Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions
International Journal of Statistical Distributions and Applications
Volume 1, Issue 1, September 2015, Pages: 27-32
Received: Sep. 27, 2015; Accepted: Oct. 8, 2015; Published: Oct. 14, 2015
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Author
Zakariya Y. Algamal, Department of Statistics and Informatics, Computer science and Mathematical College, Mosul University, Mosul, Iraq.
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Abstract
One of the problems that appear in reliability and survival analysis is how we choose the best distribution that fitted the data. Sometimes we see that the handle data have two fitted distributions. Both inverse Gaussian and gamma distributions have been used among many well-known failure time distributions with positively skewed data. The problem of selecting between them is considered. We used the logarithm of maximum likelihood ratio as a test for discriminating between these two distributions. The test has been carried out on six different data sets.
Keywords
Inverse Gaussian Distribution, Gamma Distribution, Ratio Maximum Likelihood, Discrimination
To cite this article
Zakariya Y. Algamal, Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions, International Journal of Statistical Distributions and Applications. Vol. 1, No. 1, 2015, pp. 27-32. doi: 10.11648/j.ijsd.20150101.15
Copyright
Copyright © 2015 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
A. Atkinson, A Test of Discriminating between Models, Biometrica, 56 (1969), 337-341.
[2]
A. Atkinson, A Method for Discriminating between Models (with Discussion), Journal of Royal Statistical Society, Ser. B, 32(1970), 323-353.
[3]
R. S. Chhikara and J. L. Folks, The Inverse Gaussian Distribution as a Lifetime Model, Technometrics, 19(1977), 461-468.
[4]
R. S. Chhikara and J. L. Folks, The Inverse Gaussian Distribution and Its Statistical Application- A Review (with Discussion), Journal of Royal Statistical Society, Ser. B, 40(1978), 263-289.
[5]
R. S. Chhikara and J. L. Folks, Inverse Gaussian Distribution: Theory, Methodology, and Applications, Marcel Dekker, Inc., New York, 1988.
[6]
R. Dumonceaux, C. E. Antle and G. Hass, Likelihood Ration Test for Discriminating between Two Models with Unknown Location and Scale Parameters, Technometrics, 15(1973), 19-31.
[7]
R. Dumonceaux, C. E. Antle, Discriminating between the Log-Normal and Weibull Distribution, Technometrics, 15(1973), 923-926.
[8]
M. C. Gacula and J. J. Kubala, Statistical Models for Shelf Life Failures, Journal Food Science, 40(1975), 404-409.
[9]
N. L. Johnson and S. Kotz, Continuous Univariate Distributions-1, 2nd Ed., Wiley, New York, 1995.
[10]
D. Kundua and A. Manglick, Discriminating between the Log-Normal and Gamma Distributions, Noval Research Logistic, 51(2004), 893-905.
[11]
D. Kundua and A. Manglick, Discriminating between the Log-Normal and Gamma Distributions, Journal of Applied Statistical Sciences, 14(2005), 175-187.
[12]
S. Kumagai, I. Matsunaga, K. Sugimoto,Y. Kusaka and T. Shirakawa, Assessment of occupational Exposures to Industrial Hazardous Substances (ІІІ) on the Frequency Distribution of daily Exposure Averages (8 hr TWA), Japanese Journal of Industrial Heath, 31(1989), 216-226.
[13]
S. Kumagai, I. Matsunaga, Changes in the Distribution of Short-Term Exposure Concentration with Different Averaging times, American Industrial Hygiene Association Journal, 54(1995), 24-31.
[14]
J. F. Lawless, Statistical Models and Methods for Lifetime Data, 2nd Ed., Wiley, New Jersey, 2003.
[15]
M. C. K. Tweedie, Statistical Properties of Inverse Gaussian Distribution. І, Annals Mathematical Statistics, 28(1957a), 362-377.
[16]
M. C. K. Tweedie, Statistical Properties of Inverse Gaussian Distribution. П, Annals Mathematical Statistics, 28(1957b), 696-705.
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