Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
One-Sided confidence interval estimation for Weibull Shape and scale parameters
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Keywords

Weibull distribution
rejection of a preliminary hypothesis
interval estimator
coverage probability
average length
simulation
Distribución de Weibull
rechazo de una hipótesis preliminar
estimador de intervalo
probabilidad de cubrimiento
longitud promedio
simulación

How to Cite

Mahdi, S. (2005). One-Sided confidence interval estimation for Weibull Shape and scale parameters. Revista De Matemática: Teoría Y Aplicaciones, 12(1-2), 61–72. https://doi.org/10.15517/rmta.v12i1-2.251

Abstract

In this paper, we consider the problem of one-sided conditional and unconditional interval estimation for the scale and shape parameters in a two-parameter Weibull model. The statistical inference is based upon the pivots advocated in Bain and Engelhardt, the likelihood ratio method and Birnbaum statistic. Simulation results illustrating the performance of these interval estimating methods are discussed and displayed. Empirical point estimate results obtained with the maximum likelihood, generalized moment and generalized probability weighted moment methods are also presented.

https://doi.org/10.15517/rmta.v12i1-2.251
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References

Bain, L.J.; Engelhardt, M. (1981) “Simple approximate distributional results for confidence and tolerance limits for the Weibull distribution based on maximum likelihood estimators”, Technometrics 23(1): 15–20.

Bain, L.J.; Engelhardt, M. (1991) Statistical Analysis of Reliability and Life-Testing Models. Deker, New York.

Birnbaum, Z.W. (1974) “Computers and unconventional test-statistics”, Reliability and Biometry, Statistical Analysis of Lifelength, SIAM.

Casella, G.; Berger, R.L. (2002) Statistical Inference, second Edition. Duxbury.

Hosking, J.R.M. (1986) “The theory of probability weighted moments”, Research Report RC12210, IBM Thomas J. Watson Research Center, New York.

Mahdi, S.; Ashkar, F. (2004) “Exploring generalized probability weighted moments, generalized moments and maximum likelihood estimating methods in two-parameter Weibull model”, it Journal of Hydrology 285: 62–75.

Mahdi, S. (2003) “Two-sample conditional inference in a Weibul model”, Car. Jour. Math. Comp. Sci. 11: 1–12.

Mahdi, S. (2000) “Estimation in exponential models”, Matematicki Vesnik 52: 27–45.

Mahdi, S. (1999) “Monte Carlo studies on the accuracy of an interval estimator after a preliminary test of significance procedure”, Bulletin of the International Statistical Institute, 52nd session, Book 2, Helsinki: 253–254.

Mahdi, S.; Gupta, V.P. (1993) “Conditionally specified confidence interval for the variance of a normal population”, Bull. Soc. Math. Belg. B 45(3): 245–256.

Meeks, S.L.; D’Agostino, R.B. (1983) “A note on the use of confidence limits following rejection of a null hypothesis”, The American Statistician 37: 134–136.

Wardell, D.G. (1997) “Small sample interval estimation of Bernoulli and Poisson parameters”, The American Statistician 51(4): 321–325.

Wolfram, S. (1991) Mathematica: A System for Doing Mathematics by Computer, (2nd ed.). Addison-Wesley Publishing Company, USA.

Zanakis, S.H. (1979) “Extended pattern search with transformation for the three-parameter WEI distribution”, Management Science 25: 1149–1161.

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