Research Article
Discrimination of the Gamma, Weibull and Log-Normal Distributions According to Probability of Correct Selection
Abstract
Gamma, Weibull and Log-Normal distributions are often used distributions for modelling skewed data. In this study, for a given data set the problem of selecting Gamma, Weibull or Log-Normal distributions is focused on for the modelling. Distribution of a given set of data, Gamma, Weibull or Log-Normal distribution has been decided by the probability of correct selection that is calculated by constructing Monte-Carlo simulations and asymptotic results under the null hypothesis.
Keywords
Probability of correct selection Gamma distribution Log-Normal distribution Likelihood ratio tests Weibull distribution
References
- Atkinson, A., 1969. A Test of Discriminating Between Modes, Biometrika, 56, 337-341.
- Atkinson, A., 1970. A Method for Discriminating Between Models (with discussions), Journal of the Royal Statistical society. Ser. B, 32, 323-353.
- Bain, L. J., Englehardt, M., 1980. Probability of Correct Selection of Weibull Versus Gamma Based on Likelihood Ratio. Communications in Statistics. Series A, 9, 375- 381.
- Bemardo, J. M., 1976. Algorithm As 103: Psi (Digamma) Function, J. Roy. Statist. Soc. Ser. C, 25, 315-317.
- Cox, D. R., 1961. Tests of Separate Families of Hypotheses, Proceedings of the Fourth Berkeley Symposium in Mathematical Statistics and Probability, Berkeley, University of Califonia Press, 105-123.
- Cox, D. R., 1962. Further Results on Tests of Separate Families of Hypotheses, Journal of the Royal Statistical Society, Ser. B, 24, 406-424.
- Dumonceaux, R., Antle, C.E., 1973. Discriminating Between the Log-normal and Weibull Distribution, Technometrics, 15,923-926.
- Dyer, A. R., 1973. Discrimination Procedure for Separate Families of Hypotheses, Journal of the American Statistical Association, 68, 970-974.
- Johnson, N. L., Kotz, S., Balakrishnan, N., 1994. Continuous Univariate Distributions, Volume 1, John Wiley & Sons, Inc. USA.
- Wiens, B.L., 1999. When Log-Normal and Gamma Models Give Different Results: A Case Study, American Statistician, 53, 89-93.
- White, H., 1982. Reqularity Conditions for Cox's Test of Non-nested Hypotheses, J. Econometrics, 19, 301-318.
Year 2012,
Volume: 9 Issue: 1, 11 - 20, 13.07.2012
Abstract
Gamma, Weibull ve Log-Normal dağılımları, çarpık verilerin analizi için sık kullanılan dağılımlardır. Bu çalışmada, verilen bir veri setinin, Gamma, Weibull ya da Log-Normal dağılımlardan hangisi ile modelleneceği problemi üzerinde durulmuştur. Verilen bir veri setinin dağılımının Gamma, Weibull ya da Log-Normal dağılımından hangisinden geldiğine, veri setinin dağılımının sırasıyla ilgili dağılımlara göre oluşturulan yokluk hipotezi altında Monte-Carlo simülasyonlan ve asimptotik sonuçlardan hesaplanan doğru seçim olasılıkları ile karar verilmiştir.
References
- Atkinson, A., 1969. A Test of Discriminating Between Modes, Biometrika, 56, 337-341.
- Atkinson, A., 1970. A Method for Discriminating Between Models (with discussions), Journal of the Royal Statistical society. Ser. B, 32, 323-353.
- Bain, L. J., Englehardt, M., 1980. Probability of Correct Selection of Weibull Versus Gamma Based on Likelihood Ratio. Communications in Statistics. Series A, 9, 375- 381.
- Bemardo, J. M., 1976. Algorithm As 103: Psi (Digamma) Function, J. Roy. Statist. Soc. Ser. C, 25, 315-317.
- Cox, D. R., 1961. Tests of Separate Families of Hypotheses, Proceedings of the Fourth Berkeley Symposium in Mathematical Statistics and Probability, Berkeley, University of Califonia Press, 105-123.
- Cox, D. R., 1962. Further Results on Tests of Separate Families of Hypotheses, Journal of the Royal Statistical Society, Ser. B, 24, 406-424.
- Dumonceaux, R., Antle, C.E., 1973. Discriminating Between the Log-normal and Weibull Distribution, Technometrics, 15,923-926.
- Dyer, A. R., 1973. Discrimination Procedure for Separate Families of Hypotheses, Journal of the American Statistical Association, 68, 970-974.
- Johnson, N. L., Kotz, S., Balakrishnan, N., 1994. Continuous Univariate Distributions, Volume 1, John Wiley & Sons, Inc. USA.
- Wiens, B.L., 1999. When Log-Normal and Gamma Models Give Different Results: A Case Study, American Statistician, 53, 89-93.
- White, H., 1982. Reqularity Conditions for Cox's Test of Non-nested Hypotheses, J. Econometrics, 19, 301-318.
There are 11 citations in total.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Statistics |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | July 13, 2012 |
| Published in Issue | Year 2012 Volume: 9 Issue: 1 |
