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In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

Probability · Mathematics 2018-06-22 Shane Barratt

A new four-parameter model called the Marshall-Olkin extended generalized Gompertz distribution is introduced. Its hazard rate function can be constant, increasing, decreasing, upside-down bathtub or bathtub-shaped depending on its…

Statistics Theory · Mathematics 2019-04-23 Lazhar Benkhelifa

We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet…

Methodology · Statistics 2021-06-22 Jingyu He , Nicholas Polson , Jianeng Xu

Joint species distribution models are popular in ecology for modeling covariate effects on species occurrence, while characterizing cross-species dependence. Data consist of multivariate binary indicators of the occurrences of different…

Methodology · Statistics 2025-07-08 Federica Stolf , David B. Dunson

For the first time, the Generalized Gamma Burr III (GGBIII) is introduced as an important model for problems in several areas such as actuarial sciences, meteorology, economics, finance, environmental studies, reliability, and censored data…

Methodology · Statistics 2022-08-02 Kehinde Olobatuyi

The univariate generalized extreme value (GEV) distribution is the most commonly used tool for analyzing the properties of rare events. The ever greater utilization of Bayesian methods for extreme value analysis warrants detailed…

Statistics Theory · Mathematics 2023-07-03 Likun Zhang , Benjamin A. Shaby

This paper presents likelihood-based inference methods for the family of univariate gamma-normal distributions GN({\alpha}, r, {\mu}, {\sigma}^2 ) that result from summing independent gamma({\alpha}, r) and N({\mu}, {\sigma}^2 ) random…

Applications · Statistics 2024-12-03 Massimiliano Bonamente , Dale Zimmerman

We give the new distribution named Gamma Lindley distribution (GaLD), of which the Lindley distribution (LD) is a particular case. In this paper, we discuss and add more properties. Also, an application of this distribution is given.

Applications · Statistics 2015-01-28 Halim Zeghdoudi , Sihem Nedjar

We introduce a general class of continuous univariate distributions with positive support obtained by transforming the class of two-piece distributions. We show that this class of distributions is very flexible, easy to implement, and…

Applications · Statistics 2015-11-06 Francisco J. Rubio , Yili Hong

A new family of continuous distribution is proposed by using Kumaraswamy-G (Cordeiro and de Castro, 2011) distribution as the base line distribution in the Marshal-Olkin (Marshall and Olkin, 1997) construction. A number of known…

Statistics Theory · Mathematics 2016-08-23 Laba Handique , Subrata Chakraborty

The Extended Generalized Pareto Distribution (EGPD) (Naveau et al. 2016) is a family of distribution that has been introduced to model the full range of a positive random variable but with the lower and the upper tails distributed according…

Methodology · Statistics 2022-09-13 Noémie Le Carrer , Carlo Gaetan

In this report I present a possible scenario which can lead to the emergence of a generalised Gamma distribution first presented by R. Osorio et al. as the distribution of traded volumes of stocks in financial markets. This propose is…

Data Analysis, Statistics and Probability · Physics 2007-05-23 Silvio M. Duarte Queiros

We consider the extremal properties of the highly flexible univariate extended skew-normal distribution. We derive the well-known Mills' inequalities and Mills' ratio for the extended skew-normal distribution and establish the asymptotic…

Methodology · Statistics 2018-10-01 Boris Beranger , Simone A. Padoan , Yangfan Xu , Scott A. Sisson

A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…

Quantitative Methods · Quantitative Biology 2016-02-01 Jayajit Das , Sayak Mukherjee , Susan E. Hodge

This work defines and investigates the properties of the Max-U-Exp distribution. The method of moments is applied in order to estimate its parameters. Then, by using the previous general theory about Mixed Poisson processes, developed by…

Probability · Mathematics 2024-02-15 Pavlina K. Jordanova , Evelina Veleva

We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…

Statistical Mechanics · Physics 2015-05-13 N. R. Moloney , J. Davidsen

Temporal exponential random graph models (TERGM) are powerful statistical models that can be used to infer the temporal pattern of edge formation and elimination in complex networks (e.g., social networks). TERGMs can also be used in a…

Social and Information Networks · Computer Science 2024-09-17 Yifan Huang , Clayton Barham , Eric Page , PK Douglas

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…

Statistics Theory · Mathematics 2009-10-05 Yaming Yu

A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce…

Statistical Mechanics · Physics 2015-05-14 V. V. Ryazanov

We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…

Probability · Mathematics 2018-10-26 Chuancun Yin , Xiuyan Sha