New Members of The Johnson Family of Probability Distributions

Properties and Application

Abstract

In this paper we introduce new non-mixed bimodal distributions belonging to the Johnson family of distributions (JFD) named SC and SD, where SC is a special case of SD. The SD is the only distribution among the JFD that can be both unimodal and bimodal distribution. Properties of the SD are methodically studied. The SC and SD are compared with the seven (except the normal distribution) members of the JFD for flexibility and applicability. In order to test for flexibility, a special measure called skewness-kurtosis-square is defined. The best dispersion of points with coordinates (skewness, kurtozis) occurs for the SD and for the well-known SU and SB. Two real datasets were used to test the applicability. EN turned out to be better than its competitors in terms of information criteria and results of three goodness-of-fit tests.