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Weibull Exponentiated Inverted Raleigh Distribution: Properties and Application

Saeed E. Hemeda, Mohamed S. Hamoda


In this paper a new continuous distribution with extra two parameters called the Weibull exponentiated inverse Raleigh distribution is introduced. The new distribution based on the Weibull generated family of distributions and exponentiated inverse Raleigh distribution as a baseline distribution. Important linear expansion forms for the cdf, pdf and reliability are obtained. We investigate the shapes of the density and hazard rate function. Some statistical properties of the new distribution including moments, mean residual life, quantile and generating functions, median, skewness and kurtosis and order statistics are discussed. The estimation of the model parameters is performed by the maximum likelihood method. The importance of the new distribution is examined through real data application and the results show that the new distribution can be useful to provide better fits than other lifetime models.


Weibull exponentiated inverse Raleigh distribution; Moments; Quantile function; Reliability; Mean deviation; Estimation.

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