Conditional Confidence Interval for the Scale Parameter of a Weibull Distribution

Mahdi, Smail. "Conditional Confidence Interval for the Scale Parameter of a Weibull Distribution." Serdica Mathematical Journal 30.1 (2004): 55-70. <http://eudml.org/doc/219627>.

@article{Mahdi2004,
abstract = {2000 Mathematics Subject Classification: 62F25, 62F03.A two-sided conditional confidence interval for the scale parameter θ of a Weibull distribution is constructed. The construction follows the rejection of a preliminary test for the null hypothesis: θ = θ0 where θ0 is a given value. The confidence bounds are derived according to the method set forth by Meeks and D’Agostino (1983) and subsequently used by Arabatzis et al. (1989) in Gaussian models and more recently by Chiou and Han (1994, 1995) in exponential models. The derived conditional confidence interval also suits non large samples since it is based on the modified pivot statistic advocated in Bain and Engelhardt (1981, 1991). The average length and the coverage probability of this conditional interval are compared with whose of the corresponding optimal unconditional interval through simulations. The study has shown that both intervals are similar when the population scale parameter is far enough from θ0. However, when θ is in the vicinity of θ0, the conditional interval outperforms the unconditional one in terms of length and also maintains a reasonably high coverage probability. Our results agree with the findings of Chiou and Han and Arabatzis et al. which contrast with whose of Meeks and D’Agostino stating that the unconditional interval is always shorter than the conditional one. Furthermore, we derived the likelihood ratio confidence interval for θ and compared numerically its performance with the two other interval estimators.},
author = {Mahdi, Smail},
journal = {Serdica Mathematical Journal},
keywords = {Weibull Distribution; Rejection of a Preliminary Hypothesis; Conditional and Unconditional Interval Estimator; Likelihood Ratio Interval; Coverage Probability; Average Length; Simulation; Weibull distribution; rejection of preliminary hypotheses; conditional interval estimator; unconditional interval estimator; likelihood ratio interval; coverage probability; average length; simulations},
language = {eng},
number = {1},
pages = {55-70},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Conditional Confidence Interval for the Scale Parameter of a Weibull Distribution},
url = {http://eudml.org/doc/219627},
volume = {30},
year = {2004},
}

TY - JOUR
AU - Mahdi, Smail
TI - Conditional Confidence Interval for the Scale Parameter of a Weibull Distribution
JO - Serdica Mathematical Journal
PY - 2004
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 30
IS - 1
SP - 55
EP - 70
AB - 2000 Mathematics Subject Classification: 62F25, 62F03.A two-sided conditional confidence interval for the scale parameter θ of a Weibull distribution is constructed. The construction follows the rejection of a preliminary test for the null hypothesis: θ = θ0 where θ0 is a given value. The confidence bounds are derived according to the method set forth by Meeks and D’Agostino (1983) and subsequently used by Arabatzis et al. (1989) in Gaussian models and more recently by Chiou and Han (1994, 1995) in exponential models. The derived conditional confidence interval also suits non large samples since it is based on the modified pivot statistic advocated in Bain and Engelhardt (1981, 1991). The average length and the coverage probability of this conditional interval are compared with whose of the corresponding optimal unconditional interval through simulations. The study has shown that both intervals are similar when the population scale parameter is far enough from θ0. However, when θ is in the vicinity of θ0, the conditional interval outperforms the unconditional one in terms of length and also maintains a reasonably high coverage probability. Our results agree with the findings of Chiou and Han and Arabatzis et al. which contrast with whose of Meeks and D’Agostino stating that the unconditional interval is always shorter than the conditional one. Furthermore, we derived the likelihood ratio confidence interval for θ and compared numerically its performance with the two other interval estimators.
LA - eng
KW - Weibull Distribution; Rejection of a Preliminary Hypothesis; Conditional and Unconditional Interval Estimator; Likelihood Ratio Interval; Coverage Probability; Average Length; Simulation; Weibull distribution; rejection of preliminary hypotheses; conditional interval estimator; unconditional interval estimator; likelihood ratio interval; coverage probability; average length; simulations
UR - http://eudml.org/doc/219627
ER -