# Conditional Confidence Interval for the Scale Parameter of a Weibull Distribution

Serdica Mathematical Journal (2004)

- Volume: 30, Issue: 1, page 55-70
- ISSN: 1310-6600

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topMahdi, 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 -

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