ON THE DISCRETE DISTRIBUTION GENERATED BY LEVY PROBABILITY

In this paper, we consider one-parameter regularly varying discrete distribution generated by Levy probability (RDLP). Some useful plots of the models are illustrated. Mathematically, to propose the RDLP model as a discrete distribution in bioinformatics, some common statistical facts such as unimodality, skewness to the right, upward/downward convexity, regular variation at infinity, and asymptotically constant slowly varying component are established for the model. Based on the Monte Carlo method and limited-memory Broyden–Fletcher–Goldfarb–Shanno for bound-constrained optimization, simulation studies are done to estimate bias, mean square error, and maximum likelihood estimation for the unknown parameter of the model. Some asymptotic properties and asymptotic expansions are given for useful functions. Moreover, we shall attempt to examine the RDLP model with a real count data set to show its application, and also compare it with two rival models.