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Extended Matrix Variate Hypergeometric Functions and Matrix Variate Distributions
International Journal of Mathematics and Mathematical Sciences, 2015 Hypergeometric functions of matrix arguments occur frequently in multivariate statistical analysis. In this paper, we define and study extended forms of Gauss and confluent hypergeometric functions of matrix arguments and show that they occur naturally ...
Daya K. Nagar +2 more
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Generalized Hypergeometric Distributions
Journal of the Royal Statistical Society Series B: Statistical Methodology, 1956 Summary An examination is made of the conditions under which the hypergeometric series provides discrete frequency distributions; eight sets of conditions exist. Urn model representations, other derivations and special forms are discussed. The limiting forms are positive and negative binomials and the Poisson distribution.
C. D. Kemp, Adrienne W. Kemp
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Boletim da Sociedade Paranaense de MatemáticaSeveral authors have extensively investigated beta function, hypergeometric function and confluent hypergeometric function, their extensions and generalizations due to their several application in many areas of engineering, probability theory and ...
Savita Panwar +2 more
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Distributions of the Ratio and Product of Two Independent Weibull and Lindley Random Variables
Journal of Probability and Statistics, 2020 In this paper, we derive the cumulative distribution functions (CDF) and probability density functions (PDF) of the ratio and product of two independent Weibull and Lindley random variables.
N. J. Hassan +2 more
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IncRNA‐ZFAS1, an Emerging Gate‐Keeper in DNA Damage‐Dependent Transcriptional Regulation
Advanced Science, EarlyView.LncZFAS1 plays a crucial role during DNA damage response in mammalian cells. Loss of lncZFAS1 results in deficient DNA lesion removal and reduced cell viability. Mechanistically, lncZFAS1 modulates RNAPII phosphorylation and transcription and thereby promotes both GG‐NER and TC‐NER upon UV damage.
Jiena Liu +10 more
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Bernstein-type bounds for beta distribution
Modern Stochastics: Theory and Applications, 2023 This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-Gaussian and sub-gamma bounds previously studied in this context.
Maciej Skorski
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Distribution of values of Gaussian hypergeometric functions
Pure and Applied Mathematics Quarterly, 2023 In the 1980's, Greene defined {\it hypergeometric functions over finite fields} using Jacobi sums. The framework of his theory establishes that these functions possess many properties that are analogous to those of the classical hypergeometric series studied by Gauss and Kummer.
Ono, Ken, Saad, Hasan, Saikia, Neelam
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Advanced Science, EarlyView.CTSK plays a critical role in pulmonary fibrosis. Excessive CTSK accumulation interacts with SNX9 to enhance TGF‐β1‐induced SMAD3 activation and GLS1 expression in fibroblasts, driving glutamine metabolism for collagen biosynthesis and exacerbating pulmonary fibrosis.
Mengting Chen +10 more
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Properties of Matrix Variate Beta Type 3 Distribution
International Journal of Mathematics and Mathematical Sciences, 2009 We study several properties of matrix variate beta type 3 distribution. We also derive probability density functions of the product of two independent random matrices when one of them is beta type 3.
Arjun K. Gupta, Daya K. Nagar
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Inequalities involving hypergeometric and related functions
Journal of Inequalities and Applications, 2018 An inequality is being proved which is connected to cost-effective numerical density estimation of the hyper-gamma probability distribution. The left-hand side of the inequality is a combination of two in the third parameter distinct versions of the ...
Siegfried H. Lehnigk
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