Estimation of P[Y < X] for generalized exponential distribution

Metrika

Volumn 61, Issue 3, 2005, Pages 291-308

  Kundu, Debasis ^a   Gupta, Rameshwar D ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

^b UNIVERSITY OF NEW BRUNSWICK   (Canada)

Author keywords

Asymptotic distributions; Bayes estimator; Bootstrap confidence intervals; Credible intervals; Maximum likelihood estimator; Stress strength model

Indexed keywords

EID: 21544459057     PISSN: 00261335     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001840400345     Document Type: Article

References (36)

1. Ahmad KE, Fakhry ME, Jaheen ZF (1997) Empirical Bayes estimation of P(Y 〈 X) and characterizations of the Burr-type X model. Journal of Statistical Planning and Inference 64:297-308
2. Awad AM, Azzam MM, Hamadan MA (1981) Some inference results in P(Y 〈 X) in the bivariate exponential model. Communications in Statistics - Theory and Methods 10:2515-2524
3. Chen MH, Shao QM (1999) Monte Carlo estimation of Bayesian Credible and HPD intervals. Journal of Computational and Graphical Statistics 8:69-92
4. Church JD, Harris B (1970) The estimation of reliability from stress strength relationships. Technometrics 12:49-54
5. Congdon P (2001) Bayesian Statistical Modeling. John Wiley, New York
6. Constantine K, Karson M (1986) The estimation of P(Y 〈 X) in gamma case. Communications in Statistics- Computations and Simulations 15:365-388
7. Downtown F (1973) The estimation of P(X 〉 Y) in the normal case. Technometrics 15:551-558
8. Efron B (1982) The Jackknife, the Bootstrap and other Resampling Plans. CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 38; SIAM, Philadelphia, PA
9. Ferguson TS (1967) Mathematical Statistics; A Decision Theoretic Approach. Academic Press, New York
10. Govidarajulu Z (1967) Two sided confidence limits for P(X 〉 Y) based on normal samples of X and Y. Sankhya B 29:35-40
11. Gupta RD, Gupta RC (1990) Estimation of P(a'x 〉 b'y) in the multivarite normal case. Statistics 1:91-97
12. Gupta RD, Kundu D (1999) Generalized exponential distributions. Australian and New Zealand Journal of Statistics 41:173-188
13. Gupta RD, Kundu D (2001a) Generalized exponential distributions; Different Method of Estimations. Journal of Statistical Computation and Simulation 69:315-338
14. Gupta RD, Kundu D (2001b) Exponentiated Exponential Distribution; An alternative to gamma or Weibull distribution. Biometrical Journal 43:117-130
15. Gupta RD, Kundu D (2002) Generalized exponential distributions; Statistical Inferences. Journal of Statistical Theory and Applications 1:101-118
16. Gupta RD, Kundu D (2003a) Closeness between the gamma and generalized exponential distributions. Communications in Statistics - Theory and Methods 32:705-722
17. Gupta RD, Kundu D (2003b) Discriminating between the Weibull and generalized exponential distributions. Computational Statistics and Data Analysis 43:179-196
18. Gupta RD, Kundu D (2004) Discriminating between gamma and the generalized exponential distributions. Journal of Statistical Computation and Simulation 74:107-122
19. Hall P (1988) Theoretical comparison of bootstrap confidence intervals. Annals of Statistics 16:927-953
20. Kelley GD, Kelley JA, Schucany WR. Efficient estimation of P(Y 〈 X) in the exponential case. Technometrics 1976:359-360
21. Kundu D, Gupta RD, Manglick A (2004) Discriminating between the log-normal and the generalized exponential distributions. Journal of Statistical Planning and Inference (to appear)
22. Lindley DV (1980) Approximate Bayesian methods. Trabajos de Estadistica 3:281-288
23. Mudholkar GS, Hutson AD (1996) The exponentiated Weibull family: some properties and a flood data applications. Communications in Statistics - Theory and Methods 25:3059-3083
24. Mudholkar GS, Srivastava DK (1993) Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Transactions on Reliability 42:299-302
25. Mudholkar GS, Srivastava DK, Freimer M (1995) The exponentiated Weibull family: a reanalysis of the bus-motor failure data. Technometrics 37:436-445
26. Owen DB, Craswell KJ, Hanson DL (1977) Non-parametric upper confidence bounds for P(Y 〈 X) and confidence limits for P(Y 〈 X) when X and Y are normal. Journal of the American Statistical Association 59:906-924
27. Press WH, Teukolsky SA, Vellerling WT, Flannery BP (1992) Numerical recipes in FORTRAN, the art of scientific computing, 2nd. Edition, Cambridge University Press, Cambridge
28. Raqab MZ (2002) Inference for generalized exponential distribution based on record statistics. Journal of Statistical Planning and Inference 104:339-350
29. Raqab MZ, Ahsanullah M (2001) Estimation of the location and scale parameters of the generalized exponential distribution based on order statistics. Journal of Statistical Computation and Simulation 69:109-124
30. Sathe YS, Shah SP (1981) On estimation P(Y 〈 X) for the exponential distribution. Communications in Statistics - Theory and Methods 10:39-47
31. Surles JG, Padgett WJ (1998) Inference for P (Y 〈 X) in the Burr type X model. Journal of Applied Statistical Sciences 7:225-238
32. Surles JG, Padgett WJ (2001) Inference for reliability and stress-strength for a scaled Burr-type X distribution. Lifetime Data Analysis 7:187-200
33. Tong H (1974) A note on the estimation of P(Y 〈 X) in the exponential case. Technometrics 16:625. (Errara 1975, Vol. 17; 395)
34. Tong H (1977) On the estimation of P(Y 〈 X) for exponential families. IEEE Transactions on Reliability 26:54-56
35. Woodward WA, Kelley GD (1977) Minimum variance unbiased estimation of P(Y,X) in the normal case. Technometrics 19:95-98
36. Zheng G (2002) On the Fisher information matrix in type-II censored data from the exponentiated exponential family. Biometrical Journal 44:353-357