biphasic kinetics, when the concentration was increased to more than 3.5-fold higher than that required for Hb S polymer formation. These results suggest that Gin-gamma 87 is a critical amino acid for exclusion of FS hybrids (alpha 2 beta S gamma) from nuclei formation with Hb S. Our findings also show that Val-gamma 6 in hybrids that form in mixtures of the Hb F variants with either Hb S or Hb A interacts with the hydrophobic acceptor pocket on the EF helix of an adjacent tetramer containing Thr-beta 87.

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Block, Henry W., Thomas H. Savits, and Naftali A. Langberg. "THE FAILURE RATE SHAPE FOR A MIXTURE OF TWO GAMMAS." Probability in the Engineering and Informational Sciences 29, no. 2 (January 26, 2015): 253–64. http://dx.doi.org/10.1017/s0269964814000321.

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In this paper, we continue our investigation of the shape of the failure rate of a mixture of two densities. In our recent paper, Block, Langberg and Savits [2], we introduced a variation of Glaser's method in which we emphasized the role of the mixing parameter q. There we determined all possible shapes of the failure rate function for a mixture of one exponential and one gamma density. Here we classify all possible shapes for a mixture of two gamma densities having shape parameters b, c>0 and scale parameters λ, μ>0.

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Almulihi, Ahmed, Fahd Alharithi, Sami Bourouis, Roobaea Alroobaea, Yogesh Pawar, and Nizar Bouguila. "Oil Spill Detection in SAR Images Using Online Extended Variational Learning of Dirichlet Process Mixtures of Gamma Distributions." Remote Sensing 13, no. 15 (July 29, 2021): 2991. http://dx.doi.org/10.3390/rs13152991.

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In this paper, we propose a Dirichlet process (DP) mixture model of Gamma distributions, which is an extension of the finite Gamma mixture model to the infinite case. In particular, we propose a novel online nonparametric Bayesian analysis method based on the infinite Gamma mixture model where the determination of the number of clusters is bypassed via an infinite number of mixture components. The proposed model is learned via an online extended variational Bayesian inference approach in a flexible way where the priors of model’s parameters are selected appropriately and the posteriors are approximated effectively in a closed form. The online setting has the advantage to allow data instances to be treated in a sequential manner, which is more attractive than batch learning especially when dealing with massive and streaming data. We demonstrated the performance and merits of the proposed statistical framework with a challenging real-world application namely oil spill detection in synthetic aperture radar (SAR) images.

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Ozmen, L., M. Pericin, J. Hakimi, R. A. Chizzonite, M. Wysocka, G. Trinchieri, M. Gately, and G. Garotta. "Interleukin 12, interferon gamma, and tumor necrosis factor alpha are the key cytokines of the generalized Shwartzman reaction." Journal of Experimental Medicine 180, no. 3 (September 1, 1994): 907–15. http://dx.doi.org/10.1084/jem.180.3.907.

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The Shwartzman reaction is elicited by two injections of lipopolysaccharide (LPS) in mice. The priming LPS injection is given in the footpad, whereas the lethal LPS challenge is given intravenously 24 h later. The injection of interferon gamma (IFN-gamma) or interleukin 12 (IL-12) instead of the LPS priming injection induced the lethal reaction in mice further challenged with LPS. Antibodies against IFN-gamma when given together with the priming agent, prevented the lethal reaction in mice primed with either LPS, IL-12, or IFN-gamma. Antibodies against IL-12, when given together with the priming agent, prevented the lethal reaction in mice primed with either LPS or IL-12 but not with IFN-gamma. These results strongly suggest that LPS induces the release of IL-12, that IL-12 induces the production of IFN-gamma, and that IFN-gamma is the cytokine that primes macrophages and other cell types. Upon LPS challenge, the lethal Shwartzman reaction is induced by a massive production of inflammatory cytokines that act on the target sites already sensitized by IFN-gamma. If mixtures of TNF and IL-1 or mixtures of TNF and IFN-gamma are used to challenge mice previously primed with IFN-gamma or IL-12, mortality is induced. In the same conditions, the individual cytokines or a mixture of IL-1 and IFN-gamma do not replace the LPS challenge. When the mice are primed with LPS, the combination of TNF, IL-1, and IFN-gamma induced only a partial mortality incidence suggesting that the involvement of other LPS-induced factors.

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Gleser, Leon Jay. "The Gamma Distribution as a Mixture of Exponential Distributions." American Statistician 43, no. 2 (May 1989): 115. http://dx.doi.org/10.2307/2684515.

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Huang, Wen-Jang, and Shu-Huey Chang. "On some characterizations of the mixture of gamma distributions." Journal of Statistical Planning and Inference 137, no. 9 (September 2007): 2964–74. http://dx.doi.org/10.1016/j.jspi.2006.10.011.

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Carapelle, A., and J. P. Collette. "Gamma-ray attenuation for measuring cryogenic slush mixture density." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 229, no. 1 (February 2005): 111–16. http://dx.doi.org/10.1016/j.nimb.2004.10.092.

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48

Gleser, Leon Jay. "The Gamma Distribution as a Mixture of Exponential Distributions." American Statistician 43, no. 2 (May 1989): 115–17. http://dx.doi.org/10.1080/00031305.1989.10475632.

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Song, Wanying, Ming Li, Peng Zhang, Yan Wu, Xiaofeng Tan, and Lin An. "Mixture WG $\Gamma$ -MRF Model for PolSAR Image Classification." IEEE Transactions on Geoscience and Remote Sensing 56, no. 2 (February 2018): 905–20. http://dx.doi.org/10.1109/tgrs.2017.2756621.

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Vegas-Sanchez-Ferrero, Gonzalo, Santiago Aja-Fernandez, Cesar Palencia, and Marcos Martin-Fernandez. "A Generalized Gamma Mixture Model for Ultrasonic Tissue Characterization." Computational and Mathematical Methods in Medicine 2012 (2012): 1–25. http://dx.doi.org/10.1155/2012/481923.

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Several statistical models have been proposed in the literature to describe the behavior of speckles. Among them, the Nakagami distribution has proven to very accurately characterize the speckle behavior in tissues. However, it fails when describing the heavier tails caused by the impulsive response of a speckle. The Generalized Gamma (GG) distribution (which also generalizes the Nakagami distribution) was proposed to overcome these limitations. Despite the advantages of the distribution in terms of goodness of fitting, its main drawback is the lack of a closed-form maximum likelihood (ML) estimates. Thus, the calculation of its parameters becomes difficult and not attractive. In this work, we propose (1) a simple but robust methodology to estimate the ML parameters of GG distributions and (2) a Generalized Gama Mixture Model (GGMM). These mixture models are of great value in ultrasound imaging when the received signal is characterized by a different nature of tissues. We show that a better speckle characterization is achieved when using GG and GGMM rather than other state-of-the-art distributions and mixture models. Results showed the better performance of the GG distribution in characterizing the speckle of blood and myocardial tissue in ultrasonic images.

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