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Year 2023, Volume: 52 Issue: 2, 499 - 511, 31.03.2023

Caner Tanış Buğra Saraçoğlu Akbar Asgharzadeh Mousa Abdi

https://doi.org/10.15672/hujms.847176

Abstract

References

  • [1] M. Ahsanullah and V.B. Nevzorov, Records via Probability Theory, Atlantis Press, 2015.
  • [2] F.G. Akgul, B. Senoglu and S. Acıtas, Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data, Hacet. J. Math. Stat. 47 (5), 1404–1416, 2018.
  • [3] A. Asgharzadeh, R. Valiollahi and M.Z. Raqab, Estimation of $Pr(Y<X)$ for the two-parameter generalized exponential records, Commun. Stat. - Simul. Comput. 46 (1), 379-394, 2017.
  • [4] A. Asgharzadeh, M. Abdi and C. Kuş, Interval estimation for the two-parameter pareto distribution based on record values, Selcuk J. Appl. Math. 149-161, 2011.
  • [5] A. Asgharzadeh and A. Fallah, Estimation and prediction for exponentiated family of distributions based on records, Commun. Stat. - Theory Methods 40 (1), 68-83, 2010.
  • [6] A. Asgharzadeh, On Bayesian estimation from exponential distribution based on records, J Korean Stat Soc. 38 (2), 125-130, 2009.
  • [7] N. Akdam, I. Kınacı and B. Saracoglu, Statistical inference of stress-strength reliability for the exponential power distribution based on progressive type-II censored samples, Hacet. J. Math. Stat. 46 (2), 239-253, 2017.
  • [8] B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, Records, John Wiley and Sons, New York, 1998.
  • [9] A. Baklizi, Interval estimation of the stress-strength reliability in the two-parameter exponential distribution based on records, J Stat Comput Simul. 84 (12), 2670-2679, 2014.
  • [10] A. Baklizi, Estimation of $Pr(X<Y)$ using record values in the one and two parameter exponential distributions, Commun. Stat. - Theory Methods 37 (5), 692-698, 2008.
  • [11] G.D.C. Barriga, F. Louzada and V.G. Cancho, The complementary exponential power lifetime model, Comput Stat Data Anal 55 (3) 250-1259, 2011.
  • [12] K.N. Chandler, The distribution and frequency of record values, J. Roy. Stat. Soc. B. 14 (2), 220-228, 1952.
  • [13] Z. Chen, Statistical inference about the shape parameter of the exponential power distribution, Stat Pap 40, 459-468, 1999.
  • [14] M.J. Crowder, Tests for a Family of Survival Models Based on Extremes, Recent Advances in Reliability Theory, Boston, MA: Birkhauser, 307-321, 2000.
  • [15] D. Demiray and F. Kızılaslan, Stressstrength reliability estimation of a consecutive k-out-of-n system based on proportional hazard rate family, J Stat Comput Simul. 99 (1), 159-190, 2022.
  • [16] B. Efron, The Jackknife, The Bootstrap and Other Resampling Plans, Philadelphia: Society for industrial and applied mathematics, 1982.
  • [17] G. Gencer and B. Saracoglu, Comparison of approximate Bayes estimators under different loss functions for parameters of Odd Weibull distribution, Journal of Selcuk University Natural and Applied Science, 5 (1), 18-32, 2016.
  • [18] H.A. Howloader and A.M. Hossain, Bayesian survival estimation of Pareto distribution of second kind based on failure-censored data, Comput Stat Data Anal 38 , 301-314, 2002.
  • [19] M. Jovanović, B. Milošević and M. Obradović, Estimation of stress-strength probability in a multicomponent model based on geometric distribution, Hacet. J. Math. Stat. 49 (4), 1515–1532, 2020.
  • [20] İ. Kınacı, S.J. Wu and C. Kus, Confidence intervals and regions for the generalized inverted exponential distribution based on Progressively Censored and upper records data, Revstat Stat. J. 17 (4), 429-448, 2019.
  • [21] İ. Kınacı, K. Karakaya, Y. Akdoğan amd C. Ku, Kesikli Chen Dağılımı için Bayes tahmini, Selcuk Üniversitesi Fen Fakültesi Fen Dergisi, 42 (2), 144-148, 2016.
  • [22] S. Kotz, Y. Lumelskii and M. Pensky, Stress-Strength Model and its Generalizations, World Scientific, River Edge, NJ, USA, 2003.
  • [23] F. Kızılaslan and M. Nadar, Statistical inference of $ P (X< Y) $ for the Burr Type XII distribution based on records, Hacet. J. Math. Stat. 46 (4), 713-742, 2017.
  • [24] J.F. Lawless, Statistical Models and Methods for Lifetime Data, 2nd Edition, Hoboken, NJ: John Wiley, 2003.
  • [25] L.M. Leemis, Lifetime distribution identities, IEEE Trans Reliab 35, 170-174, 1986.
  • [26] D.J. Luckett, Statistical Inference Based on Upper Record Values, College of William and Mary Undergraduate Honors Theses, Paper 577, 2013.
  • [27] M.A. Mousa and Z.F. Jaheen, Statistical inference for the Burr model based on progressively censored data, Comput. Math. with Appl. 43 (10), 1441-1449, 2002.
  • [28] M. Nadar and F. Kızılaslan, Classical and Bayesian estimation of P(X < Y ) using upper record values from Kumaraswamy’s distribution, Stat Pap 55 (3), 751-783, 2014.
  • [29] M. Obradović, M. Jovanović, B. Milosević and V. Jevremović, Estimation of P(X < Y ) for geometric-Poisson model, Hacet. J. Math. Stat. 44 (4), 949–964, 2015.
  • [30] M.B. Rajarshi and S. Rajarshi, Bathtub distribution: A review, Commun. Stat. - Theory Methods 17, 2597-2621, 1988.
  • [31] R.M. Smith and L.J. Bain, An exponential power life-testing distribution, Commun. Stat. 4 (5), 469-481, 1975.
  • [32] C. Tanış, B. Saraçoğlu, C. Kus and A. Pekgor, Transmuted complementary exponential power distribution: properties and applications, Cumhuriyet Science Journal 41 (2), 419-432, 2020.
  • [33] C. Tanış, M. Cokbarlı and B. Saraçoğlu, Approximate Bayes estimation for Log- Dagum distribution, Cumhuriyet Science Journal 40 (2), 477-486, 2019.
  • [34] C. Tanış and B. Saraçoğlu, Comparisons of six different estimation methods for log- Kumaraswamy distribution, Therm. Sci. 23 (6), 1839-1847, 2019.
  • [35] C. Tanış and B. Saraçoğlu, Statistical inference based on upper record values for the transmuted Weibull distribution, Int. J. Math. Stat. Invent. 5 (9), 18-23, 2017.
  • [36] B. Tarvirdizade and G.H. Kazemzadeh, Inference on Pr(X > Y ) Based on record values from the Burr Type X distribution, Hacet. J. Math. Stat. 45 (1), 267-278, 2016.
  • [37] B. Tarvirdizade and M. Ahmadpour, Estimation of the stressstrength reliability for the two-parameter bathtub-shaped lifetime distribution based on upper record values, Stat. Methodol. 31, 58-72, 2016.
  • [38] L. Tierney and J.B. Kadane, Accurate approximations for posterior moments and marginal densities, J Am Stat Assoc. 81 (393), 82-86, 1986.
  • [39] Z. Vidović, On MLEs of the parameters of a modified Weibull distribution based on record values, J. Appl. Stat. 46 (4), 715-724, 2019.
  • [40] T. Zhi, Maximum Likelihood Estimation of Parameters in Exponential Power Distribution with Upper Record Values, Florida International University FIU Digital Commons, Theses, 2017.

Estimation of $Pr(X<Y)$ for exponential power records

Year 2023, Volume: 52 Issue: 2, 499 - 511, 31.03.2023

Caner Tanış Buğra Saraçoğlu Akbar Asgharzadeh Mousa Abdi

https://doi.org/10.15672/hujms.847176

Abstract

In this study, we tackle the problem of estimation of stress-strength reliability $R = P r(X < Y )$ based on upper record values for exponential power distribution. We use the maximum likelihood and Bayes methods to estimate R. The Tierney-Kadane approximation is used to compute the Bayes estimation of R since the Bayes estimator can not be obtained analytically. We also derive asymptotic confidence interval based on the asymptotic distribution of the maximum likelihood estimator of R. We consider a Monte Carlo simulation study in order to compare the performances of the maximum likelihood estimators and Bayes estimators according to mean square error criteria. Finally, a real data application is presented.

Keywords

Upper record values maximum likelihood estimator Bayesian estimation asymptotic confidence interval Tierney-Kadane approximation

References

  • [1] M. Ahsanullah and V.B. Nevzorov, Records via Probability Theory, Atlantis Press, 2015.
  • [2] F.G. Akgul, B. Senoglu and S. Acıtas, Interval estimation of the system reliability for Weibull distribution based on ranked set sampling data, Hacet. J. Math. Stat. 47 (5), 1404–1416, 2018.
  • [3] A. Asgharzadeh, R. Valiollahi and M.Z. Raqab, Estimation of $Pr(Y<X)$ for the two-parameter generalized exponential records, Commun. Stat. - Simul. Comput. 46 (1), 379-394, 2017.
  • [4] A. Asgharzadeh, M. Abdi and C. Kuş, Interval estimation for the two-parameter pareto distribution based on record values, Selcuk J. Appl. Math. 149-161, 2011.
  • [5] A. Asgharzadeh and A. Fallah, Estimation and prediction for exponentiated family of distributions based on records, Commun. Stat. - Theory Methods 40 (1), 68-83, 2010.
  • [6] A. Asgharzadeh, On Bayesian estimation from exponential distribution based on records, J Korean Stat Soc. 38 (2), 125-130, 2009.
  • [7] N. Akdam, I. Kınacı and B. Saracoglu, Statistical inference of stress-strength reliability for the exponential power distribution based on progressive type-II censored samples, Hacet. J. Math. Stat. 46 (2), 239-253, 2017.
  • [8] B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, Records, John Wiley and Sons, New York, 1998.
  • [9] A. Baklizi, Interval estimation of the stress-strength reliability in the two-parameter exponential distribution based on records, J Stat Comput Simul. 84 (12), 2670-2679, 2014.
  • [10] A. Baklizi, Estimation of $Pr(X<Y)$ using record values in the one and two parameter exponential distributions, Commun. Stat. - Theory Methods 37 (5), 692-698, 2008.
  • [11] G.D.C. Barriga, F. Louzada and V.G. Cancho, The complementary exponential power lifetime model, Comput Stat Data Anal 55 (3) 250-1259, 2011.
  • [12] K.N. Chandler, The distribution and frequency of record values, J. Roy. Stat. Soc. B. 14 (2), 220-228, 1952.
  • [13] Z. Chen, Statistical inference about the shape parameter of the exponential power distribution, Stat Pap 40, 459-468, 1999.
  • [14] M.J. Crowder, Tests for a Family of Survival Models Based on Extremes, Recent Advances in Reliability Theory, Boston, MA: Birkhauser, 307-321, 2000.
  • [15] D. Demiray and F. Kızılaslan, Stressstrength reliability estimation of a consecutive k-out-of-n system based on proportional hazard rate family, J Stat Comput Simul. 99 (1), 159-190, 2022.
  • [16] B. Efron, The Jackknife, The Bootstrap and Other Resampling Plans, Philadelphia: Society for industrial and applied mathematics, 1982.
  • [17] G. Gencer and B. Saracoglu, Comparison of approximate Bayes estimators under different loss functions for parameters of Odd Weibull distribution, Journal of Selcuk University Natural and Applied Science, 5 (1), 18-32, 2016.
  • [18] H.A. Howloader and A.M. Hossain, Bayesian survival estimation of Pareto distribution of second kind based on failure-censored data, Comput Stat Data Anal 38 , 301-314, 2002.
  • [19] M. Jovanović, B. Milošević and M. Obradović, Estimation of stress-strength probability in a multicomponent model based on geometric distribution, Hacet. J. Math. Stat. 49 (4), 1515–1532, 2020.
  • [20] İ. Kınacı, S.J. Wu and C. Kus, Confidence intervals and regions for the generalized inverted exponential distribution based on Progressively Censored and upper records data, Revstat Stat. J. 17 (4), 429-448, 2019.
  • [21] İ. Kınacı, K. Karakaya, Y. Akdoğan amd C. Ku, Kesikli Chen Dağılımı için Bayes tahmini, Selcuk Üniversitesi Fen Fakültesi Fen Dergisi, 42 (2), 144-148, 2016.
  • [22] S. Kotz, Y. Lumelskii and M. Pensky, Stress-Strength Model and its Generalizations, World Scientific, River Edge, NJ, USA, 2003.
  • [23] F. Kızılaslan and M. Nadar, Statistical inference of $ P (X< Y) $ for the Burr Type XII distribution based on records, Hacet. J. Math. Stat. 46 (4), 713-742, 2017.
  • [24] J.F. Lawless, Statistical Models and Methods for Lifetime Data, 2nd Edition, Hoboken, NJ: John Wiley, 2003.
  • [25] L.M. Leemis, Lifetime distribution identities, IEEE Trans Reliab 35, 170-174, 1986.
  • [26] D.J. Luckett, Statistical Inference Based on Upper Record Values, College of William and Mary Undergraduate Honors Theses, Paper 577, 2013.
  • [27] M.A. Mousa and Z.F. Jaheen, Statistical inference for the Burr model based on progressively censored data, Comput. Math. with Appl. 43 (10), 1441-1449, 2002.
  • [28] M. Nadar and F. Kızılaslan, Classical and Bayesian estimation of P(X < Y ) using upper record values from Kumaraswamy’s distribution, Stat Pap 55 (3), 751-783, 2014.
  • [29] M. Obradović, M. Jovanović, B. Milosević and V. Jevremović, Estimation of P(X < Y ) for geometric-Poisson model, Hacet. J. Math. Stat. 44 (4), 949–964, 2015.
  • [30] M.B. Rajarshi and S. Rajarshi, Bathtub distribution: A review, Commun. Stat. - Theory Methods 17, 2597-2621, 1988.
  • [31] R.M. Smith and L.J. Bain, An exponential power life-testing distribution, Commun. Stat. 4 (5), 469-481, 1975.
  • [32] C. Tanış, B. Saraçoğlu, C. Kus and A. Pekgor, Transmuted complementary exponential power distribution: properties and applications, Cumhuriyet Science Journal 41 (2), 419-432, 2020.
  • [33] C. Tanış, M. Cokbarlı and B. Saraçoğlu, Approximate Bayes estimation for Log- Dagum distribution, Cumhuriyet Science Journal 40 (2), 477-486, 2019.
  • [34] C. Tanış and B. Saraçoğlu, Comparisons of six different estimation methods for log- Kumaraswamy distribution, Therm. Sci. 23 (6), 1839-1847, 2019.
  • [35] C. Tanış and B. Saraçoğlu, Statistical inference based on upper record values for the transmuted Weibull distribution, Int. J. Math. Stat. Invent. 5 (9), 18-23, 2017.
  • [36] B. Tarvirdizade and G.H. Kazemzadeh, Inference on Pr(X > Y ) Based on record values from the Burr Type X distribution, Hacet. J. Math. Stat. 45 (1), 267-278, 2016.
  • [37] B. Tarvirdizade and M. Ahmadpour, Estimation of the stressstrength reliability for the two-parameter bathtub-shaped lifetime distribution based on upper record values, Stat. Methodol. 31, 58-72, 2016.
  • [38] L. Tierney and J.B. Kadane, Accurate approximations for posterior moments and marginal densities, J Am Stat Assoc. 81 (393), 82-86, 1986.
  • [39] Z. Vidović, On MLEs of the parameters of a modified Weibull distribution based on record values, J. Appl. Stat. 46 (4), 715-724, 2019.
  • [40] T. Zhi, Maximum Likelihood Estimation of Parameters in Exponential Power Distribution with Upper Record Values, Florida International University FIU Digital Commons, Theses, 2017.
There are 40 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Caner Tanış 0000-0003-0090-1661

Buğra Saraçoğlu 0000-0003-1713-2862

Akbar Asgharzadeh 0000-0001-6714-4533

Mousa Abdi This is me 0000-0002-0446-9880

Publication Date March 31, 2023
Published in Issue Year 2023 Volume: 52 Issue: 2

Cite

APA Tanış, C., Saraçoğlu, B., Asgharzadeh, A., Abdi, M. (2023). Estimation of $Pr(X
AMA Tanış C, Saraçoğlu B, Asgharzadeh A, Abdi M. Estimation of $Pr(X
Chicago Tanış, Caner, Buğra Saraçoğlu, Akbar Asgharzadeh, and Mousa Abdi. “Estimation of $Pr(X
EndNote Tanış C, Saraçoğlu B, Asgharzadeh A, Abdi M (March 1, 2023) Estimation of $Pr(X
IEEE C. Tanış, B. Saraçoğlu, A. Asgharzadeh, and M. Abdi, “Estimation of $Pr(XHacettepe Journal of Mathematics and Statistics, vol. 52, no. 2, pp. 499–511, 2023, doi: 10.15672/hujms.847176.
ISNAD Tanış, Caner et al. “Estimation of $Pr(XHacettepe Journal of Mathematics and Statistics 52/2 (March 2023), 499-511. https://doi.org/10.15672/hujms.847176.
JAMA Tanış C, Saraçoğlu B, Asgharzadeh A, Abdi M. Estimation of $Pr(XHacettepe Journal of Mathematics and Statistics. 2023;52:499–511..
MLA Tanış, Caner et al. “Estimation of $Pr(X
Vancouver Tanış C, Saraçoğlu B, Asgharzadeh A, Abdi M. Estimation of $Pr(X

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