The Gamma1-Epsilon Distribution: Its Statistical Properties and Applications

Isaac Esbond Gongsin; Funmilayo Westnand Oshogboye Saporu

doi:doi:10.11648/j.ijsd.20200604.11

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The Gamma1-Epsilon Distribution: Its Statistical Properties and Applications

Isaac Esbond Gongsin, Funmilayo Westnand Oshogboye Saporu

Published in International Journal of Statistical Distributions and Applications (Volume 6, Issue 4)

Received: 4 September 2020 Accepted: 24 September 2020 Published: 17 October 2020

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Abstract

The construction of new probability distributions is an active field of research. It provides the opportunity for dynamic system modelers to choose the best model from a plethora of probability distributions that provide good fit to some data set using model selection criteria. In this study a new probability distribution function is constructed based on the gamma type-I generator, called the gamma1-epsilon distribution. Its statistical properties are described. The area under the curve of the density plots is shown through numerical integration to equal one with very minimal error margins. The density plots show shapes that are similar to many standard lifetime distributions. This implies that it is flexible to assume different shapes that can model many different random phenomena. Its hazard rate function plots also show varying shapes, namely J-shaped and bathtub-shaped, that indicate its possible use as a model for the study of survival life of biological organisms, electrical and mechanical components. The distribution is applied to the time to death of women with temporary disabilities, remission time of cancer patients and wind speed. The fits to these datasets are good with precise parameter estimates. Its compatibility with data from these dissimilar processes shows it holds a good prospect for real life application.

Published in	International Journal of Statistical Distributions and Applications (Volume 6, Issue 4)
DOI	10.11648/j.ijsd.20200604.11
Page(s)	65-70
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), 2024. Published by Science Publishing Group

Keywords

Gamma-G Family, Epsilon Distribution, Hazard Rate Function, Survival Time, Remission Time, Wind Energy

References

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[2]	Alzaatreh A, Lee C, & Famoye F (2013b). “A New Method for Generating Families of Continuous Distributions.” Metron, 71, 63–79. doi: 10.1007/s40300-013-0007-y.
[3]	Bourguignon, M., Silva, R. B. & Cordeiro, G. M. (2014) The Weibull-G family of probability distributions. Journal of Data Science, 12, 53-68.
[4]	Cordeiro, G. M., Ortega, E. M. & da Cunha, D. C. C. (2013) The exponentiated generalized class of distributions. Journal of Data Science, 11, 1-27.
[5]	Dombi, J., J´on´as, T. & T´oth, Z., E. (2018) The Epsilon Probability Distribution and its Application in Reliability Theory. Acta Polytechnica Hungarica, Vol. 15, No. 1, pp 197-216.
[6]	Eugene, N., Lee, C. & Famoye, F. (2002) Beta-normal distribution and its applications. Communication in Statistics-Theory and Methods, 31 (4), 497-512.
[7]	Forbes, C., Evans, M., Hastings, N. & Peacock, B. (2011) Statistical Distributions, Fourth Edition, New Jersey, John Wiley & Sons, Inc.
[8]	Gongsin, I. E. & Saporu, F. W. O. (2019a) On the Construction of Kumaraswamy-Epsilon Distribution with Applications, International Journal of Science and Research (IJSR), Volume 8 Issue 11, November 2019. www.ijsr.net.
[9]	Gongsin, I. E. & Saporu, F. W. O. (2019b) The Exponentiated-Epsilon Distribution: its Properties and Applications, International Journal of Science and Research (IJSR), Volume 8 Issue 12, December 2019. www.ijsr.net.
[10]	Gupta, R. C., Gupta, P. L. & Gupta, R. D. (1998) Modeling Failure Time Data by Lehmann Alternatives. Comm. Statistical Theory and Methods. 27, 887-904.
[11]	Johnson, N. L., Kotz, S., & Balakrishnan (1994) Continuous Univariate Distributions, Vol. 1, Second Edition, New York, John Wiley & Sons, Inc.
[12]	Johnson, N. L., Kotz, S., & Balakrishnan (1995) Continuous Univariate Distributions, Vol. 2, Second Edition, New York, John Wiley & Sons, Inc.
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[14]	Ristic, M. M. & Balakrishnan, N. (2012) The Gamma Exponentiated Exponential Distribution, Journal of Statistical Computation and Simulation, 82, 1191–1206. doi: 10.1080/00949655.2011.574633.
[15]	Tahir, M. H., Cordeiro, G. M., Mansoor, M., Zubair, M. and Alizadeh, M. (2014) The Weibull-Dagum Distribution: Properties and Applications, Communication in Statistics- Theory and Methods, pp 1-28, DOI: 10.1080/03610926.2014.983610.
[16]	Torabi, H. & Montazeri, N. H. (2012) The Gamma-Uniform Distribution and Its Applications, Kybernetika, 48, 16–30.
[17]	Zografos, K. & Balakrishnan, N. (2009) On families of beta and generalized gamma generated distributions and associated inference. Statistical Methodology, 6, 344-362.

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APA Style

Isaac Esbond Gongsin, Funmilayo Westnand Oshogboye Saporu. (2020). The Gamma1-Epsilon Distribution: Its Statistical Properties and Applications. International Journal of Statistical Distributions and Applications, 6(4), 65-70. https://doi.org/10.11648/j.ijsd.20200604.11

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ACS Style

Isaac Esbond Gongsin; Funmilayo Westnand Oshogboye Saporu. The Gamma1-Epsilon Distribution: Its Statistical Properties and Applications. Int. J. Stat. Distrib. Appl. 2020, 6(4), 65-70. doi: 10.11648/j.ijsd.20200604.11

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AMA Style

Isaac Esbond Gongsin, Funmilayo Westnand Oshogboye Saporu. The Gamma1-Epsilon Distribution: Its Statistical Properties and Applications. Int J Stat Distrib Appl. 2020;6(4):65-70. doi: 10.11648/j.ijsd.20200604.11

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@article{10.11648/j.ijsd.20200604.11,
  author = {Isaac Esbond Gongsin and Funmilayo Westnand Oshogboye Saporu},
  title = {The Gamma1-Epsilon Distribution: Its Statistical Properties and Applications},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {6},
  number = {4},
  pages = {65-70},
  doi = {10.11648/j.ijsd.20200604.11},
  url = {https://doi.org/10.11648/j.ijsd.20200604.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20200604.11},
  abstract = {The construction of new probability distributions is an active field of research. It provides the opportunity for dynamic system modelers to choose the best model from a plethora of probability distributions that provide good fit to some data set using model selection criteria. In this study a new probability distribution function is constructed based on the gamma type-I generator, called the gamma1-epsilon distribution. Its statistical properties are described. The area under the curve of the density plots is shown through numerical integration to equal one with very minimal error margins. The density plots show shapes that are similar to many standard lifetime distributions. This implies that it is flexible to assume different shapes that can model many different random phenomena. Its hazard rate function plots also show varying shapes, namely J-shaped and bathtub-shaped, that indicate its possible use as a model for the study of survival life of biological organisms, electrical and mechanical components. The distribution is applied to the time to death of women with temporary disabilities, remission time of cancer patients and wind speed. The fits to these datasets are good with precise parameter estimates. Its compatibility with data from these dissimilar processes shows it holds a good prospect for real life application.},
 year = {2020}
}

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TY  - JOUR
T1  - The Gamma1-Epsilon Distribution: Its Statistical Properties and Applications
AU  - Isaac Esbond Gongsin
AU  - Funmilayo Westnand Oshogboye Saporu
Y1  - 2020/10/17
PY  - 2020
N1  - https://doi.org/10.11648/j.ijsd.20200604.11
DO  - 10.11648/j.ijsd.20200604.11
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  - 65
EP  - 70
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20200604.11
AB  - The construction of new probability distributions is an active field of research. It provides the opportunity for dynamic system modelers to choose the best model from a plethora of probability distributions that provide good fit to some data set using model selection criteria. In this study a new probability distribution function is constructed based on the gamma type-I generator, called the gamma1-epsilon distribution. Its statistical properties are described. The area under the curve of the density plots is shown through numerical integration to equal one with very minimal error margins. The density plots show shapes that are similar to many standard lifetime distributions. This implies that it is flexible to assume different shapes that can model many different random phenomena. Its hazard rate function plots also show varying shapes, namely J-shaped and bathtub-shaped, that indicate its possible use as a model for the study of survival life of biological organisms, electrical and mechanical components. The distribution is applied to the time to death of women with temporary disabilities, remission time of cancer patients and wind speed. The fits to these datasets are good with precise parameter estimates. Its compatibility with data from these dissimilar processes shows it holds a good prospect for real life application.
VL  - 6
IS  - 4
ER  -

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Author Information

Isaac Esbond Gongsin

Department of Mathematical Sciences, University of Maiduguri, Maiduguri, Nigeria
Funmilayo Westnand Oshogboye Saporu

National Mathematical Centre, Kwali, Abuja, Nigeria

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Plain Text BibTeX RIS

APA Style

Isaac Esbond Gongsin, Funmilayo Westnand Oshogboye Saporu. (2020). The Gamma1-Epsilon Distribution: Its Statistical Properties and Applications. International Journal of Statistical Distributions and Applications, 6(4), 65-70. https://doi.org/10.11648/j.ijsd.20200604.11

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ACS Style

Isaac Esbond Gongsin; Funmilayo Westnand Oshogboye Saporu. The Gamma1-Epsilon Distribution: Its Statistical Properties and Applications. Int. J. Stat. Distrib. Appl. 2020, 6(4), 65-70. doi: 10.11648/j.ijsd.20200604.11

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AMA Style

Isaac Esbond Gongsin, Funmilayo Westnand Oshogboye Saporu. The Gamma1-Epsilon Distribution: Its Statistical Properties and Applications. Int J Stat Distrib Appl. 2020;6(4):65-70. doi: 10.11648/j.ijsd.20200604.11

Copy | Download

@article{10.11648/j.ijsd.20200604.11,
  author = {Isaac Esbond Gongsin and Funmilayo Westnand Oshogboye Saporu},
  title = {The Gamma1-Epsilon Distribution: Its Statistical Properties and Applications},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {6},
  number = {4},
  pages = {65-70},
  doi = {10.11648/j.ijsd.20200604.11},
  url = {https://doi.org/10.11648/j.ijsd.20200604.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20200604.11},
  abstract = {The construction of new probability distributions is an active field of research. It provides the opportunity for dynamic system modelers to choose the best model from a plethora of probability distributions that provide good fit to some data set using model selection criteria. In this study a new probability distribution function is constructed based on the gamma type-I generator, called the gamma1-epsilon distribution. Its statistical properties are described. The area under the curve of the density plots is shown through numerical integration to equal one with very minimal error margins. The density plots show shapes that are similar to many standard lifetime distributions. This implies that it is flexible to assume different shapes that can model many different random phenomena. Its hazard rate function plots also show varying shapes, namely J-shaped and bathtub-shaped, that indicate its possible use as a model for the study of survival life of biological organisms, electrical and mechanical components. The distribution is applied to the time to death of women with temporary disabilities, remission time of cancer patients and wind speed. The fits to these datasets are good with precise parameter estimates. Its compatibility with data from these dissimilar processes shows it holds a good prospect for real life application.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - The Gamma1-Epsilon Distribution: Its Statistical Properties and Applications
AU  - Isaac Esbond Gongsin
AU  - Funmilayo Westnand Oshogboye Saporu
Y1  - 2020/10/17
PY  - 2020
N1  - https://doi.org/10.11648/j.ijsd.20200604.11
DO  - 10.11648/j.ijsd.20200604.11
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  - 65
EP  - 70
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20200604.11
AB  - The construction of new probability distributions is an active field of research. It provides the opportunity for dynamic system modelers to choose the best model from a plethora of probability distributions that provide good fit to some data set using model selection criteria. In this study a new probability distribution function is constructed based on the gamma type-I generator, called the gamma1-epsilon distribution. Its statistical properties are described. The area under the curve of the density plots is shown through numerical integration to equal one with very minimal error margins. The density plots show shapes that are similar to many standard lifetime distributions. This implies that it is flexible to assume different shapes that can model many different random phenomena. Its hazard rate function plots also show varying shapes, namely J-shaped and bathtub-shaped, that indicate its possible use as a model for the study of survival life of biological organisms, electrical and mechanical components. The distribution is applied to the time to death of women with temporary disabilities, remission time of cancer patients and wind speed. The fits to these datasets are good with precise parameter estimates. Its compatibility with data from these dissimilar processes shows it holds a good prospect for real life application.
VL  - 6
IS  - 4
ER  -

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