A New Class of Transmuted Inverse Weibull Distribution for Reliability Analysis

SYNOPTIC ABSTRACT

A generalized version of the three-parameter transmuted inverse Weibull distribution is introduced in this article. This distribution generalizes the following distributions: (a) transmuted inverse exponential, (b) transmuted inverse Rayleigh, (c) inverse Weibull. The properties of the transmuted inverse Weibull distribution are discussed. This model is capable of modeling various shapes of aging and failure criteria. Here we present the relationship between shape parameter, probability density function, cumulative distribution function, reliability function, hazard function, percentile life, mean, variance, coefficient of variation, coefficient of skewness, and coefficient of kurtosis. We derive the moments, geometric mean, harmonic mean, entropy, mean deviation, and examine the order statistics with their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. The usefulness of the new distribution is shown by application to real data and comparison with other distributions.

Key Words and Phrases::

• reliability functions
• moment estimation
• order statistics
• maximum likelihood estimation

Acknowledgment

The authors are thankful for comments and suggestions by the referees and especially appreciated the Editor-in-Chief for their valuable comments and suggestions to improve this article.