Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions

Zakariya Y. Algamal

doi:doi:10.11648/j.ijsd.20150101.15

| Peer-Reviewed

Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions

Zakariya Y. Algamal

Published in International Journal of Statistical Distributions and Applications (Volume 1, Issue 1)

Received: 27 September 2015 Accepted: 8 October 2015 Published: 14 October 2015

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

Published in	International Journal of Statistical Distributions and Applications (Volume 1, Issue 1)
DOI	10.11648/j.ijsd.20150101.15
Page(s)	27-32
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Inverse Gaussian Distribution, Gamma Distribution, Ratio Maximum Likelihood, Discrimination

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.

Cite This Article

Plain Text BibTeX RIS

APA Style

Zakariya Y. Algamal. (2015). Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions. International Journal of Statistical Distributions and Applications, 1(1), 27-32. https://doi.org/10.11648/j.ijsd.20150101.15

Copy | Download

ACS Style

Zakariya Y. Algamal. Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions. Int. J. Stat. Distrib. Appl. 2015, 1(1), 27-32. doi: 10.11648/j.ijsd.20150101.15

Copy | Download

AMA Style

Zakariya Y. Algamal. Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions. Int J Stat Distrib Appl. 2015;1(1):27-32. doi: 10.11648/j.ijsd.20150101.15

Copy | Download

@article{10.11648/j.ijsd.20150101.15,
  author = {Zakariya Y. Algamal},
  title = {Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {1},
  number = {1},
  pages = {27-32},
  doi = {10.11648/j.ijsd.20150101.15},
  url = {https://doi.org/10.11648/j.ijsd.20150101.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20150101.15},
  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.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions
AU  - Zakariya Y. Algamal
Y1  - 2015/10/14
PY  - 2015
N1  - https://doi.org/10.11648/j.ijsd.20150101.15
DO  - 10.11648/j.ijsd.20150101.15
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 27
EP  - 32
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20150101.15
AB  - 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.
VL  - 1
IS  - 1
ER  -

Copy | Download

Author Information

Zakariya Y. Algamal

Department of Statistics and Informatics, Computer science and Mathematical College, Mosul University, Mosul, Iraq.

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Zakariya Y. Algamal. (2015). Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions. International Journal of Statistical Distributions and Applications, 1(1), 27-32. https://doi.org/10.11648/j.ijsd.20150101.15

Copy | Download

ACS Style

Zakariya Y. Algamal. Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions. Int. J. Stat. Distrib. Appl. 2015, 1(1), 27-32. doi: 10.11648/j.ijsd.20150101.15

Copy | Download

AMA Style

Zakariya Y. Algamal. Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions. Int J Stat Distrib Appl. 2015;1(1):27-32. doi: 10.11648/j.ijsd.20150101.15

Copy | Download

@article{10.11648/j.ijsd.20150101.15,
  author = {Zakariya Y. Algamal},
  title = {Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {1},
  number = {1},
  pages = {27-32},
  doi = {10.11648/j.ijsd.20150101.15},
  url = {https://doi.org/10.11648/j.ijsd.20150101.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20150101.15},
  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.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Using Maximum Likelihood Ratio Test to Discriminate Between the Inverse Gaussian and Gamma Distributions
AU  - Zakariya Y. Algamal
Y1  - 2015/10/14
PY  - 2015
N1  - https://doi.org/10.11648/j.ijsd.20150101.15
DO  - 10.11648/j.ijsd.20150101.15
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 27
EP  - 32
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20150101.15
AB  - 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.
VL  - 1
IS  - 1
ER  -

Copy | Download