In this paper, binomial difference ideals are studied. Three canonical representations for Laurent binomial difference ideals are given in terms of the reduced Gröbner basis of Z[x]-lattices, regular and coherent difference ascending chains, and partial characters over Z[x]-lattices, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, and perfect a...

Background and aims: Multiple sclerosis (MS) is an inflammatory disease of the central nervous system.The impact of the number of attacks on the disease is undeniable. The aim of this study was to analyze thenumber of attacks in these patients.Methods: In this descriptive-analytical study, the registered data of 1840 MS patients referred to the MS clinicof Ayatollah Kash...

We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the Poisson, binomial, beta-binomial, and negative binomial distributions. Our results also establish connections between the entropy functions and to the Riemann z...

INTRODUCTION Count data are often collected in chronic disease research, and sometimes these data have a skewed distribution. The number of unhealthy days reported in the Behavioral Risk Factor Surveillance System (BRFSS) is an example of such data: most respondents report zero days. Studies have either categorized the Healthy Days measure or used linear regression models. We used alternative r...

Clinicians need to predict the number of involved nodes in breast cancer patients in order to ascertain severity, prognosis, and design subsequent treatment. The distribution of involved nodes often displays over-dispersion-a larger variability than expected. Until now, the negative binomial model has been used to describe this distribution assuming that over-dispersion is only due to unobserve...

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 theorem based on the notion of relative log-concavity is shown to unify various specific results for the Poisson, binomial, negative binomial, and gamma distr...

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 theorem based on the notion of relative log-concavity is shown to unify various specific results for the Poisson, binomial, negative binomial, and gamma distr...

An asymptotic series in Ramanujan’s second notebook (Entry 10, Chapter 3) is concerned with the behavior of the expected value of φ(X) for large λ where X is a Poisson random variable with mean λ and φ is a function satisfying certain growth conditions. We generalize this by studying the asymptotics of the expected value of φ(X) when the distribution of X belongs to a suitable family indexed by...

We give necessary and sufficient conditions for existence and infinite divisibility of α-determinantal processes. For that purpose we use results on negative binomial and ordinary binomial multivariate distributions.

the problem of estimating the parameter ?, when it is restricted to an interval of the form , in a class of discrete distributions, including binomial negative binomial discrete weibull and etc., is considered. we give necessary and sufficient conditions for which the bayes estimator of with respect to a two points boundary supported prior is minimax under squared log error loss function. for s...