A Compound Class of Geometric and Lifetimes Distributions
Said Hofan Alkarni*
Identifiers and Pagination:Year: 2013
First Page: 1
Last Page: 5
Publisher Id: TOSPJ-5-1
Article History:Received Date: 12/12/2012
Revision Received Date: 2/1/2013
Acceptance Date: 14/1/2013
Electronic publication date: 3/5/2013
Collection year: 2013
open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
A new lifetime class with decreasing failure rateis introduced by compounding truncated Geometric distribution and any proper continuous lifetime distribution. The properties of the proposed class are discussed, including a formal proof of its probability density function, distribution function and explicit algebraic formulae for its reliability and failure rate functions. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. A formal equation for Fisher information matrix is derived in order to obtaining the asymptotic covariance matrix. This new class of distributions generalizes several distributions which have been introduced and studied in the literature.