Properties and Potentials of Gumbel Power Function Distribution to Rainfall and Wind Speed Datasets

Abstract

The objective of this paper is to present the properties and potentials of Gumbel Power function (GuPF) distribution to rainfall and wind speed datasets using the T-X methodology. The density and hazard rate function of the GuPF distribution are unimodal and increasing respectively. Statistical properties of the new distribution such as quantile, moments, and probability weighted moments (PWMs), order statistics and entropy are derived. The Maximum likelihood estimation method is used to estimate the parameters of the proposed model. The superiority of GuPF distribution over other distributions with the same baseline is illustrated using two environmental datasets.

Keywords

• Power function; Gumbel distribution; Transformed-Transformer; Moments; Estimation