On New Invertible Skew and Symmetric Distributions

Cláudia Raquel da Rocha Eirado ； Pushpa Narayan Rathie

《Statistics Research Letters》 3卷 (2014/11) Pp. 17-22

並列摘要

The study of new distributions is necessary concerning data that often do not fit to already known distributions. The aim of this work is to present new skew symmetric and asymmetric distributions, their applications in economic, financial, and climate areas. There are three types of distributions proposed: an asymmetric distribution, a symmetric version on the real line, and a skew distribution generated from the symmetric version. Those are applied to analyze the following: three data sets and to produce graphical representations of the fit. The climate data refer to a set containing the annual rainfall in the city of Los Angeles, between 1878 and 1998 provided online at the National Weather Service (NWS) of the United States of America. The applications in the economic-financial area have two data sets; the first of which refers to the percentage returns calculated from daily exchange rates for the Real (Brazil) and Dollar (Canada) against the U.S. dollar between January 3, 2000 and May 20, 2011 released by the Federal Reserve; and the second deals with the energy consumption in kg of oil per capita by 136 countries in 1997 released by the World Bank.

並列關鍵字

Data Sets ； Skew and Symmetric Distributions and Densities Functions ； Maximum Likelihood Estimation ； H-function ； Hypergeometric Function