Abstract
In this paper, we derive explicit expressions for Bonferroni Curve (BC), Bonferroni index (BI), Lorenz Curve (LC) and Gini index (GI) for the Marshall-Olikn Exponential (MOE) distribution, which have mainly concern with some aspects like poverty, welfare, decomposability, reliability, sampling and inference. We also establish several recurrence relations satisfied by the single and the product moments of progressive Type-II right censored order statistics from MOE distribution, to enable one to evaluate the single and product moments of all order in a simple recursive way.
Highlights
Marshall and Olkin (1997) proposed a new method for adding a parameter to a family of distributions. They consider a two-parameter generalization of the one-parameter exponential distribution as one parameter exponential family of distributions is not broad enough to model data from various real contexts, which plays a central role in reliability and life time data analysis
To obtain the recurrence relations for the product moments of progressive Type-II right censored order statistics from Marshall-Olkin exponential distribution, we have from equation (3.1), μr(,Rs:1m,R:n2,...,Rm)(i, j)
Substituting α = 1 in Theorems 3.1-3.8, we obtain recurrence relations for single and product moments of progressive Type-II right censored order statistics from standard exponential distribution, which are in agreement with the results established by Aggarwala and Balakrishnan (1996), Balakrishnan and Aggarwala (2000, pp. 42-49)
Summary
Marshall and Olkin (1997) proposed a new method for adding a parameter to a family of distributions They consider a two-parameter generalization of the one-parameter exponential distribution as one parameter exponential family of distributions is not broad enough to model data from various real contexts, which plays a central role in reliability and life time data analysis. Gaver and Lewis (1980) developed a first order autoregressive time series model with exponential stationary marginal distribution. If we substitute equation (1.3) into equation (1.1), we get the so called Marshall-Olkin exponential (MOE) distribution (cf Salah et al, 2009). This distribution has been used by Ghitany et al (2005) for analyzing censored samples.
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