THERMAL SCIENCE

International Scientific Journal

Sofi Mudasir

,

Ajaz A. Bhat

,

Sheikh P. Ahmad

,

Aasimeh Rehman

,

Taghreed M. Jawa

,

Neveen Sayed-Ahmed

,

Ahlam H. Tolba

A DUAL APPROACH TO PARAMETER ESTIMATION CLASSICAL VS. BAYESIAN METHODS IN POWER RAYLEIGH MODELLING

ABSTRACT
In this article, we investigated the problem of estimating the parameters of power Rayleigh distribution using a range of classical and Bayesian estimate strategies. For applied statisticians and reliability engineers, parameter estimation provides a guide for choosing the best method of estimating the model parameters. Six frequentist estimation methods, including maximum likelihood estimation, Cramer-von Mises estimation, Anderson-Darling estimation, least square estimation, weighted least square estimation, and maximum product of spacing estimation, were taken into consideration when estimating the parameters of the power Rayleigh model. The expressions for Bayes estimators of the scale parameter are derived under squared error and precautionary loss functions and utilizing extensions of Jeffrey's prior and natural conjugate priors. To investigate the finite sample properties of the parameter estimations, Monte Carlo simulations are also performed. Finally, two applications to real data are used to highlight the versatility of the suggested model and the comparison is made with the Rayleigh and some of its well-known extensions such as exponentiated Rayleigh and weighted Rayleigh distributions.
KEYWORDS
power Rayleigh distribution, Cramer Von-Mises estimation, Anderson-Darling estimation, weighted least square estimation
PAPER SUBMITTED: 2024-06-20
PAPER REVISED: 2024-09-12
PAPER ACCEPTED: 2024-10-20
PUBLISHED ONLINE: 2025-01-25
DOI REFERENCE: https://doi.org/10.2298/TSCI2406877M
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2024, VOLUME 28, ISSUE Issue 6, PAGES [4877 - 4894]
REFERENCES
  1. Rayleigh, J., On the Resultant of a Large Number of Vibrations of the Same Pitch and of Arbitrary Phase, Philosophical Magazine, 5th Series, 10 (1980), 60, pp. 73-78
  2. Johnson, N. L., et al., Continuous Univariate Distributions, Wiley-Interscience, New York, USA, 1994, Vol. 1
  3. Siddiqui, M. M., On the Genesis and Properties of the Rayleigh Distribution, Communications in Statistics-Theory and Methods, 17 (1988), 7, pp. 2513-2523
  4. Miller, R. G., Sackrowitz, H. B., Lifetime Data: Statistical Models and Methods, John Wiley and Sons, New York, USA, 2002
  5. Howlader, H. A., Hossain, A., On Bayesian Estimation and Prediction from Rayleigh Distribution Based on Type-II Censored Data, Comm. in Statistics-Theory and Methods, 24 (1995), 9, pp. 2249-2259
  6. Kim, C., Han, K., Estimation of the Scale Parameter of the Rayleigh Distribution under General Progressive Censoring, Journal of the Korean Statistical Society, 38 (2009), 3, pp. 239-246
  7. Surles, J. G., Padgett, W. J., Inference for Reliability and Stress-Strength for a Scaled Burr Type X Distribution, Lifetime Data Analysis, 7 (2001), 2, pp. 187-200
  8. Merovci, F., Transmuted Rayleigh Distribution, Austrian Journal of Statistics, 42 (2013), 1, pp. 21-31
  9. Merovci, F., Elbatal, I., Weibull-Rayleigh Distribution: Theory and Applications, Applied Mathematics and Information Sciences, 9 (2015), 5, pp. 1-11
  10. Mudasir, S., et al., Weighted Rayleigh Distribution Revisited Via Informative and Non-Informative Priors, Pakistan Journal of Statistics, 35 (2019), 4, pp. 321-348
  11. Ramadan, A. T., et al., Generalized Power Akshaya Distribution and Its Applications, Open Journal of Modelling and Simulation, 9 (2021), 4, pp. 323-338
  12. Gomaa, R. S., et al., The Unit Alpha-Power Kum-Modified Size-Biased Lehmann Type II Distribution: Theory, Simulation, and Applications, Symmetry, 15 (2023), 6, 1283
  13. Bhat, A. A., et al., The Odd Lindley Power Rayleigh Distribution: Properties, Classical and Bayesian Estimation with Applications, Scientific African, 20 (2023), e01736
  14. Bhat, A. A., Ahmad, S. P., A New Generalization of Rayleigh Distribution: Properties and Applications, Pakistan Journal of Statistics, 36 (2020), 3, pp. 225-250
  15. Anderson, T. W., Darling, D. A., A test of Goodness of Fit, Journal of the American Statistical Association, 49 (1954), 268, pp. 765-769
  16. Macdonald, P. D. M., Comment on An Estimation Procedure for Mixtures of Distributions by Choi and Bulgren, J. Royal Statistical Society, Series B (Statistical Methodology), 33 (1971), 2 , pp. 326-329
  17. Swain, J. J., et al., Least-Squares Estimation of Distribution Functions in Johnson's Translation System, Journal of Statistical Computation and Simulation, 29 (1988), 4, pp. 271-297
  18. Cheng, R. C. H., Amin, N. A. K., Estimating Parameters in Continuous Univariate Distributions with a Shifted Origin, J. Royal Statistical Society, Series B (Statistical Methodology), 45 (1983), 3, pp. 394-403
  19. Ranneby, B., The Maximum Spacing Method, An Estimation Method Related to the Maximum Likelihood Method, Scandinavian Journal of Statistics, 11 (1984), 2, pp. 93-112
  20. Al-Kutubi, H. S., On Comparison Estimation Procedures for Parameter and Survival Function Exponential Distribution Using Simulation, Ph. D. thesis, College of Ibn Al-Hatham, Baghdad University, Baghdad, Iraq, 2005
  21. Legendre, A. M., New Methods for the Determination of Orbits of Comets, Courcier, Paris, France, 1805
  22. Gauss, C. F., Least Squares Method for the Combinations of Observations (Translated by J. Bertrand 1955), Mallet-Bachelier, Paris, France, 1810
  23. Norstrom, J. G., The Use of Precautionary Loss Function in Risk Analysis, IEEE Transactions on Reliability, 45 (1996), 3, pp. 400-403
  24. Calabria, R., Pulcini, G., Bayes 2-Sample Prediction for the Inverse Weibull Distribution, Communications in Statistics-Theory and Methods, 23 (1994), 6, pp. 1811-1824
  25. Badar, M. G., Priest. A. M., Statistical Aspects of Fiber and Bundle Strength in Hybrid Composites Progress in Science and Engineering Composites, Proceedings, Tokyo ICCM-IV, Tokyo, Japan, 1982, pp. 1129-1136
  26. Akarawak, E. E., et al., The Inverted Gompertz-Frechet Distribution with Applications, Sci. African, 21 (2023), 4, e01769
  27. Alsadat, N., et al., Classical and Bayesian Estimation for the Extended Odd Weibull Power Lomax Model with Applications, AIP Advances, 13 (2023), 9, pp. 1-20
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A dual approach to parameter estimation classical vs. Bayesian methods in power Rayleigh modelling

2025 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence