TITLE:
Gumbel-Exponentiated Weibull {Logistic} Lifetime Distribution and Its Applications
AUTHORS:
Kizito Ebere Anyiam, Iheanyi Sidney Onyeagu
KEYWORDS:
Gumbel Distribution, Exponentiated Weibull, Logistic Distribution, Bimodal Densities, Hazard Function, Maximum Likelihood, Order Statistics, Quantile Function, Shannon Entropy, Simulation, T-R (Y) Family
JOURNAL NAME:
Open Journal of Statistics,
Vol.11 No.5,
October
15,
2021
ABSTRACT: A new generalized exponentiated Weibull model called Gumbel-exponentiated Weibull {Logistic}
distribution is introduced and studied. The new distribution extends the
exponentiated Weibull distribution with additional parameters and bimodal
densities. Some new and earlier distributions formed the sub-models of the
proposed distribution. The mathematical properties of the new distribution
including expressions for the hazard function, survival function, moments,
order statistics, mean deviation and absolute mean deviation from the mean, and
entropy were derived. Monte Carlo simulation study was carried out to assess
the finite sample behavior of the parameter estimates by maximum likelihood estimation
approach. The superiority of the new generalized exponentiated Weibull
distribution over some competing distributions was proved empirically using the
fitted results from three real life datasets.