Weighted Weibull Distribution: Properties and Estimation
We take a closer look at the weighted Weibull distribution. First, we study the structural properties of the probability density function, hazard rate, and mean residual lifetime functions of this distribution. We put forward the estimation for the parameters of the weighted Weibull distribution via maximum likelihood estimation technique. We also obtain expected Fisher’s information matrix, as well as discuss the existence and uniqueness of the maximum likelihood estimates. With regard to Bayesian inference of the unknown parameters, we are using importance sampling technique to calculate Bayes estimates and the corresponding highest posterior density intervals. We perform a data analysis for illustrative purposes.
KeywordsBayes estimator Expected Fisher’s information matrix Importance sampling Maximum likelihood estimator Weighted Weibull distribution
AMS Subject Classification: MSC (2000)62F15 62F10 62F99
Unable to display preview. Download preview PDF.
- Fisher, R. A. 1934. The effect of methods of ascertainment upon the estimation of frequencies. Ann. Eng., 6, 13–25.Google Scholar
- Patil, G. P. 2002. Weighted distributions. Encycloped. Environ., 4, 2369–2377.Google Scholar
- Rao, C. R. 1965. On discrete distributions arising out of methods of ascertainment. In Classical and contagious discrete distributions, ed. G. P. Patil, 320–332. Calcutta, India: Pergamon Press and Statistical Publishing Society.Google Scholar