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A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
Two-sided statistical tests and p-values are well defined only when the test statistic in question has a symmetric distribution. A new two-sided p-value called conditional p-value $P_C$ is introduced here. It is closely related to the…
Recently it has been observed that the bivariate generalized linear failure rate distribution can be used quite effectively to analyze lifetime data in two dimensions. This paper introduces a more general class of bivariate distributions.…
We propose in this paper a random intercept Poisson model in which the random effect distribution is assumed to follow a generalized log-gamma (GLG) distribution. We derive the first two moments for the marginal distribution as well as the…
This note shows that the matrix forms of several one-parameter distribution families satisfy a hierarchical low-rank structure. Such families of distributions include binomial, Poisson, and $\chi^2$ distributions. The proof is based on a…
In this short note we provide an analytical formula for the conditional covariance matrices of the elliptically distributed random vectors, when the conditioning is based on the values of any linear combination of the marginal random…
Arnold & Manjunath (2021) claim that the bivariate pseudo-Poisson distribution is well suited to bivariate count data with one equidispersed and one overdispersed marginal, owing to its parsimonious structure and straightforward parameter…
We consider estimation of the structural distribution function of the cell probabilities of a multinomial sample in situations where the number of cells is large. We review the performance of the natural estimator, an estimator based on…
Count data take on non-negative integer values and are challenging to properly analyze using standard linear-Gaussian methods such as linear regression and principal components analysis. Generalized linear models enable direct modeling of…
We consider component-wise equivariant estimation of order restricted location/scale parameters of a general bivariate distribution under quite general conditions on underlying distributions and the loss function. This paper unifies various…
We propose a multivariate probability distribution for categorical and ordinal random variables. To this end, we use the Grassmann distribution in conjunction with dummy encoding of categorical and ordinal variables. To realize the…
The binomial and Poisson distributions have interesting relationships with the beta and gamma distributions, respectively, which involve their cumulative distribution functions and the use of conjugate priors in Bayesian statistics. We…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
In this paper, we introduce the concept of hyperbolic valued random variables, their expectation and moments. We develop the hyperbolic analogue of Binomial and Poisson distributions. We study some of the properties of expectation on the…
Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…
In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset…
We investigate the Conway--Maxwell multivariate Bernoulli distributions, a family of multivariate Bernoulli distributions derived from the Conway--Maxwell-binomial distribution. We show that it is possible to set the parametrization such…
This paper will be devoted to study weighted (deformed) free Poisson random variables from the viewpoint of orthogonal polynomials and statistics of non-crossing partitions. A family of weighted (deformed) free Poisson random variables will…
A common approach to analyze a covariate-sample count matrix, an element of which represents how many times a covariate appears in a sample, is to factorize it under the Poisson likelihood. We show its limitation in capturing the tendency…