Related papers: The COM-negative binomial distribution: modeling o…
We introduce and study a subclass of joint Bernoulli distributions which has the palindromic property. For such distributions the vector of joint probabilities is unchanged when the order of the elements is reversed. We prove for binary…
In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties,…
A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of…
One may consider three types of statistical inference: Bayesian, frequentist, and group invariance-based. The focus here is on the last method. We consider the Poisson and binomial distributions in detail to illustrate a group invariance…
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…
In both Tweedie and geometric Tweedie models, the common power parameter $p\notin(0,1)$ works as an automatic distribution selection. It mainly separates two subclasses of semicontinuous ($1<p<2$) and positive continuous ($p\geq 2$)…
Zero inflation is a common nuisance while monitoring disease progression over time. This article proposes a new observation driven model for zero inflated and over-dispersed count time series. The counts given the past history of the…
We present the asymptotic distribution for two-sided tests based on the profile likelihood ratio with lower and upper boundaries on the parameter of interest. This situation is relevant for branching ratios and the elements of unitary…
Extended geometric distribution is defined and its mixture is characterized by the property of having completely monotone probability sequence. Also, convolution equations and probability generating functions are used to characterize…
In this paper, a new mixed Poisson distribution is introduced. This new distribution is obtained by utilizing mixing process, with Poisson distribution as mixed distribution and Transmuted Exponential distribution as mixing distribution.…
We study the nonclassical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found…
Categorical data are often observed as counts resulting from a fixed number of trials in which each trial consists of making one selection from a prespecified set of categories. The multinomial distribution serves as a standard model for…
We consider a type of nonnormal approximation of infinitely divisible distributions that incorporates compound Poisson, Gamma, and normal distributions. The approximation relies on achieving higher orders of cumulant matching, to obtain…
Binomial distributions capture the probabilities of `heads' outcomes when a (biased) coin is tossed multiple times. The coin may be identified with a distribution on the two-element set {0,1}, where the 1 outcome corresponds to `head'. One…
The generalized negative binomial distribution (GNB) is a new flexible family of discrete distributions that are mixed Poisson laws with the mixing generalized gamma (GG) distributions. This family of discrete distributions is very wide and…
A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…
We approximate the distribution of the sum of independent but not necessarily identically distributed Bernoulli random variables using a shifted binomial distribution where the three parameters (the number of trials, the probability of…
The product of two zero mean correlated normal random variables, and more generally the sum of independent copies of such random variables, has received much attention in the statistics literature and appears in many application areas.…
This paper describes a compound Poisson-based random effects structure for modeling zero-inflated data. Data with large proportion of zeros are found in many fields of applied statistics, for example in ecology when trying to model and…
In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains some new sub-models such as the bivariate generalized…