The return period of heterogeneous climate data with a new invertible distribution

Abstract

One of the most widely used risk measures in environmental studies is the return period (T ) associated with a given level of return. Its calculation requires knowledge of the distribution function fitted to the data. Thus, the efficiency of T depends on the distribution that fits the data well. Except for models of finite mixtures of distributions, bimodal distributions are scarce and are necessary to adequately model climatic and hydrological data. In this work, we propose a simple method to obtain T based on a new invertible bimodal distribution. To illustrate its applicability, we consider the bimodal invertible Weibull distribution (IBW). Several properties of the IBW distribution were studied and the performance of the maximum likelihood estimates of the parameters was tested using Monte Carlo simulation. Finally, the return period was calculated for a temperature dataset.