The location-scale family of generalized Maxwell distributions: theory and applications to annual rainfall records

This article introduces a location-scale family of Maxwell distributions for modelling the total annual rainfall of India from 1901 to 2014. It is shown that the distribution is quite flexible for modelling increasing and bathtub shaped failure rate data sets. The basic properties including moments, entropy, identifiability, conditional moments, mean residual life and stochastic ordering are explicitly derived here. Maximum likelihood estimation along with asymptotic confidence intervals are discussed. The score functions are also provided to compute the asymptotic confidence intervals of the parameters. The applicability of the distribution for Rainfall data is assessed and compared with 3-parameter Weibull and Gamma distributions. It is observed from the goodness-of-fit criteria that the rainfall data set is nicely fitted by the proposed distribution.