| Summary: | 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.
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