Development of Weibull Exponentiated G-Family of Distributions with its Statistics and Properties

Abstract

The Weibull Exponentiated G (WEG) family is a newly proposed class of probability distributions formed by combining the Weibull distribution with the Exponentiated family of distributions. The resulting family introduces two additional shape parameters, α and β, thereby providing substantial exibility in modelling phenomena with complicated tails and non-monotone hazard rates. Applications to risk analysis, survival analysis, and reliability engineering are of particular interest. This paper presents the derivation of the WEG family, derives its fundamental statistical properties including the survival function, hazard function, and quantile function, and develops maximum likelihood estimation (MLE) for two important special submodels: the Weibull Exponentiated Exponential Distribution (WEED) and the Weibull Exponentiated Rayleigh Distribution (WERD). Moment expressions including the mean, variance, skewness, and kurtosis are derived for both submodels via power series and binomial expansion techniques. A Monte Carlo simulation study concerms that the MLE estimators are asymptotically unbiased and consistent for both submodels............

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