Comparison of the percentile estimation method and mixture (maximum likelihood and least square) method for estimating parameters of Johnson bounded distribution

The Johnson Bonded Distribution (JSBD) is one of the distributions belonging to the Johnson Distribution family (JD) This family is considered one of the flexible distributions that enable it to represent the random behaviour of many phenomena. The method of percentile estimation and the Mixture method (Maximum Likelihood & Least Square) were used to find estimates of the distribution parameters. The simulation results showed the advantage of the Mixture method at large sample sizes, the accuracy of the two methods is close at average sample sizes.