187
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Inverse Lindley distribution: different methods for estimating their PDF and CDF

, &
Pages 604-623 | Received 17 Nov 2022, Accepted 20 Sep 2023, Published online: 08 Oct 2023

References

  • Lindley D. Fiducial distributions and Bayes theorem. J R Stat Soc. 1958;20:102–107.
  • Almalki S, Nadarajah S. Modifications of the Weibull distribution: a review. Reliab Eng Syst Saf. 2014;124:32–55. doi: 10.1016/j.ress.2013.11.010
  • Almalki S, Yuan J. A new modified Weibull distribution. Reliab Eng Syst Saf. 2013;111:164–170. doi: 10.1016/j.ress.2012.10.018
  • Langlands A, Gore S. Long-term survival of patients with breast cancer: a study of the curability of the disease. British Med J. 1979;2(6200):1247–1251. doi: 10.1136/bmj.2.6200.1247
  • Efron B. Logistic regression, survival analysis, and the Kaplan–Meier curve. J Am Stat Assoc. 1988;83(402):414–425. doi: 10.1080/01621459.1988.10478612
  • Prentice RL. Exponential survivals with censoring and explanator variables. Biometrika. 1973;60(2):279–288. doi: 10.1093/biomet/60.2.279
  • Bennett S. Log-logistic regression models for survival data. J R Stat Soc Ser C (Appl Stat). 1983;32:165–171.
  • Erto P, Rapone M. Non-informative and practical Bayesian confidence bounds for reliable life in the Weibull model. Reliab Eng. 1984;7(3):181–191. doi: 10.1016/0143-8174(84)90016-7
  • Murthy D, Xie M, Jiang R. Weibull models. Hoboken: John Wiley Sons; 2004.
  • Kundu D, Howlader H. Bayesian inference and prediction of the inverse Weibull distribution for type II censored data. Comput Stat Data Anal. 2010;54(6):1547–1558. doi: 10.1016/j.csda.2010.01.003
  • Sharma VK, Singh SK, Singh U, et al. The inverse Lindley distribution: a stress-strength reliability model. arXiv:1405.6268v1 [stat.AP] Vol. 24, 2014. p. 1–17.
  • Sharma V, Singh S, Singh U. A new upside-down bathtub shaped hazard rate model for survival data analysis. Appl Math Comput. 2014;239:242–253.
  • Sharma V, Singh S, Singh U, et al. The inverse Lindley distribution: a stress-strength reliability model with applications to head and neck cancer data. J Indust Product Eng. 2015;32(3):162–173. doi: 10.1080/21681015.2015.1025901
  • Glen A. On the inverse gamma as a survival distribution. J Qual Technol. 2011;43(2):158–166. doi: 10.1080/00224065.2011.11917853
  • Mead M. Generalized inverse gamma distribution and its applications in reliability communications. Commun Stat Theory Methods. 2015;44(7):1426–1435. doi: 10.1080/03610926.2013.768667
  • Bjerkedal T. Acquisition of resistance in Guinea pigs infected with different doses of virulent Tubercle Bacilli. Am J Epidemiol. 1960;72(1):130–148. doi: 10.1093/oxfordjournals.aje.a120129
  • Bagheri SF, Alizadeh M, Baloui Jamkhaneh E, et al. Evaluation and comparison of estimations in the generalized exponential-Poisson distribution. J Stat Comput Simul. 2014;84(11):2345–2360. doi: 10.1080/00949655.2013.793342
  • Bagheri SF, Alizadeh M, Nadarajah S, et al. Efficient estimation of the PDF and the CDF of the Weibull extension model. Commun Stat Simul Comput. 2016;45(6):2191–2207. doi: 10.1080/03610918.2014.894059
  • Bagheri SF, Alizadeh M, Nadarajah S. Efficient estimation of the PDF and the CDF of the exponentiated Gumbel distribution. Commun Stat Simul Comput. 2016;45(1):339–361. doi: 10.1080/03610918.2013.863922
  • Alizadeh M, Bagheri SF, Baloui Jamkhaneh E, et al. Estimates of the PDF and the CDF of the exponentiated Weibull distribution. Braz J Probab Stat. 2015;29(3):695–716. doi: 10.1214/14-BJPS240
  • Maiti SS, Mukherjee I. On estimation of the PDF and CDF of the Lindley distribution. Commun Stat Simul Comput. 2018;47(5):1370–1381. doi: 10.1080/03610918.2017.1311919
  • Maleki Jebely F, Zare K, Deiri E. Efficient estimation of the PDF and the CDF of the inverse Rayleigh distribution. J Stat Comput Simul. 2018;88(1):75–88. doi: 10.1080/00949655.2017.1378656
  • Glaser RE. Bathtub and related failure rate characterizations. J Am Stat Assoc. 1980;75(371):667–672. doi: 10.1080/01621459.1980.10477530
  • Al-Mutairi DK, Ghitany ME, Kundu D. Inferences on stress-strength reliability from Lindley distribution. Commun Stat Theory Methods. 2013;42(8):1443–1463. doi: 10.1080/03610926.2011.563011
  • Lehmann EL, Scheffe H. Completeness, similar regions and unbiased estimation. Sankhya. 1955;15:219–236.
  • 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
  • Berger JO. Statistical decision theory and Bayesian analysis. New York: Springer Verlag; 1985.
  • Asgharzadeh A, Ng HKT, Valiollahi R, et al. Statistical inference for Lindley model based on type II censored data. J Stat Theory Appl. 2017;16(2):178–197. doi: 10.2991/jsta.2017.16.2.4
  • Makkar P, Srivastava PK, Singh RS, et al. Bayesian survival analysis of head and neck cancer data using lognormal model. Commun Stat Theory Methods. 2014;43(2):392–407. doi: 10.1080/03610926.2012.664233
  • Sharma V, Singh S, Singh U, et al. The generalized inverse Lindley distribution: a new inverse statistical model for the study of upside-down bathtub survival data. Commun Stat Theory Methods. 2016;45(19):5709–5729. doi: 10.1080/03610926.2014.948206

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.