Abstract
This paper introduces a new three-parameter distribution called inverse generalized power Weibull distribution. This distribution can be regarded as a reciprocal of the generalized power Weibull distribution. The new distribution is characterized by being a general formula for some well-known distributions, namely inverse Weibull, inverse exponential, inverse Rayleigh and inverse Nadarajah-Haghighi distributions. Some of the mathematical properties of the new distribution including the quantile, density, cumulative distribution functions, moments, moments generating function and order statistics are derived. The model parameters are estimated using the maximum likelihood method. The Monte Carlo simulation study is used to assess the performance of the maximum likelihood estimators in terms of mean squared errors. Two real datasets are used to demonstrate the flexibility of the new distribution as well as to demonstrate its applicability.
Highlights
Weibull distribution is one of the most important distributions used in reliability engineering and other disciplines
This paper aims to introduce a reciprocal of the generalized power Weibull distribution named inverse generalized power Weibull (IGPW) distribution and studies its mathematical properties
Let X is a random variable of IGPW distribution, the density function of the k-th order statistics of the IGPW distribution is fk:n(x) n! (k−1)!(n−k)!
Summary
Weibull distribution is one of the most important distributions used in reliability engineering and other disciplines. Haghighi and Nikulin (2006) proposed a new extension of Weibull distribution called the generalized power Weibull distribution. Some extensions of the generalized power Weibull distribution proposed by many authors, such as. Proposed the transmuted generalized power Weibull distribution and Pena-Ramirez et al. (2018) proposed The exponentiated power generalized Weibull distribution. This paper aims to introduce a reciprocal of the generalized power Weibull distribution named inverse generalized power Weibull (IGPW) distribution and studies its mathematical properties. The motivations for deriving the inverse generalized power Weibull distribution are to provide more usefulness and flexibility of the ordinary distribution and to improve its goodness-of-fit in comparison with the well-known distributions in lifetime data analysis.
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