A scale parameters and modified reliability estimation for the inverse exponential rayleigh distribution | [Pakistan Journal of Statistics • 2024]

Author(s):

1. Shurooq A.K. AL-Sultany: Department of Mathematics, College of Science Mustansiriyah University, Baghdad, Iraq

Abstract:

This paper present methods for estimating a scale parameters and modified reliability for the Inverse Exponential Rayleigh Distribution include Maximum Likelihood, rank set sampling and Cramér-von-Mises Estimations. In all the mentioned estimation methods, the Newton-Raphson iterative numerical method was used. Then a simulation was conducted to compare the three methods with six cases and different sample sizes. The comparisons between scale parameter estimates were based on values from Mean Square Error while it was based on values from Integrated Mean Square Error for the estimates of the modified reliability function. The results show that Cramér-von-Mises (MCV) estimators is the best among the other two methods for estimating the modified reliability function.

Page(s): 403-414

DOI: DOI not available

Published: Journal: Pakistan Journal of Statistics, Volume: 40, Issue: 4, Year: 2024

Keywords:

Maximum Likelihood Estimation , Rank set sampling , CramérvonMises Estimation , modified reliability integral square error , Inverse Exponential Rayleigh Distribution

References:

[1] Al-Sultany S.A.,Mohammed S.A. .2018 .Comparison between Bayesian and Maximum Likelihood Methods for parameters and the Reliability function of Perks Distribution. Science Journal, 59(1B) : 369-376.

[2] Al-Sultany S.A.,Mohammed S.A.,Part II .2017 .Mixture of two Inverse Exponential Distribution Based on Fuzzy Data. , : 73-81.

[3] Hussein L.K.,Hussein I.H.,Rasheed H.A. .2023 .Exponential Rayleigh distribution: Approximate non - Bayesian estimation parameters and survival function. AIP Conf. Proc. 2414, (040089) : .

[4] Mohammed M.J.,Mohammed A.T. .2021 .Parameter estimation of inverse exponential Rayleigh distribution based on classical methods. Int. J. Nonlinear Anal. Appl., 12(1) : 935-944.

[5] Macdonald P. .1971 .An estimation procedure for mixtures of distributions. Journal of the Royal Statistical Society, 20 : 102-107.

[6] Noaman A.A.,Ahmed S.A.,Hawash M.K. .2020 .Constructing a new mixed probability distribution with fuzzy reliability estimation. Periodicals of Engineering and Natural Sciences, 8(2) : 590-601.

[7] Kareem S.A. .2020 .A Comparison between Two Shape Parameters Estimators for (Burr-XII) Distribution. Science Journal, 17(3) : 973-979.

Citations

Downloads

Views