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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]

In this work an extension of Erlang distribution have been introduced, which is in fact a generalization of Erlang distribution. This generalization is derived by applying power transformation technique and it gives more flexibility to investigate complex real life data. The distinct structural properties of the formulated distribution including moments, moment generating function, skewness, kurtosis, incomplete moments, mode, median, order statistics, different measure of entropies, mean deviations, Bonferroni and Lorenz curves have been discussed. In addition expressions for survival function, hazard rate function, reverse hazard rate function and mean residual 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 established distribution parameters are performed by maximum likelihood estimation method. Eventually the versatility of the established distribution is examined through two real life data sets related to engineering and medical science. [ABSTRACT FROM AUTHOR]