Estimation of P(X > Y) for the power Lindley distribution based on progressively type II right censored samples

References

• Al-Mutairi DK, Ghitany ME, Gupta RC. Estimation of reliability in a series system with random sample size. Comput Stat Data Anal. 2011;55:964–972. doi: 10.1016/j.csda.2010.07.027
   Web of Science ®Google Scholar
• Al-Mutairi DK, Ghitany ME, Kundu D. Inferences on stress-strength reliability from Lindley distributions. Commun Stat - Theory Methods. 2013;42:1443–1463. doi: 10.1080/03610926.2011.563011
   Web of Science ®Google Scholar
• Gupta RC, Ghitany ME, Al-Mutairi DK. Estimation of reliability in a parallel system with random sample size. Math Comput Simul. 2012;83:44–55. doi: 10.1016/j.matcom.2012.06.017
   Web of Science ®Google Scholar
• Asgharzadeh A, Valiollahi R, Raqab MZ. Estimation of the stress-strength reliability for the generalized logistic distribution. Stat Methodol. 2013;15:73–94. doi: 10.1016/j.stamet.2013.05.002
   Web of Science ®Google Scholar
• Ghitany ME, Al-Mutairi DK, Aboukhamseen SM. Estimation of the reliability of a stress-strength system from power Lindley distributions. Commun Stat - Simul Comput. 2015;44:118–136. doi: 10.1080/03610918.2013.767910
   Web of Science ®Google Scholar
• Shahriyari S, MirMostafaee SMTK, Ormoz E, et al. Estimation of the reliability parameter for the Poisson-Lomax distribution; 2019, Submitted.
   Google Scholar
• Balakrishnan N, Aggarwala R. Progressive censoring: theory, methods, and applications. Boston: Birkhäuser; 2000.
   Google Scholar
• Dey S, Singh S, Tripathi YM, et al. Estimation and prediction for a progressively censored generalized inverted exponential distribution. Stat Methodol. 2016;32:185–202. doi: 10.1016/j.stamet.2016.05.007
   Google Scholar
• Asgharzadeh A, Valiollahi R, Raqab MZ. Stress-strength reliability of Weibull distribution based on progressively censored samples. SORT. 2011;35:103–124.
   Web of Science ®Google Scholar
• Saraçolu B, Kinaci I, Kundu D. On estimation of R=P(Y<X) for exponential distribution under progressive type-II censoring. J Stat Comput Simul. 2012;82:729–744. doi: 10.1080/00949655.2010.551772
   Web of Science ®Google Scholar
• Valiollahi R, Asgharzadeh A, Raqab MZ. Estimation of P(Y<X) for Weibull distribution under progressive type-II censoring. Commun Stat - Theory Methods. 2013;42:4476–4498. doi: 10.1080/03610926.2011.650265
   Web of Science ®Google Scholar
• Rezaei S, Noughabi RA, Nadarajah S. Estimation of stress-strength reliability for the generalized Pareto distribution based on progressively censored samples. Ann Data Sci. 2015;2:83–101. doi: 10.1007/s40745-015-0033-0
   Google Scholar
• Akdam N, Kinaci I, Saraçolu B. Statistical inference of stress-strength reliability for the exponential power (EP) distribution based on progressive type-II censored samples. Hacet J Math Stat. 2017;46:239–253.
   Web of Science ®Google Scholar
• Guo L, Gui W. Statistical inference of the reliability for generalized exponential distribution under progressive type-II censoring schemes. IEEE Trans Reliab. 2018;67:470–480. doi: 10.1109/TR.2018.2800039
   Web of Science ®Google Scholar
• Babayi S, Khorram E. Inference of stress-strength for the type-II generalized logistic distribution under progressively type-II censored samples. Commun Stat - Simul Comput. 2018;47:1975–1995. doi: 10.1080/03610918.2017.1332214
   Web of Science ®Google Scholar
• Yadav AS, Singh SK, Singh U. Estimation of stress-strength reliability for inverse Weibull distribution under progressive type-II censoring scheme. J Ind Prod Eng. 2018;35:48–55.
   Web of Science ®Google Scholar
• Yadav AS, Singh SK, Singh U. Bayesian estimation of R=P[Y<X] for inverse Lomax distribution under progressive type-II censoring scheme. Int J Syst Assur Eng Manag. 2019;10:905–917. doi: 10.1007/s13198-019-00820-x
   Web of Science ®Google Scholar
• Kohansal A, Rezakhah S. Inference of R=P(Y<X) for two-parameter Rayleigh distribution based on progressively censored samples. Statistics. 2019;53:81–100. doi: 10.1080/02331888.2018.1546306
   Web of Science ®Google Scholar
• Ghitany ME, Al-Mutairi DK, Balakrishnan N, et al. Power Lindley distribution and associated inference. Comput Stat Data Anal. 2013;64:20–33. doi: 10.1016/j.csda.2013.02.026
   Web of Science ®Google Scholar
• Alizadeh M, MirMostafaee SMTK, Altun E, et al. The odd log-logistic Marshall-Olkin power Lindley distribution: properties and applications. J Stat Manag Syst. 2017;20:1065–1093. doi: 10.1080/09720510.2017.1367479
   Web of Science ®Google Scholar
• Alizadeh M, MirMostafaee SMTK, Ghosh I. A new extension of power Lindley distribution for analyzing bimodal data. Chil J Stat. 2017;8:67–86.
   Web of Science ®Google Scholar
• MirMostafaee SMTK, Alizadeh M, Altun E, et al. The exponentiated generalized power Lindley distribution: properties and applications. Appl Math. 2019;34:127–148. doi: 10.1007/s11766-019-3515-6
   Web of Science ®Google Scholar
• Sharma VK, Singh SK, Singh U. Classical and Bayesian methods of estimation for power Lindley distribution with application to waiting time data. Commun Stat Appl Methods. 2017;24:193–209.
   Web of Science ®Google Scholar
• Valiollahi R, Raqab MZ, Asgharzadeh A, et al. Estimation and prediction for power Lindley distribution under progressively type II right censored samples. Math Comput Simul. 2018;149:32–47. doi: 10.1016/j.matcom.2018.01.005
   Web of Science ®Google Scholar
• Pak A, Dey S. Statistical inference for the power Lindley model based on record values and inter-record times. J Comput Appl Math. 2019;347:156–172. doi: 10.1016/j.cam.2018.08.012
   Web of Science ®Google Scholar
• Balakrishnan N. Progressive censoring methodology: an appraisal. Test. 2007;16:211–259. doi: 10.1007/s11749-007-0061-y
   Web of Science ®Google Scholar
• Varian HR. A Bayesian approach to real estate assessment. In: Fienberg SE, Zellner A, editors. Studies in Bayesian econometrics and statistics in honor of Leonard J. Savage. Amsterdam: North-Holland; 1975. p. 195–208.
   Google Scholar
• Calabria R, Pulcini G. An engineering approach to Bayes estimation for the Weibull distribution. Microelectron Reliab. 1994;34:789–802. doi: 10.1016/0026-2714(94)90004-3
   Web of Science ®Google Scholar
• Calabria R, Pulcini G. Point estimation under asymmetric loss functions for left-truncated exponential samples. Commun Stat - Theory Methods. 1996;25:585–600. doi: 10.1080/03610929608831715
   Web of Science ®Google Scholar
• Zellner A. Bayesian estimation and prediction using asymmetric loss functions. J Am Stat Assoc. 1986;81:446–451. doi: 10.1080/01621459.1986.10478289
   Web of Science ®Google Scholar
• Dey S, Dey T, Luckett DJ. Statistical inference for the generalized inverted exponential distribution based on upper record values. Math Comput Simul. 2016;120:64–78. doi: 10.1016/j.matcom.2015.06.012
   Web of Science ®Google Scholar
• Singh S, Tripathi YM. Estimating the parameters of an inverse Weibull distribution under progressive type-I interval censoring. Stat Pap. 2018;59:21–56. doi: 10.1007/s00362-016-0750-2
   Web of Science ®Google Scholar
• Geweke J. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In Bernardo JM, Berger JO, Dawid AP, Smith AFM, editors. Bayesian statistics 4. Oxford, UK; Clarendon Press; 1992. p. 169–193.
   Google Scholar
• Raftery AE, Lewis SM. Comment: one long run with diagnostics: implementation strategies for Markov chain Monte Carlo. Stat Sci. 1992;7:493–497. doi: 10.1214/ss/1177011143
   Google Scholar
• Raftery AE, Lewis SM. Implementing MCMC. In Gilks WR, Richardson S, Spiegelhalter DJ, editors. Practical Markov chain Monte Carlo. UK: Chapman and Hall/CRC; 1996. p. 115–130.
   Google Scholar
• Heidelberger P, Welch PD. Simulation run length control in the presence of an initial transient. Oper Res. 1983;31:1109–1144. doi: 10.1287/opre.31.6.1109
   Web of Science ®Google Scholar
• Heidelberger P, Welch PD. A spectral method for confidence interval generation and run length control in simulations. Commun ACM. 1981;24:233–245. doi: 10.1145/358598.358630
   Web of Science ®Google Scholar
• Heidelberger P, Welch PD. Adaptive spectral methods for simulation output analysis. IBM J Res Dev. 1981;25:860–876. doi: 10.1147/rd.256.0860
   Web of Science ®Google Scholar
• Schruben LW. Detecting initialization bias in simulation output. Oper Res. 1982;30:569–590. doi: 10.1287/opre.30.3.569
   Web of Science ®Google Scholar
• Schruben L, Singh H, Tierney L. A test of initialization bias hypotheses in simulation output. Technical Report 471, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York; 1980.
   Google Scholar
• Schruben L, Singh H, Tierney L. Optimal tests for initialization bias in simulation output. Oper Res. 1983;31:1167–1178. doi: 10.1287/opre.31.6.1167
   Web of Science ®Google Scholar
• Makhdoom I, Nasiri P, Pak A. Bayesian approach for the reliability parameter of power Lindley distribution. Int J Syst Assur Eng Manag. 2016;7:341–355. doi: 10.1007/s13198-016-0476-5
   Web of Science ®Google Scholar
• Ghitany ME, Atieh B, Nadarajah S. Lindley distribution and its application. Math Comput Simul. 2008;78:493–506. doi: 10.1016/j.matcom.2007.06.007
   Web of Science ®Google Scholar
• Proschan F. Theoretical explanation of observed decreasing failure rate. Technometrics. 1963;5:375–383. doi: 10.1080/00401706.1963.10490105
   Web of Science ®Google Scholar
• R Core Team R: A language and environment for statistical computing. Vienna, Austria; R Foundation for Statistical Computing; 2018.
   Google Scholar
• Bellosta CJG. ADGofTest: Anderson-Darling GoF test, R package version 0.3; 2015. Available from: https://CRAN.R-project.org/package=ADGofTest.
   Google Scholar
• Adler A. lamW: Lambert-W function, R package version 1.3.0; 2017. Available from: https://CRAN.R-project.org/package=lamW.
   Google Scholar
• Hasselman B. nleqslv: Solve systems of nonlinear equations, R package version 3.3.2; 2018. Available from: https://CRAN.R-project.org/package=nleqslv.
   Google Scholar
• Plummer M, Best N, Cowles K, et al. CODA: convergence diagnosis and output analysis for MCMC. R News. 2006;6:7–11.
   Google Scholar
• Plummer M, Best N, Cowles K, et al. coda: Output analysis and diagnostics for MCMC, R package version 0.19-2; 2018. Available From: https://CRAN.R-project.org/package=coda.
   Google Scholar
• Mersmann O, Trautmann H, Steuer D, et al. truncnorm: Truncated normal distribution, R package version 1.0-8; 2018. Available from: https://CRAN.R-project.org/package=truncnorm.
   Google Scholar