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The current study establishes a new three parameter Rayleigh distribution that is based on the inverse Weibull-G family and is an extension of the Rayleigh distribution. The formulation is known as the inverse Weibull-Rayleigh distribution (IWRD). The distinct structural properties of the formulated distribution including moments, moment generating function, order statistics, quantile function, and Renyi entropy have been discussed. In addition expressions for survival function, hazard rate function and reverse hazard rate function are obtained explicitly. The behaviour of probability density function (p.d.f) and cumulative distribution function (c.d.f) are illustrated through different graphs. The estimation of the formulated distribution parameters are performed by maximum likelihood estimation method. A simulation analysis has been carried out to evaluate and compare the effectiveness of estimators in terms of their bias, variance and mean square error (MSE). Eventually, the usefulness of the formulated distribution is illustrated by means of real data sets which are related distinct areas of science. [ABSTRACT FROM AUTHOR]

The family of distributions which are derived from baseline distributions drag the attention of researchers from past recent years. In this paper we introduce an extension of Gumbel type-II by using transmutation approach suggested by Shaw and Buckley (2007). Several distributional properties of the explored distribution, such as moments, moment generating function, quantile function, reliability analysis, order statistics, and Renyi entropy, have been discussed. Various diagrams depict the behaviour of the probability density function (pdf) and cumulative distribution function (cdf). The parameters of the explored distribution are calculated by using the well-known maximum likelihood procedure. Eventually, the utility of the explored distribution is shown using real life data sets. [ABSTRACT FROM AUTHOR]