Approximating a binomial distribution by a suitable normal distribution is a well known practice, and widely discussed in introductory level statistics books. Recently it has been shown (in Chang et al. (2008)) that the skew-normal distributions can provide a far better approximation than the normal ones. This article revisits the approximation issue and other related inferential aspects. Thoug...

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 intraclass correlation. Even though numerical integration methods are in general required for deriving the marginal models, we obtain the multivariate negati...

For a Markov chain X = {Xi, i = 1, 2, . . . , n} with the state space {0, 1}, the random variable S := ∑n i=1 Xi is said to follow a Markov binomial distribution. The exact distribution of S, denoted as LS, is very computationally intensive for large n [see Gabriel (1959) and Bhat and Lal (1988)] and this paper concerns suitable approximate distributions for LS when X is stationary. We conclude...

in this study, the spatial distribution of overwintered adults of sunn pest, eurygaster integriceps puton, was investigated by using dispersion parameters and indices, mathematical distribution, and regression techniques in rainfed wheat fields by sample size of 1 m2 in 2009 and 2010. the dispersion parameters including: mean-variance test and clumping parameter () showed that the overwintered ...

We assume that product i has a constant hazard of adjusting, fi, in each month, where fi ∼ Beta(a, b). Let us denote the product’s lifetime by ni. These assumptions imply that the total number of price changes in a product’s lifetime is distributed according to the binomial distribution, xi ∼ Bin(ni, fi). We assume, furthermore, that fi is distributed according to the beta distribution, fi ∼ Be...

Characterizing the information carried by neural populations in the brain requires accurate statistical models of neural spike responses. The negative-binomial distribution provides a convenient model for over-dispersed spike counts, that is, responses with greater-than-Poisson variability. Here we describe a powerful data-augmentation framework for fully Bayesian inference in neural models wit...