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A Journal of Theoretical and Applied Statistics
Volume 52, 2018 - Issue 2
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Original Articles

Bayesian inference using product of spacings function for Progressive hybrid Type-I censoring scheme

, &
Pages 345-363 | Received 13 Jun 2016, Accepted 09 Nov 2017, Published online: 22 Nov 2017

References

  • Epstein B. Truncated life tests in the exponential case. Ann Math Stat. 1954;25(3):555–564. doi: 10.1214/aoms/1177728723
  • Epstein B. Estimation from life test data. Technometrics. 1960;2(4):447–454. doi: 10.1080/00401706.1960.10489911
  • Chen SM, Bhattacharyya GK. Exact confidence bounds for an exponential parameter under hybrid censoring. Commun Statist Theory Methods. 1987;16(8):2429–2442. doi: 10.1080/03610928708829516
  • Fairbanks K, Madsen R, Dykstra R. A confidence interval for an exponential parameter from a hybrid life test. J Am Stat Assoc. 1982;77(377):137–140. doi: 10.1080/01621459.1982.10477776
  • Draper N, Guttman I. Bayesian analysis of hybrid life tests with exponential failure times. Ann Inst Stat Math. 1987;39(1):219–225. doi: 10.1007/BF02491461
  • Jeong HS, Park JI, Yum BJ. Development of (r,t) hybrid sampling plans for exponential lifetime distributions. J Appl Stat. 1996;23(6):601–608. doi: 10.1080/02664769623964
  • Gupta RD, Kundu D. Hybrid censoring schemes with exponential failure distribution. Commun Statist Theory Methods. 1998;27(12):3065–3083. doi: 10.1080/03610929808832273
  • Herd GR. Estimation of the parameters of a population from a multi-censored sample. Retrospective Theses and Dissertations. 1956. Available from: http://lib.dr.iastate.edu/rtd/12873
  • Cohen AC. Progressively censored samples in life testing. Technometrics. 1963;5(3):327–339. doi: 10.1080/00401706.1963.10490102
  • Krishna H, Kumar K. Reliability estimation in Lindley distribution with progressively type {II} right censored sample. Math Comput Simul. 2011;82(2):281–294. doi: 10.1016/j.matcom.2011.07.005
  • Mousa MAMA, Jaheen ZF. Statistical inference for the burr model based on progressively censored data. Comput Math Appl. 2002;43(10):1441–1449. doi: 10.1016/S0898-1221(02)00110-4
  • Balakrishnan N, Han D, Iliopoulos G. Exact inference for progressively Type-I censored exponential failure data. Metrika. 2011;73(3):335–358. doi: 10.1007/s00184-009-0281-0
  • WuS-J, ChenY-J, ChangC-T. Statistical inference based on progressively censored samples with random removals from the Burr type XII distribution. J Stat Comput Simul. 2007;77(1):19–27. doi: 10.1080/10629360600569204
  • Singh SK, Singh U, Kumar M. Bayesian estimation for poisson–exponential model under progressive Type-II censoring data with binomial removal and its application to ovarian cancer data. Comm Statist Simulation Comput. 2016;45(9):3457–3475. doi: 10.1080/03610918.2014.948189
  • Singh SK, Singh U, Kumar M. Estimation of parameters of generalized inverted exponential distribution for progressive type-II censored sample with binomial removals. J Probab Stat. 2013;2013. Hindawi Publishing Corporation, p. 1–12.
  • Balakrishnan N, Aggarwala R. Progressive censoring: theory, methods, and applications. Basel: Birkhäuser; 2000.
  • Balakrishnan N, Cramer E. The art of progressive censoring - applications to reliability and quality. Basel: Birkhäuser; 2014.
  • Childs A, Chandrasekar B, Balakrishnan N. Exact likelihood inference for an exponential parameter under progressive hybrid censoring schemes. Boston, MA: Birkhäuser; 2008. p. 319–330. Chapter 23.
  • Kundu D, Joarder A. Analysis of Type-II progressively hybrid censored data. Comput Stat Data Anal. 2006;50(10):2509–2528. doi: 10.1016/j.csda.2005.05.002
  • YuenH–K, TseS-K. Parameters estimation for weibull distributed lifetimes under progressive censoring with random removeals. J Stat Comput Simul. 1996;55(1–2):57–71. doi: 10.1080/00949659608811749
  • Tse SK, Yang C, Yuen HK. Statistical analysis of weibull distributed lifetime data under Type II progressive censoring with binomial removals. J Appl Stat. 2000;27(8):1033–1043. doi: 10.1080/02664760050173355
  • Tse SK, Yuen HK. Expected experiment times for the weibull distribution under progressive censoring with random removals. J Appl Stat. 1998;25(1):75–83. doi: 10.1080/02664769823313
  • Cohen AC. Progressively censored sampling in the three parameter log-normal distribution. Technometrics. 1976;18(1):99–103. doi: 10.2307/1267922
  • Cohen AC, Norgaard NJ. Progressively censored sampling in the three-parameter gamma distribution. Technometrics. 1977;19(3):333–340. doi: 10.1080/00401706.1977.10489556
  • Balakrishnan N. Progressive censoring methodology: an appraisal. Test. 2007;16(2):211–259. doi: 10.1007/s11749-007-0061-y
  • Ghitany ME, Atieh B, Nadarajah S. Lindley distribution and its application. Math Comput Simul. 2008;78(4):493–506. doi: 10.1016/j.matcom.2007.06.007
  • Sharma VK, Singh SK, Singh U, et al. The inverse Lindley distribution: a stress-strength reliability model with application to head and neck cancer data. J Ind Prod Eng. 2015;32(3):162–173.
  • Cheng RCH, Amin NAK. Estimating parameters in continuous univariate distributions with a shifted origin. J R Stat Soc. 1983;45(3):394–403.
  • Ranneby B. The maximum spacing method: an estimation method related to the maximum likelihood method. Scand J Stat. 1984;11(2):93–112.
  • Anatolyev S, Kosenok G. An alternative to maximum likelihood based on spacings. Econ Theory. 2005;21(2):472–476. doi: 10.1017/S0266466605050255
  • Cheng RCH, Traylor L. Non-regular maximum likelihood problems. J R Stat Soc Ser B. 1995;97(1):3–44.
  • Basu S, Singh SK, Singh U. Parameter estimation of inverse Lindley distribution for Type-I censored data. Comput Stat. 2017;32(1):367–385. doi: 10.1007/s00180-016-0704-0
  • Coolen FPA, Newby MJ. A note on the use of the product of spacings in Bayesian Inference. Technische Universiteit Eindhoven; 1990. Available from: https://pure.tue.nl/ws/files/1918253/338185.pdf
  • Singh U, Singh SK, Singh RK. Product spacings as an alternative to likelihood for Bayesian inferences. J Stat Appl Probab. 2014;3(2):179–188. doi: 10.12785/jsap/030208
  • Singh U, Singh SK, Singh RK. A comparative study of traditional estimation methods and maximum product spacings method in generalized inverted exponential distribution. J Stat Appl Probab. 2014;3(2):153–169. doi: 10.12785/jsap/030206
  • Singh RK, Singh SK, Singh U. Maximum product spacings method for the estimation of parameters of generalized inverted exponential distribution under Progressive Type II Censoring. J Stat Manag Syst. 2016;19(2):219–245. Doi:10.1080/09720510.2015.1023553
  • Cheng RCH, Iles TC. Corrected maximum likelihood in non-regular problems. J R Stat Soc. 1987;49(1):95–101.
  • Huzurbazar VS. The likelihood equation, consistency and the maxima of the likelihood function. Ann Eugen. 1947;14(1):185–200. doi: 10.1111/j.1469-1809.1947.tb02394.x
  • Pitman EJG. Some basic theory for statistical inference, Vol. 7. London: Chapman and Hall; 1979.
  • Shao Y, Hahn MG. Maximum product of spacings method: a unified formulation with illustration of strong consistency. Illinois J Math. 1999;43(3):489–499.
  • Cheng RCH, Stephens MA. A goodness-of-fit test using moran's statistic with estimated parameters. Biometrika. 1989;76(2):385–392. doi: 10.1093/biomet/76.2.385
  • Ghosh K, Jammalamadaka SR. A general estimation method using spacings. J Stat Plan Inference. 2001;93(1):71–82. doi: 10.1016/S0378-3758(00)00160-9
  • Coolen FPA, Newby MJ. Bayesian estimation of location parameters in life distributions. Reliab Eng Syst Safe. 1994;45(3):293–298. doi: 10.1016/0951-8320(94)90146-5
  • Roberts GO, Smith AFM. Simple conditions for the convergence of the Gibbs sampler and metropolis-hastings algorithms. Stoch Process Their Appl. 1994;49(2):207–216. doi: 10.1016/0304-4149(94)90134-1
  • Chib S, Greenberg E. Understanding the metropolis-hastings algorithm. Am Stat. 1995;49(4):327–335.
  • Robert CP, Casella G. Monte Carlo statistical methods. New York: Springer; 2004.
  • Chen MH, Shao QM. Monte Carlo estimation of Bayesian credible and HPD intervals. J Comput Graph Stat. 1999;8(1):69–92.
  • Kamps U, Cramer E. On distributions of generalized order statistics. Statistics. 2001;35(3):269–280. doi: 10.1080/02331880108802736
  • Singh SK, Singh U, Sharma VK. Expected total test time and Bayesian estimation for generalized Lindley distribution under progressively type-II censored sample where removals follow the beta-binomial probability law. Appl Math Comput. 2013;222:402–419.
  • Berger JO. Statistical decision theory and Bayesian analysis. New York: Springer; 1985.

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