Estimations and Prediction from the Inverse Rayleigh Model Based on Lower Record Statistics
A.I. Shawky1 and M. M. Badr2
1Department of Statistics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah
21589, Saudi Arabia.
2Department of Statistics, Faculty of Science for Girls, King Abdulaziz University, P.O. Box
70973, Jeddah 21577, Saudi Arabia.
Abstract: This article considers estimation of the unknown parameters for the inverse Rayleigh distribution (IRD) based on lower record values. We consider the maximum likelihood (ML) and Bayesian inference of the unknown parameters of the model, as well as the reliability and cumulative hazard rate functions. The Bayes estimators are obtained relative to both symmetric (squared error) and asymmetric (linear exponential (LINEX)) loss functions. It is noticed that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Bayesian prediction interval of the future record values are obtained as well. Finally, practical examples using real record values are given to illustrate the application of the results.
[A.I. Shawky and M. M. Badr. Estimations and Prediction from the Inverse Rayleigh Model Based on Lower Record Statistics. Life Sci J 2012;9(1):985-990] (ISSN:1097-8135). http://www.lifesciencesite.com. 142
Key words: Bayesian inference; Squared error loss function; LINEX loss function; Maximum likelihood function; Reliability; Failure rate; Record values; Inverse Rayleigh distribution. Full Text 142