Methods for Estimating the Parameters of the Power Function Distribution.

Abstract

In this paper, we present some methods for estimating the parameters of the two parameter Power function distribution. We use the least squares method (L.S.M), relative least squares method (R.L.S.M) and ridge regression method (R.R.M). Sampling behavior of the estimates is indicated by a monte carlo simulation. We use total deviation (T.D) and mean square error (M.S.E) to identify the best estimator among them. We determine the best method of estimation using different values for the parameters and different sample size.

On a Power Transformation of Half-Logistic Distribution

“…Let 1 < 2 < ⋅ ⋅ ⋅ < be the times of failure arranged in ascending order and is the sample size. Then ( ) is estimated as in Zaka and Akhter [11], using Bernards' median rank method given bŷ(…”

Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution

“…He derived the Bayes estimators for the scale parameter in Inverse Weibull distribution, by considering Quasi, Gamma and uniform priors under square error, entropy and precautionary loss function. Zaka and Akhter [18] derived the different estimation methods for the parameters of Power function distribution. Zaka and Akhter [19] discussed the different modifications of the parameter estimation methods and proved that the modified estimators appear better than the traditional maximum likelihood, moments and percentile estimators.…”

Moments of Power Function Distribution Based on Ordered Random Variables and Characterization

“…ii) Letting m tends to 1  in (28), we deduce the explicit expression for the product moments of upper k record values for the power function distribution in view of (27) and (26) in the form…”