A Weibull Generated Exponentiated Exponential Model: Properties and Bayes Interval Prediction

• Main Authors: Essam K. AL-Hussaini, Alaa H. Abdel-Hamid
• Format: Article
• Language: English
• Published: Atlantis Press 2015-11-01
• Series: Journal of Statistical Theory and Applications (JSTA)
• Subjects: Composed distributions; Weibull and exponentiated exponential distributions; one- and two-sample Bayes interval prediction; simulation.
• Online Access: https://www.atlantis-press.com/article/25845142.pdf

Motivated by the fact that the so-called Weibull generated exponentiated exponential distribution (WGEED) accommodates for non-monotone as well as monotone hazard rate functions (HRFs), we give some properties of this WGEED and explore its use in life testing by obtaining Bayes prediction intervals of future observables. The survival function (SF) of the WGEED is constructed by composing a Weibull cumulative distribution function (CDF) with –ln [exponentiated exponential] CDF. Some properties of the WGEED are given and prediction intervals of future observables, using the one- and two-sample schemes, are obtained. A comparison between the WGEE and the Weibull distributions, based on Kolmogorov-Smirnov goodness of fit test, shows that the former fits better than the latter. Real life data shows the possibility of using the WGEED in analyzing lifetime data. Numerical examples of one- and two- sample Bayes interval prediction are given to illustrate the procedure and a simulation study is made to compute the coverage probabilities and the average lengths of intervals.