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On the compound Poisson-gamma distribution

Christopher Withers, Saralees Nadarajah (2011)

Kybernetika

The compound Poisson-gamma variable is the sum of a random sample from a gamma distribution with sample size an independent Poisson random variable. It has received wide ranging applications. In this note, we give an account of its mathematical properties including estimation procedures by the methods of moments and maximum likelihood. Most of the properties given are hitherto unknown.

On the compound α(t)-modified Poisson distribution

Katarzyna Steliga, Dominik Szynal (2015)

Applicationes Mathematicae

In this paper we introduce compound α(t)-modified Poisson distributions. We obtain the compound Delaporte distribution as the special case of the compound α(t)-modified Poisson distribution. The characteristics of α(t)-modified Poisson and some compound distributions with gamma, exponential and Panjer summands are presented.

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

German Bernhart, Jan-Frederik Mai, Matthias Scherer (2015)

Dependence Modeling

Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choicewhen modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper...

On the continuity of invariant statistics

Nguyen Van Ho (1978)

Aplikace matematiky

The aim of this paper is to establish theorems on the absolute continuity of translation as well as scale invariant statistics in general, from which the related results by Hodges-Lehmann and Puri-Sen follow. The continuity relations between the joint cdf of a random vector and its marginal cdf's are also considered.

On the distributions of R m n + ( j ) and ( D m n + , R m n + ( j ) )

Jagdish Saran, Kanwar Sen (1982)

Aplikace matematiky

The contents of the paper is concerned with the two-sample problem where F m ( x ) and G n ( x ) are two empirical distribution functions. The difference F m ( x ) - G n ( x ) changes only at an x i , i = 1 , 2 , ... , m + n , corresponding to one of the observations. Let R m n + ( j ) denote the subscript i for which F m ( x i ) - G n ( x i ) achieves its maximum value D m n + for the j th time ( j = 1 , 2 , ... ) . The paper deals with the probabilities for R m n + ( j ) and for the vector ( D m n + , R m n + ( j ) ) under H 0 : F = G , thus generalizing the results of Steck-Simmons (1973). These results have been derived by applying the random walk model.

On the exact distribution of L1(vc) of Votaw.

Giorgio Pederzoli, Puspha N. Rathie (1987)

Trabajos de Estadística

This paper deals with the exact distribution of L1(vc) of Votaw. The results are given in terms of Meijer's G-function as well as in series form suitable for computation of percentage points.

On the generalization and estimation for the double Poisson distribution.

Mohamed M. Shoukri (1982)

Trabajos de Estadística e Investigación Operativa

The bivariate forms of many important discrete probability distributions have been studied by many statisticians. The trinomial, the double Poisson, the bivariate negative binomial, and the bivariate logarithmic series distributions are in fact the bivariate generalizations of the well known univariate distributions. A systematic account of various families of distributions of bivariate discrete random variables have been given by Patil and Joshi (11), Johnson and Kotz (4), and Mardia (9) in their...

On the outstanding elements and record values in the exponential and gamma populations.

G. S. Lingappaiah (1981)

Trabajos de Estadística e Investigación Operativa

Outstanding elements and recorded values are discussed in this paper as related to exponential and gamma populations. First, the problem of prediction is considered when there are available, k sets of independent observations from a general-type exponential distribution. In such a case, prediction of the nk-th record value in the k-th set is made in terms of ni-th (i = 1, ..., k-1) record values from other (k-1) sets. For this purpose a predictive distribution is obtained. Secondly, the distribution...

On the properties of the Generalized Normal Distribution

Thomas L. Toulias, Christos P. Kitsos (2014)

Discussiones Mathematicae Probability and Statistics

The target of this paper is to provide a critical review and to enlarge the theory related to the Generalized Normal Distributions (GND). This three term (position, scale shape) distribution is based in a strong theoretical background due to Logarithm Sobolev Inequalities. Moreover, the GND is the appropriate one to support the Generalized entropy type Fisher's information measure.

On the ratio of gamma and Rayleigh random variables

Saralees Nadarajah (2007)

Applicationes Mathematicae

The gamma and Rayleigh distributions are two of the most applied distributions in engineering. Motivated by engineering issues, the exact distribution of the quotient X/Y is derived when X and Y are independent gamma and Rayleigh random variables. Tabulations of the associated percentage points and a computer program for generating them are also given.

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