Divergence Between Doubly Truncated Random Variables And Its Application

In order to describe the differences in the distribution functions of random variables,Cox and Czanner proposed the concept of Cox-Czanner divergence in 2016,which has gradually become a hot topic in applied statistics research,and successively proposed the concept of Cox-Czanner divergence of left and right truncation of random variables.However,neither the Cox-Czanner divergence nor the Cox-Czanner divergence of left and right truncation of random variables can well describe the difference of the distribution function of two random variables on the specified interval.Therefore,we put forward the concept of doubly truncated random variable Cox-Czanner divergence and carried out research.Based on the analysis of the divergence of left and right truncated random variables,the concepts of the divergence between doubly truncated random variables and the weighted divergence are proposed.The upper and lower bounds of the divergence of doubly truncated random variables are given,and the distribution characteristics and monotonicity of the divergence of doubly truncated random variables are discussed.Furthermore,the effects of monotone transformation on the divergence and weighted divergence of doubly truncated random variables are studied,and the properties of the divergence and weighted divergence of doubly truncated random variables under monotone transformation are revealed,and the divergence of doubly truncated random variables is discussed in terms of the proportional failure model,proportional inverse failure model and proportional dominance model.Finally,the divergence of doubly truncated random variables is demonstrated through the data.The empirical results show that,in some specific cases,the divergence between doubly truncated random variables is better than the divergence between left and right truncated random variables to describe the differences in the distribution of random variables.