APPLICATIONS OF A BIVARIATE EXPONENTIAL DISTRIBUTION WITH LINEAR STRUCTURES IN FRACTAL STATISTICS

Abstract

This paper explores the properties of a bivariate exponential distribution with linear structures where the Pearson product moment correlation exists as proposed by Iyer et al. (2002). These properties were then used as the basis for constructing a Pearson-type correlation of the underlying fractal random variables obtained from the marginal distributions of the bivariate exponential distribution. A link function h (.) which defines the relationship between the correlation values obtained from the bivariate exponential distribution and the correlation values obtained from the bivariate fractal distribution whose fractal dimensions exceed 3 was obtained. The results were then applied to analyze the Philippine data on typhoons, casualties, and damage from 1960 to 2013. The results obtained by applying the link function h (.) revealed that while the estimated damage (D) and number of casualties (C) correlated significantly, the corresponding economic impact (X) and number of people affected (Y) were not. In order to link the latter two variables, information on the characteristics of the casualties’ viz. breadwinner or not, are needed.