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Binomial data with unknown sizes often appear in biological and medical sciences. The previous methods either use the Poisson approximation or the quasi-likelihood approach. A full likelihood approach is proposed by treating unknown sizes…

Several bivariate beta distributions have been proposed in the literature. In particular, Olkin and Liu (2003) proposed a 3 parameter bivariate beta model, which Arnold and Ng (2011) extend to 5 and 8 parameter models. The 3 parameter model…

Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…

The negative multinomial distribution is a multivariate generalization of the negative binomial distribution. In this paper, we consider the problem of estimating an unknown matrix of probabilities on the basis of observations of negative…

Multivariate distributions often carry latent structures that are difficult to identify and estimate, and which better reflect the data generating mechanism than extrinsic structures exhibited simply by the raw data. In this paper, we…

The technique of wrapping of a univariate probability distribution is very effective in getting a circular form of the underlying density. In this article, we introduce the circular (wrapped) version of xgamma distribution and study its…

Recent theoretical developments revived the interest in charged particle multiplicities and their wide-spread parametrization, the negative binomial distribution (NBD). The central observable of the studies is the Shannon entropy of the…

Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…

Many data sets cannot be accurately described by standard probability distributions due to the excess number of zero values present. For example, zero-inflation is prevalent in microbiome data and single-cell RNA sequencing data, which…

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…

Optimum parameter estimation methods require knowledge of a parametric probability density that statistically describes the available observations. In this work we examine Bayesian and non-Bayesian parameter estimation problems under a…

Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn…

In this work we show that the latest LHC data on multiplicity moments $C_2-C_5$ are well described by a two-step model in the form of a convolution of the Poisson distribution with energy-dependent source function. For the source function…

Most statistical software packages implement numerical strategies for computation of maximum likelihood estimates in random effects models. Little is known, however, about the algebraic complexity of this problem. For the one-way layout…

In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB)…

We develop simple methods for constructing likelihoods and parameter priors for learning about the parameters and structure of a Bayesian network. In particular, we introduce several assumptions that permit the construction of likelihoods…

Negative binomial regression is essential for analyzing over-dispersed count data in in comparative studies, but parameter estimation becomes computationally challenging in large screens requiring millions of comparisons. We investigate…

We study the problem of parameter estimation based on infection data from an epidemic outbreak on a graph. We assume that successive infections occur via contagion; i.e., transmissions can only spread across existing directed edges in the…

The main object of this article is to present an extension of the zero-inflated Poisson-Lindley distribution, called of zero-modified Poisson-Lindley. The additional parameter $\pi$ of the zero-modified Poisson-Lindley has a natural…

We consider the problem of estimating the distribution underlying an observed sample of data. Instead of maximum likelihood, which maximizes the probability of the ob served values, we propose a different estimate, the high-profile…