Subhadip Pal, Ph.D., Department of Bioinformatics and Biostatistics, University of Louisville

"The Modified-Half-Normal Distribution: Pertinency, Properties and an Efficient Sampling Scheme"

We introduce a novel family of probability distributions named Modified-Half-Normal distributions. It is supported on the positive part of the real line and its probability density function is proportional to x→ xα−1 exp(−βx2 + γx)I(x > 0). The parameters α and β are positive real numbers while the parameter γ can be any real number. We discuss its relevance in the literature and study a few of its distributional properties. The normalizing constant of the distribution transpires to be a Fox-Wright Psi function while the moments are ratios of appropriate Fox-Wright Psi functions. From the standpoint of the Bayesian procedures, the usefulness of the distribution is similar to that of the Generalized Inverse Gaussian Distribution (Devroye, 2014; Hormann and Leydold, 2014). The availability of its efficient sampling will facilitate various Markov Chain Monte Carlo algorithms appearing from diverse statistical models. Therefore, a major focus of this article is the development of a uniformly efficient algorithm for generating random samples from the distribution.

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