Parameter Estimation of the Weighted Generalized Inverse Weibull Distribution

Abstract

Weighted distributions are used widely in many fields of real life such as medicine, ecology, reliability, and so on. The idea of weighted distributions was given by Fisher and studied by Rao in a unified manner who pointed out that in many situations the recorded observations cannot be considered as a random sample from the original distribution. This can be due to nonobservability of some events, damage caused to the original observations or adoption of unequal probability sampling procedure. In this paper, we have proposed weighted version of generalized inverse Weibull distribution known as weighted generalized inverse Weibull distribution (WGIWD). Classical and Bayesian methods of estimation were proposed for estimating the parameters of the new model. The usefulness of the new model was demonstrated by applying it to a real-life data set.

Keywords

• Generalized inverse Weibull distribution
• Weighted generalized inverse Weibull distribution
• Loss function
• Bayesian estimation