Abstract
This work, deals with Kumaraswamy distribution. Kumaraswamy (1976, 1978) showed well known probability distribution functions such as the normal, beta and log-normal but in (1980) Kumaraswamy developed a more general probability density function for double bounded random processes, which is known as Kumaraswamy’s distribution. Classical maximum likelihood and Bayes methods estimator are used to estimate the unknown shape parameter (b). Reliability function are obtained using symmetric loss functions by using three types of informative priors two single priors and one double prior. In addition, a comparison is made for the performance of these estimators with respect to the numerical solution which are found using expansion method. The results showed that the reliability estimator under Rn and R3 is the best.
Highlights
The Kumaraswamy distribution is a family of continuous probability distribution defined on (0, 1), which has many similarities to the beta distribution, but it takes advantage of an invertible closed from cumulative distribution function
The posterior distribution of the unknown parameter b of Kumaraswamy distribution (KD) have been obtained by substitute equation (8) in equation (7): βα bα 1 e bβ bn (b 1)
We have the of KD which has been obtained by combining posterior distribution of the unknown parameter b equation (7) with equation (12) as: π (b 3 t) bn (b 1)
Summary
The Kumaraswamy distribution is a family of continuous probability distribution defined on (0, 1), which has many similarities to the beta distribution, but it takes advantage of an invertible closed from cumulative distribution function. Singh and et al (2012) (8) discussed Bayes estimators of reliability function of inverted exponential distribution using informative and non-informative priors a long with the comparison of them. Bayes Estimator (BE):(9, 10, 11) From Bayes’ rule the posterior probability density function of unknown parameter b, results by combining the likelihood function L (a , b t )
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