×
Kundu, Debasis; Gupta, Rameshwar D.; Manglick, Anubhav

Discriminating between the log-normal and generalized exponential distributions. (English) Zbl 1054.62013

J. Stat. Plann. Inference 127, No. 1-2, 213-227 (2005).
Summary: The two-parameter generalized exponential distribution was recently introduced by R. D. Gupta and D. Kundu [Aust. N. Z. J. Stat. 41, 173–188 (1999)]. It is observed that the generalized exponential distribution can be used quite effectively to analyze skewed data sets as an alternative to the more popular log-normal distribution. We use the ratio of the maximized likelihoods in choosing between the log-normal and generalized exponential distributions. We obtain asymptotic distributions of the logarithm of the ratio of the maximized likelihoods and use them to determine the required sample size to discriminate between the two distributions for a user specified probability of correct selection and tolerance limit.

Cited in 28 Documents

MSC:

62E20 Asymptotic distribution theory in statistics
62F99 Parametric inference
62E10 Characterization and structure theory of statistical distributions

Keywords:

Asymptotic distributions; Generalized exponential distribution; Kolmogorov-Smirnov distances; Likelihood ratio test statistic
PDF BibTeX XML Cite
\textit{D. Kundu} et al., J. Stat. Plann. Inference 127, No. 1--2, 213--227 (2005; Zbl 1054.62013)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Atkinson, A., A test for discriminating between models, Biometrika, 56, 337-347, (1969) · Zbl 0193.16601
[2] Atkinson, A., A method for discriminating between models (with discussions), J. roy. statist. soc. ser. B, 32, 323-353, (1970) · Zbl 0225.62020
[3] Bain, L.J.; Englehardt, M., Probability of correct selection of Weibull versus gamma based on likelihood ratio, Comm. statist. ser. A, 9, 375-381, (1980) · Zbl 0455.62077
[4] Bain, L.J.; Englehardt, M., Statistical analysis of reliability and lifetime model, (1991), Marcel Dekker New York
[5] Chambers, E.A.; Cox, D.R., Discriminating between alternative binary response models, Biometrika, 54, 573-578, (1967)
[6] Chen, W.W., On the tests of separate families of hypotheses with small sample size, J. statist. comput. simulations, 2, 183-187, (1980) · Zbl 0457.62024
[7] Cox, D.R., 1961. Tests of separate families of hypotheses. Proceedings of the Fourth Berkeley Symposium in Mathematical Statistics and Probability, Berkeley, University of California Press, Berkley, CA, pp.105-123. · Zbl 0201.52102
[8] Cox, D.R., Further results on tests of separate families of hypotheses, J. roy. statist. soc. ser. B, 24, 406-424, (1962) · Zbl 0131.35801
[9] Dyer, A.R., Discrimination procedure for separate families of hypotheses, J. amer. statist. assoc, 68, 970-974, (1973) · Zbl 0271.62073
[10] Dumonceaux, R.; Antle, C.E., Discriminating between the log-normal and Weibull distribution, Technometrics, 15, 4, 923-926, (1973) · Zbl 0269.62024
[11] Fearn, D.H.; Nebenzahl, E., On the maximum likelihood ratio method of deciding between the Weibull and gamma distribution, Comm. statist. theory methods, 20, 2, 579-593, (1991) · Zbl 0724.62028
[12] Gupta, R.D.; Kundu, D., Generalized exponential distributions, Austral. NZ J. statist, 41, 2, 173-188, (1999) · Zbl 1007.62503
[13] Gupta, R.D.; Kundu, D., Exponentiated exponential distributionan alternative to gamma and Weibull distributions, Biometrical J, 43, 1, 117-130, (2001) · Zbl 0997.62076
[14] Gupta, R.D.; Kundu, D., Generalized exponential distributionsdifferent methods of estimations, J. statist. comput. simulation, 69, 4, 315-338, (2001)
[15] Gupta, R.D.; Kundu, D., Generalized exponential distributionsstatistical inferences, J. statist. theory appl, 1, 101-118, (2002)
[16] Gupta, R.D., Kundu, D., 2003a. Discriminating between the Weibull and generalized exponential distributions. Comput. Statist. Data Anal. 43, 179-196. · Zbl 1429.62060
[17] Gupta, R.D., Kundu, D., 2003b. Discriminating between the gamma and generalized exponential distributions. J. Statist. Comput. Simulation, to appear. · Zbl 1429.62060
[18] Jackson, O.A.Y., Some results on tests of separate families of hypotheses, Biometrika, 55, 355-363, (1968)
[19] Jackson, O.A.Y., Fitting a gamma or log-normal distribution to fiber-diameter measurements on wool tops, Appl. statist, 18, 70-75, (1969)
[20] Johnson, N., Kotz, S., Balakrishnan, N., 1995. Continuous Univariate Distribution, Vol. 1. Wiley, New York.
[21] Pereira, B.de, Empirical comparison of some tests of separate families of hypotheses, Metrika, 25, 219-234, (1978) · Zbl 0408.62017
[22] Press et al., 1993. Numerical Recipes in C. Cambridge University Press, Cambridge.
[23] Quesenberry, C.P.; Kent, J., Selecting among probability distributions used in reliability, Technometrics, 24, 1, 59-65, (1982)
[24] Raqab, M.Z., Inference for generalized exponential distribution based on record statistics, J. statist. plann. inference, 104, 2, 339-350, (2002) · Zbl 0992.62013
[25] Raqab, M.Z.; Ahsanullah, M., Estimation of the location and scale parameters of the generalized exponential distribution based on order statistics, J. statist. comput. simulation, 69, 2, 109-124, (2001) · Zbl 1151.62309
[26] White, H., Regularity conditions for Cox’s test of non-nested hypotheses, J. econometrics, 19, 301-318, (1982) · Zbl 0539.62032
[27] Wiens, B.L., When log-normal and gamma models give different resultsa case study, Amer. statist, 53, 2, 89-93, (1999)
[28] Zheng, G., On the Fisher information matrix in type-II censored data from the exponentiated exponential family, Biometrical J, 44, 3, 353-357, (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.