Yıl 2023,
Cilt: 52 Sayı: 2, 499 - 511, 31.03.2023
Caner Tanış
,
Buğra Saraçoğlu
,
Akbar Asgharzadeh
,
Mousa Abdi
Kaynakça
- [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
Yıl 2023,
Cilt: 52 Sayı: 2, 499 - 511, 31.03.2023
Caner Tanış
,
Buğra Saraçoğlu
,
Akbar Asgharzadeh
,
Mousa Abdi
Öz
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.
Kaynakça
- [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.