On Transmuted Four Parameters Generalized Log-Logistic Distribution

Femi Samuel Adeyinka; Akintayo Kehinde Olapade

doi:doi:10.11648/j.ijsd.20190502.12

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On Transmuted Four Parameters Generalized Log-Logistic Distribution

Femi Samuel Adeyinka, Akintayo Kehinde Olapade

Published in International Journal of Statistical Distributions and Applications (Volume 5, Issue 2)

Received: 5 May 2019 Accepted: 5 June 2019 Published: 16 July 2019

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Abstract

In this article we transmute the four parameters generalized log-logistic distribution using quadratic rank transmutation map to develop a transmuted four parameters generalized log-logistic distribution. The quadratic rank transmutation map helps to introduce extra parameter into the baseline distribution to enhance more flexibility in the analysis of data in various disciplines such as reliability analysis in engineering, survival analysis, medicine, biological sciences, actuarial science, finance and insurance. The mathematical properties such as moments, quantile, mean, median, variance, skewness and kurtosis of this distribution are discussed. The reliability and hazard functions of the four parameters generalized log-logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the four parameters generalized log-logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density functions of the four parameters generalized log-logistic distribution are considered. The parameter estimation is done by the maximum likelihood method. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the four parameters generalized log-logistic distribution has a better goodness of fit than its parent model. We hope this model will serve as an alternative to the existing ones in fitting positive real data.

Published in	International Journal of Statistical Distributions and Applications (Volume 5, Issue 2)
DOI	10.11648/j.ijsd.20190502.12
Page(s)	32-37
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), 2019. Published by Science Publishing Group

Keywords

Log-Logistic Distribution, Reliability Function, Hazard Rate Function, Parameter Estimation, Order Statistics, Transmutation

References

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Femi Samuel Adeyinka, Akintayo Kehinde Olapade. (2019). On Transmuted Four Parameters Generalized Log-Logistic Distribution. International Journal of Statistical Distributions and Applications, 5(2), 32-37. https://doi.org/10.11648/j.ijsd.20190502.12

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ACS Style

Femi Samuel Adeyinka; Akintayo Kehinde Olapade. On Transmuted Four Parameters Generalized Log-Logistic Distribution. Int. J. Stat. Distrib. Appl. 2019, 5(2), 32-37. doi: 10.11648/j.ijsd.20190502.12

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AMA Style

Femi Samuel Adeyinka, Akintayo Kehinde Olapade. On Transmuted Four Parameters Generalized Log-Logistic Distribution. Int J Stat Distrib Appl. 2019;5(2):32-37. doi: 10.11648/j.ijsd.20190502.12

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@article{10.11648/j.ijsd.20190502.12,
  author = {Femi Samuel Adeyinka and Akintayo Kehinde Olapade},
  title = {On Transmuted Four Parameters Generalized Log-Logistic Distribution},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {5},
  number = {2},
  pages = {32-37},
  doi = {10.11648/j.ijsd.20190502.12},
  url = {https://doi.org/10.11648/j.ijsd.20190502.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20190502.12},
  abstract = {In this article we transmute the four parameters generalized log-logistic distribution using quadratic rank transmutation map to develop a transmuted four parameters generalized log-logistic distribution. The quadratic rank transmutation map helps to introduce extra parameter into the baseline distribution to enhance more flexibility in the analysis of data in various disciplines such as reliability analysis in engineering, survival analysis, medicine, biological sciences, actuarial science, finance and insurance. The mathematical properties such as moments, quantile, mean, median, variance, skewness and kurtosis of this distribution are discussed. The reliability and hazard functions of the four parameters generalized log-logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the four parameters generalized log-logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density functions of the four parameters generalized log-logistic distribution are considered. The parameter estimation is done by the maximum likelihood method. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the four parameters generalized log-logistic distribution has a better goodness of fit than its parent model. We hope this model will serve as an alternative to the existing ones in fitting positive real data.},
 year = {2019}
}

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TY  - JOUR
T1  - On Transmuted Four Parameters Generalized Log-Logistic Distribution
AU  - Femi Samuel Adeyinka
AU  - Akintayo Kehinde Olapade
Y1  - 2019/07/16
PY  - 2019
N1  - https://doi.org/10.11648/j.ijsd.20190502.12
DO  - 10.11648/j.ijsd.20190502.12
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  - 32
EP  - 37
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20190502.12
AB  - In this article we transmute the four parameters generalized log-logistic distribution using quadratic rank transmutation map to develop a transmuted four parameters generalized log-logistic distribution. The quadratic rank transmutation map helps to introduce extra parameter into the baseline distribution to enhance more flexibility in the analysis of data in various disciplines such as reliability analysis in engineering, survival analysis, medicine, biological sciences, actuarial science, finance and insurance. The mathematical properties such as moments, quantile, mean, median, variance, skewness and kurtosis of this distribution are discussed. The reliability and hazard functions of the four parameters generalized log-logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the four parameters generalized log-logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density functions of the four parameters generalized log-logistic distribution are considered. The parameter estimation is done by the maximum likelihood method. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the four parameters generalized log-logistic distribution has a better goodness of fit than its parent model. We hope this model will serve as an alternative to the existing ones in fitting positive real data.
VL  - 5
IS  - 2
ER  -

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Author Information

Femi Samuel Adeyinka

Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria
Akintayo Kehinde Olapade

Department of Mathematics, Obafemi Awolowo University, Ile-Ife, Nigeria

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APA Style

Femi Samuel Adeyinka, Akintayo Kehinde Olapade. (2019). On Transmuted Four Parameters Generalized Log-Logistic Distribution. International Journal of Statistical Distributions and Applications, 5(2), 32-37. https://doi.org/10.11648/j.ijsd.20190502.12

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ACS Style

Femi Samuel Adeyinka; Akintayo Kehinde Olapade. On Transmuted Four Parameters Generalized Log-Logistic Distribution. Int. J. Stat. Distrib. Appl. 2019, 5(2), 32-37. doi: 10.11648/j.ijsd.20190502.12

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AMA Style

Femi Samuel Adeyinka, Akintayo Kehinde Olapade. On Transmuted Four Parameters Generalized Log-Logistic Distribution. Int J Stat Distrib Appl. 2019;5(2):32-37. doi: 10.11648/j.ijsd.20190502.12

Copy | Download

@article{10.11648/j.ijsd.20190502.12,
  author = {Femi Samuel Adeyinka and Akintayo Kehinde Olapade},
  title = {On Transmuted Four Parameters Generalized Log-Logistic Distribution},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {5},
  number = {2},
  pages = {32-37},
  doi = {10.11648/j.ijsd.20190502.12},
  url = {https://doi.org/10.11648/j.ijsd.20190502.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20190502.12},
  abstract = {In this article we transmute the four parameters generalized log-logistic distribution using quadratic rank transmutation map to develop a transmuted four parameters generalized log-logistic distribution. The quadratic rank transmutation map helps to introduce extra parameter into the baseline distribution to enhance more flexibility in the analysis of data in various disciplines such as reliability analysis in engineering, survival analysis, medicine, biological sciences, actuarial science, finance and insurance. The mathematical properties such as moments, quantile, mean, median, variance, skewness and kurtosis of this distribution are discussed. The reliability and hazard functions of the four parameters generalized log-logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the four parameters generalized log-logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density functions of the four parameters generalized log-logistic distribution are considered. The parameter estimation is done by the maximum likelihood method. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the four parameters generalized log-logistic distribution has a better goodness of fit than its parent model. We hope this model will serve as an alternative to the existing ones in fitting positive real data.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - On Transmuted Four Parameters Generalized Log-Logistic Distribution
AU  - Femi Samuel Adeyinka
AU  - Akintayo Kehinde Olapade
Y1  - 2019/07/16
PY  - 2019
N1  - https://doi.org/10.11648/j.ijsd.20190502.12
DO  - 10.11648/j.ijsd.20190502.12
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  - 32
EP  - 37
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20190502.12
AB  - In this article we transmute the four parameters generalized log-logistic distribution using quadratic rank transmutation map to develop a transmuted four parameters generalized log-logistic distribution. The quadratic rank transmutation map helps to introduce extra parameter into the baseline distribution to enhance more flexibility in the analysis of data in various disciplines such as reliability analysis in engineering, survival analysis, medicine, biological sciences, actuarial science, finance and insurance. The mathematical properties such as moments, quantile, mean, median, variance, skewness and kurtosis of this distribution are discussed. The reliability and hazard functions of the four parameters generalized log-logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the four parameters generalized log-logistic distribution are established and the relationships between the probability density functions of the minimum and maximum order statistics of the parent model and the probability density functions of the four parameters generalized log-logistic distribution are considered. The parameter estimation is done by the maximum likelihood method. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using it to fit relevant data. The study is concluded by demonstrating that the four parameters generalized log-logistic distribution has a better goodness of fit than its parent model. We hope this model will serve as an alternative to the existing ones in fitting positive real data.
VL  - 5
IS  - 2
ER  -

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