Abstract
In this paper we study various reliability properties of a Weibull inverse exponential distribution. The maximum likelihood and Bayes estimates of unknown parameters and reliability characteristics are obtained. Bayes estimates are obtained with respect to the squared error loss function under proper and improper prior situations. We use the Lindley method and the Metropolis–Hastings algorithm to compute the Bayes estimates. Interval estimation is also considered. Asymptotic and highest posterior density intervals of unknown parameters are constructed in this respect. We perform a numerical study to compare the performance of all methods and obtain comments based on this study. We also analyze two real data sets for illustration purposes. Finally a conclusion is presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alzaatreh A, Famoye F, Lee C (2013) Weibull-Pareto distribution and its applications. Commun Stat-Theor Methods 42:1673–1691
Bourguignon M, Silva RB, Cordeiro GM (2014) The Weibull-G family of probability distributions. J Data Sci 12:53–68
Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57:97–109
Lin C, Duran B, Lewis T (1989) Inverted gamma as a life distribution. Microelectron Reliab 29:619–626
Lindley DV (1980) Trab Estad 31:223–237
Mudholkar GS, Srivastava DK (1993) Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans Reliab 42:299–302
Mudholkar GS, Hutson AD (1996) The exponentiated Weibull family: some properties and a flood data application. Commun Stat-Theor Methods 25:3059–3083
Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equations of state calculations by fast computing machines. J Chem Phys 21:1087–1092
Mead ME, Abd-Eltawab AR (2014) A note on Kumaraswamy Fréchet distribution. Aust J Basic Appl Sci 8:294–300
Nichols MD, Padgett WJ (2006) A bootstrap control chart for Weibull percentiles. Qual Reliab Eng Int 22:141–151
Smith RL, Naylor JC (1987) A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Appl Stat 36:358–369
Tahir MH, Cordeiro GM, Alzaatreh A, Mansoor M, Zubair M (2014) A new Weibull-Pareto distribution: properties and applications. Commun Stat Simul Comput 15:3548–3567
Tahir MH, Zubair M, Mansoor M, Cordeiro GM, Alizadeh M, Hamedani GG (2016) A new Weibull- G family of distribution. Hacet J Math Stat 45:629–647
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chandrakant, Rastogi, M.K. & Tripathi, Y.M. On a Weibull-Inverse Exponential Distribution. Ann. Data. Sci. 5, 209–234 (2018). https://doi.org/10.1007/s40745-017-0125-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40745-017-0125-0