The Weighted Inverse Weibull Distribution

International Journal of Research and Innovation in Applied Science (IJRIAS) | Volume VII, Issue IV, April 2022 | ISSN 2454–6194

The Weighted Inverse Weibull Distribution

Adetunji K. Ilori¹, Damilare Matthew Oladimeji^2
1Statistics Programme, National Mathematical Center, Abuja, Nigeria
Kaduna-Lokoja Expressway, Sheda, Kwali, Abuja.
²Department of Statistics, University of Abuja, FCT, Nigeria

Abstract: This paper introduces the Weighted Inverse Weibull distribution as inverse weighting of the Inverse Weibull distribution. Its various basic statistical properties were explicitly derived and the method of maximum likelihood estimation was used in estimating the model parameters. The model was applied to two real life data sets and its performance and flexibility was assessed with respect to existing distribution using the log-likelihood and Akaike Information Criteria as basis for judgment.

Keywords: Exponential distribution, Generalization, Inversion, Statistical Properties, Weighted distributions, Azzalini.

I.INTRODUCTION

The exponential distribution has been considered in literature to be effective to analyse lifetime data as a result of its analytical tractability. Although, one-parameter exponential distribution has a lot of interesting properties such as memoryless; one of the major disadvantages of this distribution is that it has a constant hazard function. Moreover, the graph of its probability density function (PDF) is a decreasing function. As a result of this reason several generalizations and weighting of the exponential and Weibull distributions have been developed in the literature. For instance, generalized exponential (GE) distribution as considered by Gupta and Kundu, (2000) is different extension from the exponential distribution. The generalized exponential distribution has increasing or unimodal PDFs, and monotone hazard functions Kanpur, (2015).
Weighted distribution theory gives unified approach to dealing with problem of specifying an appropriate and effective distribution, when the existing distribution is not suitable to capture the entire behaviour of a data set. The concept of weighted distribution was introduced by Fisher (1934) and latter put in unifying form by Rao (1965). Let X denote a non negative continuous random variable with its probability density function , then the probability density function of the weight random variable is given by

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