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Bayesian Analysis for the Modified Frechet–Exponential Distribution with Covid-19 Application

Year 2023, Volume: 44 Issue: 3, 602 - 609, 29.09.2023

Neriman Akdam

https://doi.org/10.17776/csj.1320712

Abstract

In this manuscript, the maximum likelihood estimators and Bayes estimators for the parameters of the modified Frechet–exponential distribution. Because the Bayes estimators cannot be obtained in closed forms, the approximate Bayes estimators are computed using the idea of Lindley’s approximation method under squared-error loss function. Then, the approximate Bayes estimates are compared with the maximum likelihood estimates in terms of mean square error and bias values using Monte Carlo simulation. Finally, real data sets belonging to COVID-19 death cases in Europe and China to are used to demonstrate the emprical results belonging to the approximate Bayes estimates, the maximum likelihood estimates.

Keywords

Modified Frechet–Exponential distribution Bayes estimator Lindley’s approximation Monte Carlo simulation Squared-error loss function.

References

  • [1] Nadarajah S., Kotz S., The Exponentiated Frechet Distribution, Interstat Electronic Journal, 14 (2003) 01-07.
  • [2] da Silva R. V., de Andrade T. A., Maciel D. B., Campos R. P., Cordeiro G. M., A New Lifetime Model: The Gamma Extended Frechet Distribution, Journal of Statistical Theory and Applications, 12(1) (2013) 39-54.
  • [3] Krishna E., Jose K. K., Alice T., Ristic M. M., The Marshall-Olkin Frechet Distribution, Communications in Statistics-Theory and Methods, 42(22) (2013) 4091-4107.
  • [4] Afify Z., Yousof H. M., Cordeiro G. M., Ortega E. M. M., Nofal Z. M., The Weibull Frechet Distribution and Its Applications, Journal of Applied Statistics, 43(14) (2016) 2608- 2626.
  • [5] Ali M., Khalil A., Mashwani W. K., Alrajhi S., Al-Marzouki S., Shah K., A Novel Fréchet-Type Probability Distribution: its properties and applications, Mathematical Problems in Engineering, (2022) 1-14.
  • [6] Alsadat N., Ahmad A., Jallal M., Gemeay A. M., Meraou M. A., Hussam E., Hossain M. M., The Novel Kumaraswamy Power Frechet Distribution with Data Analysis Related to Diverse Scientific Areas, Alexandria Engineering Journal, 70 (2023) 651-664.
  • [7] Farhat A. T., Ramadan D. A., El-Desouky B.S., Statistical Inference of Modified Frechet–Exponential Distribution with Applications to Real-Life Data, Appl. Math. Inf. Sci., 17(1) (2023) 109-124.
  • [8] Touw A. E., Bayesian Estimation of Mixed Weibull Distributions, Reliability Engineering & System Safety, 94(2) (2009) 463-47.
  • [9] Dey S., Bayesian Estimation of the Parameter and Reliability Function of an Inverse Rayleigh Distribution, Malaysian Journal of Mathematical Sci., 6(1) (2012) 113-124.
  • [10] Abbas K., Yincai T., Comparison of Estimation Methods for Frechet Distribution with Known Shape, Caspian Journal of Applied Sciences Research, 1(10) (2012) 58-64.
  • [11] Kundu D., Gupta A.K., Bayes Estimation for the Marshall–Olkin Bivariate Weibull Distribution, Computational Statistics and Data Analysis, 57(2013) 271–281.
  • [12] Dey S., Dey. T., Kundu D., Two-Parameter Rayleigh Distribution: Different Methods of Estimation, American Journal of Mathematical and Management Sci., 33(1) (2014) 55-74.
  • [13] Abbas K., Abbasi N. Y., Ali A., Khan S. A., Manzoor S., Khalil A., Khalil U., Khan M. D., Hussain Z., Altaf M., Bayesian Analysis of Three-Parameter Frechet Distribution with Medical Applications, Hindawi Computational and Mathematical Methods in Medicine, 9089856 (2019) 8.
  • [14] Ramos P. L., Louzada F., Ramos E., The Fréchet Distribution: Estimation and Application - An Overview, Journal of Statistics & Management Systems, 23(3) (2020) 549–578.
  • [15] Ahmad H. A. H., Almetwally E. M., Marshall-Olkin Generalized Pareto Distribution: Bayesian and Non Bayesian Estimation, Pak. J. Stat. Oper. Res., 16 (1) (2020) 21-33.
  • [16] Almongy H. M., Almetwally E.M., Aljohani H.M., Alghamdi A. S., Hafez E. H., A New Extended Rayleigh Distribution with Applications of COVID-19 Data, Results in Physics, 23 (2021) 104012.
  • [17] EL-Sagheer R. M., Shokr E. M., Mahmoud M. A. W., El-Desouky B.,Inferences for Weibull Fréchet Distribution Using a Bayesian and Non-Bayesian Methods on Gastric Cancer Survival Times, Hindawi Computational and Mathematical Methods in Medicine, 9965856 (2021) 12.
  • [18] Lindley D.V., Approximate Bayesian Methods, Trabajos de Estadistica, 31 (1980) 223-237.
  • [19] Ahmad K.E., Jaheen Z.F., Approximate Bayes Estimators Applied to the Inverse Gaussian Lifetime Model, Computers Math. Applic., 12 (1995) 39-47.
  • [20] Kundu D., Gupta R.D., Generalized Exponential Distribution: Bayesian Estimations, Computational Statistics & Data Analysis, 52 (2008) 1873-1883.
  • [21] Preda V., Panaitescu E., Constantinescu A., Bayes Estimators of Modified-Weibull Distribution Parameters using Lindley's Approximation, Wseas Transactions on Mathematics, 7 ( 2010) 539-549.
  • [22] Singh S.K., Singh U., Yadav A.S., Bayesian Estimation of Marshall–Olkin Extended Exponential Parameters under Various Approximation Techniques, Hacettepe Journal of Mathematics and Statistics, 43(2) (2014) 347 – 360.
  • [23] Akdam N., Kınacı İ., Saraçoğlu B., Statistical Inference of Stress-Strength Reliability for the Exponential Power (EP) Distribution based on Progressive Type-II Censored Samples, Hacettepe Journal of Mathematics and Statistics, 46 (2017) 239-253.
  • [24] Çiftci F., Saraçoğlu B., Akdam N., Akdoğan Y., Estimation of Stress-Strength Reliability for Generalized Gompertz Distribution under Progressive Type-II Censoring, Hacettepe Journal of Mathematics and Statistics, (2023).
  • [25] Akdam N., Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine, Symmetry, 15(9) (2023) 1754.
  • [26] Sindhu T. S., Shafiq A., Al-Mdallal Q.M, Exponentiated Transformation of Gumbel Type-II Distribution for Modeling COVID-19 Data, Alexandria Engineering Journal, 60(1) (2021) 671-689.

Year 2023, Volume: 44 Issue: 3, 602 - 609, 29.09.2023

Neriman Akdam

https://doi.org/10.17776/csj.1320712

Abstract

References

  • [1] Nadarajah S., Kotz S., The Exponentiated Frechet Distribution, Interstat Electronic Journal, 14 (2003) 01-07.
  • [2] da Silva R. V., de Andrade T. A., Maciel D. B., Campos R. P., Cordeiro G. M., A New Lifetime Model: The Gamma Extended Frechet Distribution, Journal of Statistical Theory and Applications, 12(1) (2013) 39-54.
  • [3] Krishna E., Jose K. K., Alice T., Ristic M. M., The Marshall-Olkin Frechet Distribution, Communications in Statistics-Theory and Methods, 42(22) (2013) 4091-4107.
  • [4] Afify Z., Yousof H. M., Cordeiro G. M., Ortega E. M. M., Nofal Z. M., The Weibull Frechet Distribution and Its Applications, Journal of Applied Statistics, 43(14) (2016) 2608- 2626.
  • [5] Ali M., Khalil A., Mashwani W. K., Alrajhi S., Al-Marzouki S., Shah K., A Novel Fréchet-Type Probability Distribution: its properties and applications, Mathematical Problems in Engineering, (2022) 1-14.
  • [6] Alsadat N., Ahmad A., Jallal M., Gemeay A. M., Meraou M. A., Hussam E., Hossain M. M., The Novel Kumaraswamy Power Frechet Distribution with Data Analysis Related to Diverse Scientific Areas, Alexandria Engineering Journal, 70 (2023) 651-664.
  • [7] Farhat A. T., Ramadan D. A., El-Desouky B.S., Statistical Inference of Modified Frechet–Exponential Distribution with Applications to Real-Life Data, Appl. Math. Inf. Sci., 17(1) (2023) 109-124.
  • [8] Touw A. E., Bayesian Estimation of Mixed Weibull Distributions, Reliability Engineering & System Safety, 94(2) (2009) 463-47.
  • [9] Dey S., Bayesian Estimation of the Parameter and Reliability Function of an Inverse Rayleigh Distribution, Malaysian Journal of Mathematical Sci., 6(1) (2012) 113-124.
  • [10] Abbas K., Yincai T., Comparison of Estimation Methods for Frechet Distribution with Known Shape, Caspian Journal of Applied Sciences Research, 1(10) (2012) 58-64.
  • [11] Kundu D., Gupta A.K., Bayes Estimation for the Marshall–Olkin Bivariate Weibull Distribution, Computational Statistics and Data Analysis, 57(2013) 271–281.
  • [12] Dey S., Dey. T., Kundu D., Two-Parameter Rayleigh Distribution: Different Methods of Estimation, American Journal of Mathematical and Management Sci., 33(1) (2014) 55-74.
  • [13] Abbas K., Abbasi N. Y., Ali A., Khan S. A., Manzoor S., Khalil A., Khalil U., Khan M. D., Hussain Z., Altaf M., Bayesian Analysis of Three-Parameter Frechet Distribution with Medical Applications, Hindawi Computational and Mathematical Methods in Medicine, 9089856 (2019) 8.
  • [14] Ramos P. L., Louzada F., Ramos E., The Fréchet Distribution: Estimation and Application - An Overview, Journal of Statistics & Management Systems, 23(3) (2020) 549–578.
  • [15] Ahmad H. A. H., Almetwally E. M., Marshall-Olkin Generalized Pareto Distribution: Bayesian and Non Bayesian Estimation, Pak. J. Stat. Oper. Res., 16 (1) (2020) 21-33.
  • [16] Almongy H. M., Almetwally E.M., Aljohani H.M., Alghamdi A. S., Hafez E. H., A New Extended Rayleigh Distribution with Applications of COVID-19 Data, Results in Physics, 23 (2021) 104012.
  • [17] EL-Sagheer R. M., Shokr E. M., Mahmoud M. A. W., El-Desouky B.,Inferences for Weibull Fréchet Distribution Using a Bayesian and Non-Bayesian Methods on Gastric Cancer Survival Times, Hindawi Computational and Mathematical Methods in Medicine, 9965856 (2021) 12.
  • [18] Lindley D.V., Approximate Bayesian Methods, Trabajos de Estadistica, 31 (1980) 223-237.
  • [19] Ahmad K.E., Jaheen Z.F., Approximate Bayes Estimators Applied to the Inverse Gaussian Lifetime Model, Computers Math. Applic., 12 (1995) 39-47.
  • [20] Kundu D., Gupta R.D., Generalized Exponential Distribution: Bayesian Estimations, Computational Statistics & Data Analysis, 52 (2008) 1873-1883.
  • [21] Preda V., Panaitescu E., Constantinescu A., Bayes Estimators of Modified-Weibull Distribution Parameters using Lindley's Approximation, Wseas Transactions on Mathematics, 7 ( 2010) 539-549.
  • [22] Singh S.K., Singh U., Yadav A.S., Bayesian Estimation of Marshall–Olkin Extended Exponential Parameters under Various Approximation Techniques, Hacettepe Journal of Mathematics and Statistics, 43(2) (2014) 347 – 360.
  • [23] Akdam N., Kınacı İ., Saraçoğlu B., Statistical Inference of Stress-Strength Reliability for the Exponential Power (EP) Distribution based on Progressive Type-II Censored Samples, Hacettepe Journal of Mathematics and Statistics, 46 (2017) 239-253.
  • [24] Çiftci F., Saraçoğlu B., Akdam N., Akdoğan Y., Estimation of Stress-Strength Reliability for Generalized Gompertz Distribution under Progressive Type-II Censoring, Hacettepe Journal of Mathematics and Statistics, (2023).
  • [25] Akdam N., Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine, Symmetry, 15(9) (2023) 1754.
  • [26] Sindhu T. S., Shafiq A., Al-Mdallal Q.M, Exponentiated Transformation of Gumbel Type-II Distribution for Modeling COVID-19 Data, Alexandria Engineering Journal, 60(1) (2021) 671-689.
There are 26 citations in total.

Details

Primary Language English
Subjects Biostatistics, Statistical Analysis, Statistical Theory, Probability Theory
Journal Section Natural Sciences
Authors

Neriman Akdam 0000-0002-0204-6657

Publication Date September 29, 2023
Submission Date June 28, 2023
Acceptance Date September 12, 2023
Published in Issue Year 2023Volume: 44 Issue: 3

Cite

APA Akdam, N. (2023). Bayesian Analysis for the Modified Frechet–Exponential Distribution with Covid-19 Application. Cumhuriyet Science Journal, 44(3), 602-609. https://doi.org/10.17776/csj.1320712
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