International Journal of Statistics and Reliability Engineering

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Vol 10, No 2:

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Deduction of Discrete〖 K〗^th- Order Equilibrium Weibull Distribution With the Help of Ceiling Transformation

Abstract

A generalization of some discrete well-known probability distributions (viz., Weibull, geometric, gamma, Maxwell, and Chi-square) has been introduced using the concept of weighted probability distributions. The introduced model is discrete - order Equilibrium Weibull Distribution (DKEWD). The important property of DKEWD is that it can be used to describe various sorts of hazard rates. In other words, expressing the increasing, decreasing, constant, and upward bathtub hazard rates is helpful. DKEWD is an adequate model for describing the random behavior of different data sets. The parameters of the introduced model are estimated using the maximum likelihood estimation technique. A simulation study is carried out to analyze the asymptotic normality behavior of MLE’s using the Anderson-Darling test statistic. The behavior of bias and MSE is observed with the increase in sample size. Finally, a comparison has been made between DKEWD, its sub-models, and some other introduced extensions of discrete Weibull distribution in terms of best fit, using the Akaike information criterion (AIC).

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ISSN(P) 2350-0174

ISSN(O) 2456-2378

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