On a functional defined by means of Kullback-Leibler measure and its statistical applications

Abstract

In the present study, we define a functional by means of Kullback-Leibler (K-L) measure for continuous random variables and consider its properties. By virtue of this functional, we suggest a new generalization of K-L optimization principle (GKOP). Due to the defined GKOP, it is possible to obtain the probability distribution of the system which is closer to the true distribution in the sense of K-L measure. Finally, the distributions of yearly wind speed data measured in 2001, 2000, 1999 are found by using GKOP and compared with the Weibull distribution which is widely used to determine distribution of wind speed. The Weibull distribution, whose parameters are estimated using maximum likelihood method, shows worse fits considered all years than the distribution derived from GKOP. Although principles based on information theory have been used in a variety of field, the obtained distributions though GKOP are the first time to be applied to the wind energy field.