Comparison of Two New Robust Parameter Estimation Methods for the Power Function Distribution

Abstract

Estimation of any probability distribution parameters is vital because imprecise and biased estimates can be misleading. In this study, we investigate a flexible power function distribution and introduced new two methods such as, probability weighted moments, and generalized probability weighted methods for its parameters. We compare their results with L-moments, trimmed L-moments by a simulation study and a real data example based on performance measures such as, mean square error and total deviation. We concluded that all the methods perform well in the case of large sample size (n>30), however, the generalized probability weighted moment method performs better for small sample size.

Efficient estimation of Pareto model: Some modified percentile estimators

“…In order to compare efficiency and accuracy of different estimators, Total Mean Square Error (TMSE) and Total Relative Deviation (TRD) were used as performance indices. These measures are frequently used as performance criterion when different estimators (or estimation strategies) are compared through Monte Carlo simulation [ 28 , 29 , 32 – 39 ].…”

Stress-Strength Reliability and Randomly Censored Model of Two-Parameter Power Function Distribution

“…e power function distribution is studied by many authors. For example, Kleiber and Kotz [4] showed that the power function distribution is a particular case of the Pareto distribution, Bhatt [5] discussed the characterization of the power function distribution through expectation, Chang [6] considered the power function distribution and discussed its characterizations with the use of independence of record values, Lutful and Ahsanullah [7] used the linear function of the order statistics for the estimation of the power function distribution, Malik [8] calculated expressions for the exact moments of order statistics for the power function distribution, Saran and Pandey [9] estimated the power function distribution and its characterizations by kth record value, Saleem et al [10] derived the Bayesian estimators for the nite mixture model of power function distribution with a censored sample, Shahzad et al [11] compared the L-moments method and Trim L-moments methods for the power function distribution, and Shakeel et al [12] used the probability weighted moments method and the generalized probability weighted method to estimate the power function distribution.…”

Classical and Bayesian Estimation of Two-Parameter Power Function Distribution

“…The power function distribution is studied by many authors. For example, Kleiber and Kotz [3] showed that the power function distribution is a particular case of Pareto distribution, Bhatt [4] discussed the characterization of the power function distribution through expectation, Chang [5] considered the power function distribution and discussed its characterizations with the use of independence of record values, Lutful and Ahsanullah [6] used the linear function of the order statistics for estimation of the power function distribution, Malik [7] calculated expressions for the exact moments of order statistics for the power function distribution, Saran and Pandey [8] estimated the power function distribution and its characterizations by kth record value, Saleem et al [9] derived Bayesian estimators for the finite mixture model of power function distribution with censored sample, Shahzad et al [10] compared the L-moments method and Trim L-moments methods for the power function distribution and Shakeel et al [11] used the probability weighted moments method and the generalized probability weighted method to estimate the power function distribution. This paper presents the comparison of maximum likelihood estimation and Bayesian estimation using a complete sample from the power function distribution.…”