Volume no :7, Issue no: 1, March (2012)

Journal of Statistics: Advances in Theory and Applications

THE EXPONENTIAL NEGATIVE BINOMIAL DISTRIBUTION: A CONTINUOUS BRIDGE BETWEEN UNDER AND OVER DISPERSION ON A LIFETIME MODELLING STRUCTURE

Author's: FRANCISCO LOUZADA, PATRICK BORGES and VICENTE CANCHO
Pages: [67] - [83]
Received Date: March 26, 2012
Submitted by:

Abstract

In this paper, we propose a new three parameter distribution with decreasing failure rate distribution. The new distribution contains as particular cases, the exponential geometric and the exponential Poisson distributions proposed by Adamidis and Loukas [3] and Kus [11], respectively. Consequently, as an advantage, it allows for under-dispersion and over-dispersion with respect to a Poisson distribution. We derive expressions for the quantile, r-th raw moments of the new distribution, including the mean and variance, the order statistics, the r-th moment of the order statistics, and the Rényi and Shannon entropy measures. Estimation is carried out via maximum likelihood.

Keywords

exponential distribution, entropy measures, moments, negative binomial distribution, order statistics.