A mixture Weibull-Rayleigh distribution and its application

Abstract

In this paper, we introduced a mixture Weibull-Rayleigh (MWR) distribution, which was generated by the twocomponent mixture distribution, i.e., Weibull-Rayleigh and length-biased Weibull-Rayleigh distributions. We studied its properties such as the rth moment, the survival function and the sub-model of the MWR distribution. We used the maximum likelihood estimation, the maximum product of spacing estimators, the Anderson-Darling minimum distance estimators and the Cramer-von Mises minimum distance estimators to estimate the parameters of the MWR distribution. Comparing with the lognormal, Weibull-Rayleigh, length-biased Weibull-Rayleigh, mixture generalized gamma and mixture exponentiated inverted Weibull distributions, we present an application of the MWR distribution on fitting hydrological datasets. We found that the MWR distribution provided a better fitting among these distributions. Therefore, we applied the MWR distribution to predict the return periods of such data.

Keywords

• weibull-rayleigh distribution
• maximum product of spacing estimators
• anderson-darling minimum distance estimators