Alpha power exponentiated Teissier distribution with application to climate datasets

In the global warming era, discovering new probability distribution for modelling the meteorological parameters is highly desirable. Particularly, in some instances, experts’ interest lies mainly in the extreme values like maximum rainfall, temperature, level of flood water, etc. In this article, we introduced a probability distribution for modelling annual maximum rainfall and temperature of four locations in India. We derived statistical properties of the proposed model like survival function, hazard rate function, median, mode, skewness, kurtosis, etc. The proposed model exhibits decreasing, increasing, and uni-modal density functions including bathtub-shaped, increasing, and decreasing hazard rates. Parameters of the proposed model were estimated using the method of maximum likelihood estimation. At last, four real-life datasets, two of annual maximum rainfall and another two of temperature, were used to show the efficiency of the proposed model. Four distributions, namely Gumbel (type 1 generalized extreme value distribution), Fréchet (type 2 generalized extreme value distribution), Teissier, and exponentiated Teissier distributions, were used for comparison with the proposed model. Later, we calculated the return level of both datasets for different return periods. And the 95% bootstrap confidence intervals are constructed for the parameters of the proposed model.