THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Ahmed Jumanah Darwish

STATISTICAL PROPERTIES AND APPLICATIONS FOR EXPONENTIATED EXPONENTIAL RAYLEIGH DISTRIBUTION

ABSTRACT
Modelling in lifetime phenomena is a significant issue in many scientific areas. Sometimes many standard models lack superiority in modelling data set. Designing a new form of probability distribution by using different techniques has received a widely attention in statistical theory in the recent years. In this paper, we formulated exponentiated exponential Rayleigh (EER) distribution. We discussed the reliability and hazard rate functions of the EER distribution and computed the quantile, median, skewness and kurtosis. Moreover, the correlations between the parameters and the median, skewness, and kurtosis are investigated. Bayesian and non-Bayesian approaches are adopted to estimate the unknown parameters of EER distribution. In Bayesian approach, we are used Markov Chen Monte Carlo (MCMC) method to obtain the approximate Bayes point estimate. The proposed distribution is used to analyze, light-emitting diodes data, strength of glass fibers data and Wheaton River data. The estimation results of the EER distribution are compared with exponential Rayleigh, Rayleigh, and exponential distributions.
KEYWORDS
exponentiated and T-X family of distributions, Rayleigh distribution, MCMC technique, Bayes estimation, Maximum likelihood estimation
PAPER SUBMITTED: 2024-07-24
PAPER REVISED: 2024-10-10
PAPER ACCEPTED: 2024-10-25
PUBLISHED ONLINE: 2025-01-25
DOI REFERENCE: https://doi.org/10.2298/TSCI2406895D
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2024, VOLUME 28, ISSUE Issue 6, PAGES [4895 - 4906]
REFERENCES
  1. Gupta, R. C., Modelling Failure Time Data by Lehman Alternatives, Communications in Statistics-Theory and Methods, 2 (1998), 7, pp. 887-904
  2. Gupta, R. D., Kundu, D., Exponentiated Exponential Family: An Alternative to Gamma and Weibull Distributions, Biometrical Journal: Journal of Mathematical Methods in Biosciences, 43 (2001), 1, pp. 117-130
  3. Nadarajah, S., Kotz, S., The Exponentiated type Distributions, Acta Applicandae Mathenatica, 92 (2006), Sept., pp. 97-111
  4. Sarhan, A. M., Apaloo, J., Exponentiated Modified Weibull Extension Distibution, Reliability Engineering and System Safety, 112 (2013), Apr., pp. 137-144
  5. Alzaatreh, A., et al., A New Method for Generating Families of Continuous Distributions, Metron, 71 (2013), Apr., pp. 63-79
  6. Nofal, Z. M., et al., The Generalized Transmuted-G Family of Distributions, Communications in Statistics-Theory and Methods, 46 (2016), 8, pp. 4119-4136
  7. Afify, Z., et al., The Kumaraswamy Transmuted-G Family of Distributions: Properties and Applications, Journal of Data Science, 14 (2016), 2, pp. 245-270
  8. Afify, A., et al., The Beta Transmute-H Family for Lifetime Data, Statistics and its Interface, 10 (2017), 3, pp. 505-520
  9. Jayakumar, K., Girish Babu, M., T-Transmuted X Family of Distributions, Statistica, Anno LXXVII, 77 (2017), 3, pp. 251-276
  10. Rayleigh, J., The Results of a Large Number of Vibrations of the Same Pitch and of Arbitrary Phase, Philosophical Magazine, 10 (1980), 60, pp. 73-78
  11. Raqab, M. Z. Wilson, W. M., Bayesian Prediction of the Total Time on Test Using Doubly Censored Rayleigh Data, A Journal of Statistical Computation and Simulation, 72 (2022), 10, pp. 781-789
  12. Ajami, M., Jahanshahi, S. M. A., Parameter Estimation in Weighted Rayleigh Distribution, Journal of Modern Applied Statistical Methods, 16 (2017), 2, pp. 256-276
  13. Moore, D. F., Applied Survival Analysis Using R, Springer, Cham, Switzerland, 2016
  14. Modarres, M., et al., Reliability Engineering and Risk Analysis: A Practical Guide, 3rd ed., Taylor and Francis Group, London, UK, 2017
  15. Miller, J. R., Survival Analysis, 2nd ed., John Wiley and Sons, New York, USA, 2011
  16. Gilchrist, W., Statistical Modelling with Quantile Functions, Chapman and Hall, CRC Press, New York, UDA, 2000
  17. Kenney, J. F., Keeping, E. S., Mathematics of Statistics, 3rd Edition, Princeton, N. J., USA, 1962
  18. Moors, J., A Quantile Alternative for Kurtosis, Journal of the Royal Statistical Society: Series D, (The Statistician), 37 (1988), 1, pp. 25-32
  19. Albassam, M., et al., Weibull Distribution under Inderminacy with Applications, AIMS Mathematics, 8 (2023), 5, pp. 10745-10757
  20. Choulakian, V., Stephens, M. A., Goodness-of-Fit Tests for the Generalized Pareto Distribution, Technometrics, 43 (2011), 4, pp. 478-484
  21. Smith, R. L., Naylor, J. C., A Comparison of Maximum Likelihood and Bayesian Estimators for Three-Parameter Weibull Distribution, Journal of the Royal Statistical Society: Series C (Applied Statistics), 36 (1987), 3, pp. 358-369
PDF VERSION [DOWNLOAD]
Statistical properties and applications for exponentiated exponential Rayleigh distribution

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