A New Way to Identify the Family of Continuous Probability Distributions and Estimation of Population Parameter(s)

Abstract

Identification of the distribution for a sample data in literature is a subjective approach based on the pre-assumptions of the distribution of that data and hence difficult for non/new statistician. The main objective of the current research is to provide a new methodology that is not exactly based upon subjective approach. By adjusting the width of the bars of the histogram we find the ordinates which show the height of each bar and provide base for our work. The true relative variances of the ordinates of some continuous probability distributions are calculated and then the pattern of these true relative variances of the ordinates is examined after dividing them into groups. Each group shows some specific distribution. Each group consist of one or more than one ranges of true relative variances of the ordinates. A procedure to compute the sample relative variances of the ordinates is defined. A comparison of true relative variances of the ordinates with sample relative variances of the ordinates provided the basis for identification of the family of probability distribution and also the members of family of distribution.