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Journal of Statistical Theory and Practice

, Volume 9, Issue 2, pp 250–265 | Cite as

Weighted Weibull Distribution: Properties and Estimation

  • Sanku Dey
  • Tanujit Dey
  • M. Z. Anis
Article

Abstract

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.

Keywords

Bayes estimator Expected Fisher’s information matrix Importance sampling Maximum likelihood estimator Weighted Weibull distribution 

AMS Subject Classification: MSC (2000)

62F15 62F10 62F99 

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Copyright information

© Grace Scientific Publishing 2015

Authors and Affiliations

  1. 1.Department of StatisticsSt. Anthony’s CollegeShillong, MeghalayaIndia
  2. 2.Department of MathematicsCollege of William & MaryWilliamsburgUSA
  3. 3.SQC & OR UnitIndian Statistical InstituteCalcuttaIndia

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