Abstract
In this paper, a likelihood based analysis is developed and applied to obtain confidence intervals and p values for the stress-strength reliability R = P(X < Y) with right truncated exponentially distributed data. The proposed method is based on theory given in Fraser et al. (Biometrika 86:249–264, 1999) which involves implicit but appropriate conditioning and marginalization. Monte Carlo simulations are used to illustrate the accuracy of the proposed method.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Al-Hussanini E, Mousa M, Sultar K (1997) Parametric and nonparametric estimation of P(Y < X) for finite mixtures of log-normal components. Commun Stat Theory Methods 26:1269–1289
Awad A, Azzam M, Hamdan M (1981) Some inference results on P(Y < X) in the bivariate model. Commun Stat Theory Methods 10:2515–2525
Barndorff-Nielsen OE (1986). Inference on full and partial parameters, based on the standardized signed log-likelihood ratio– Biometrika 73:307–322
Barndorff-Nielsen OE (1991) Modified signed log-likelihood ratio– Biometrika 78:557–563
Cox DR, Hinkley DV (1974) Theoretical statistics–Chapman and Hall, London
Doganaksoy N, Schmee J (1993) Comparisons of approximate confidence intervals for distributions used in life-data analysis. Technometrics 35:175–184
Downton F (1973) The estimation of P(Y < X). in the normal case– Technometrics 15:551–558
Enis P, Geisser S (1971) Estimation of the probability that Y < X– J Am Stat Assoc 66:162–168
Fraser DAS, Reid N (1995) Ancillaries and third order significance– Utilitas Math 7:33–55
Fraser DAS, Reid N, Wu J (1999) A simple general formula for tail probabilities for frequentist and Bayesian infernce– Biometrika 86:249–264
Helperin M, Gilbert P, Lachin J (1987) Distribution-free confidence intervals for P(X 1 < X 2). Biometrics 43:71–80
Hamdy M (1995) Distribution-free confidence intervals for P(X < Y) based on independent samples of X and Y. Commun Stat Simulation Comput 24:1005–1017
Reid N (1996) Likelihood and higher-order approximations to tail areas: a review and annotated bibliography. Can J Stat 24:141–166
Severeni T (2000) Likelihood methods in statistics. Oxford University Press, New York
Tong H (1974) A note on the estimation of P(Y < X) in the exponential case. Technometrics 16:625
Tong H (1975) Letter to the editor. Technometrics 17:393
Wong ACM, Wu J (2000) Practical small-sample asymptotics for distributions used in life-data analysis. Technometrics 42:149–155
Woodward W, Kelly G (1977) Minimum variance unbiased estimation of P(Y < X) in the normal case. Technometrics 19:95–98
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jiang, L., Wong, A.C.M. A note on inference for P(X < Y) for right truncated exponentially distributed data. Stat Papers 49, 637–651 (2008). https://doi.org/10.1007/s00362-006-0034-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-006-0034-3