# A New Generalized Exponentiated Weibull Distribution: Properties and Applications

## Keywords:

Weibull model, lifetime distributions, exponentiated generalized distribution, moments, maximum likelihood estimation## Abstract

The Weibull distribution is the most important statistical distribution to study the data especially from reliability theory. We propose a new generalized exponentiated Weibull distribution which is developed by using the exponentiated Weibull distribution and exponentiated generalized Weibull distribution. Various well-known lifetime distributions are particular case of the proposed distribution. The failure rate of the newly constructed distribution is monotone and non-monotone such as bathtub, unimodal, increasing and decreasing. Thus, the proposed model seems more flexible. Some important mathematical properties of the proposed distribution are studied and simple expressions for the generating function, moments, mean deviations, entropy, and order statistics density are provided.

Some important aspects of the distribution are also discussed numerically and graphically. Parameters

are estimated by using popular technique of maximum likelihood. We apply newly developed model

to two real data sets and make comparison with some well-known sub-models. We explore that the

proposed model is more flexible and useful as compared to the particular sub-models for modeling

lifetime, skewed and survival time data.

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