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 nonobserv-ability 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.

Highlights

  • In many observational studies for wild life, human, fish population or insect, every unit in the population does not have the same chance of being included in the sample

  • Rao identified various situations that can be modeled by weighted distributions

  • Ahamad / Journal of Statistical Theory and Applications 20(2) 395–406. These situations refer to instances where the recorded observations cannot be considered as a random sample from the original distributions

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Summary

INTRODUCTION

In many observational studies for wild life, human, fish population or insect, every unit in the population does not have the same chance of being included in the sample. In such cases, sampling frames are not well defined and recorded observations are biased. Ahamad / Journal of Statistical Theory and Applications 20(2) 395–406 These situations refer to instances where the recorded observations cannot be considered as a random sample from the original distributions. The probability density function of generalized inverse Weibull distribution is given by f (x). The density function in Equation (5) is known as weighted generalized inverse Weibull distribution (WGIWD). The cumulative distribution function (cdf) of weighted generalized inverse Weibull distribution (WGIWD) is (

Using Extension of Jeffrey’s Prior
PARAMETER ESTIMATION UNDER NEW LOSS FUNCTION
Posterior Mean and Posterior Variance of Under Extension of Jeffrey’s Prior
DATA ANALYSIS
CONCLUSION
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