Discrete-valued time series modeling has witnessed numerous bivariate first-order integer-valued autoregressive process or BINAR(1) processes based on binomial thinning and different innovation distributions. These are mainly focused over-dispersion. This paper aims to propose new distributions a recently proposed over-dispersed distribution: the Poisson 2S-Lindley distribution. The distributio...

Constructing a bivariate distribution with specific marginals and correlation has been a challenging problem since 1930s. In this survey we shall focus on the recent developments on the FGM-related distributions, including Sarmanov and Lee’s distributions, Baker’s distributions and Bayramoglu’s distributions. This complements the most recent works of (i) the review by Sarabia and Gómez-Déniz (2...

Gamma distributions, which contain the exponential as a special case, have a distinguished place in the representation of near-Poisson randomness for statistical processes; typically, they represent distributions of spacings between events or voids among objects. Here we look at the properties of the Shannon entropy function and calculate its corresponding flow curves, relating them to examples...

Interest in predicting protein backbone conformational angles has prompted the development of modeling and inference procedures for bivariate angular distributions. We present a Bayesian approach to density estimation for bivariate angular data that uses a Dirichlet process mixture model and a bivariate von Mises distribution. We derive the necessary full conditional distributions to fit the mo...