Class Of Power Series Distributions Research Articles

A Compound Class of Inverse-Power Muth and Power Series Distributions

This paper introduces the inverse-power Muth power series model, which is a composition of the inverse-power Muth and the class of power series distributions. The use of the Bell distribution in this context is emphasized for the first time in the literature. Probability density, survival and hazard functions are studied, as well as their moments. Using the stochastic representation of the model, the maximum-likelihood estimators are implemented by the use of the expectation-maximization algorithm, while standard errors are calculated using Oakes’ method. Monte Carlo simulation studies are conducted to show the performance of the maximum-likelihood estimators in finite samples. Two applications to real datasets are shown, where our proposal is compared with some models based on power series compositions.

Asymptotically minimum variance unbiased estimation for a class of power series distributions

The problem of finding an asymptotically minimum variance unbiased estimator (A.M.V.U.E.) for the parameter of certain truncated power series distributions, is discussed, when the generating function of their coefficients are i) polynomials of binomial type ii) generalized ascending factorials iii) polynomials with coefficients the well known Eulerian numbers.