On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application

Femi Samuel Adeyinka

doi:doi:10.11648/j.ijtam.20190502.12

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On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application

Femi Samuel Adeyinka

Published in International Journal of Theoretical and Applied Mathematics (Volume 5, Issue 2)

Received: 9 August 2019 Accepted: 29 August 2019 Published: 16 September 2019

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Abstract

Transmutation of baseline distributions has gained popularity in the last decade and many authors have studied the some transmuted distributions such as exponential, Weilbul, gamma, Pareto, normal and many more. This article will focus on the transmutation of type I generalized logistic distribution using quadratic rank transmutation map to develop a transmuted type I generalized logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its parent model to enhance more flexibility in the analysis of data in various disciplines such as biological sciences, actuarial science, finance and insurance. The graphs of the probability density function (pdf) and cumulative distribution function (cdf) of the model for different values of parameters are illustrated respectively. The mathematical properties such as moment generating function, quantile, median and characteristic function of this distribution are discussed. The probability density functions of the minimum and maximum order statistics of the transmuted type I generalized 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 function of the transmuted type I generalized logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using the model to fit relevant data. The study is concluded by demonstrating the performance of transmuted type I generalized logistic distribution over its parent model.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 5, Issue 2)
DOI	10.11648/j.ijtam.20190502.12
Page(s)	31-36
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

Logistic Distribution, Parameter Estimation, Order Statistics, Transmutation

References

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[3]	Aryal, G. R, and Tsokos, C. P. (2009). On the transmuted extreme value distribution with application. Nonlinear Analysis: Theory, Methods and Application.71 (12), el401-el407.
[4]	Aryal, G. R, and Tsokos, C. P. (2011). Transmuted Weilbull distribution: A generalization of Weilbull probability distribution. European Journal of Pure and Applied Mathematics. 4 (2), 89-102.
[5]	Aryal, G. R. (2013). Transmuted log-logistic distribution. Journal of Statistics Applications and probability. 2 (1), 11-20.
[6]	Merovci, F., Alizadeh, M., and Hamedani, G. (2016). Another Generalized Transmuted Family of Distributions: Properties and Applications. Austrian Journal of Statistics. 45, 71-93.
[7]	Merovci, F., Elbatal, I. (2014). Transmuted Lindley-geometric Distribution and its Applications. Journal of Statistics Applications and Probability. 3 (1), 77-91.
[8]	Merovci, F. (2014). Transmuted Generalized Rayleigh Distribution. Journal of Statistics Applications and Probability. 3 (1), 9-20.
[9]	Merovci, F., Puka, L. (2014). Transmuted Pareto Distribution. Probstat.7, 1-11.
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[11]	AL-Kadim, K. A. and Mohammed, M. H. (2017). The cubic transmuted Weibull distribution. Journal of University of Babylon, 3: 862876.
[12]	Granzoto, D. C. T., Louzada, F., and Balakrishnan, N. (2017). Cubic rank transmuted distributions: Inferential issues and applications. Journal of statistical Computation and Simulation.
[13]	Rahman M. M, Al-Zahrani B, Shahbaz M. Q (2018). A general transmuted family of distributions. Pak J Stat Oper Res 14: 451-469.
[14]	Adeyinka F. S, and Olapade, A. K. (2019). On Transmuted Four Parameters Generalized Log-Logistic Distribution. International Journal of Statistical Distributions and Applications. 5 (2): 32-37.
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[17]	Adeyinka F. S. (2019). On the Performance of Transmuted Logistic Distribution: Statistical Properties and Application. Budapest International Research in Exact Sciences (BirEx) Journal. 1 (3): 34-42.
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Femi Samuel Adeyinka. (2019). On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application. International Journal of Theoretical and Applied Mathematics, 5(2), 31-36. https://doi.org/10.11648/j.ijtam.20190502.12

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Femi Samuel Adeyinka. On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application. Int. J. Theor. Appl. Math. 2019, 5(2), 31-36. doi: 10.11648/j.ijtam.20190502.12

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AMA Style

Femi Samuel Adeyinka. On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application. Int J Theor Appl Math. 2019;5(2):31-36. doi: 10.11648/j.ijtam.20190502.12

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@article{10.11648/j.ijtam.20190502.12,
  author = {Femi Samuel Adeyinka},
  title = {On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {5},
  number = {2},
  pages = {31-36},
  doi = {10.11648/j.ijtam.20190502.12},
  url = {https://doi.org/10.11648/j.ijtam.20190502.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20190502.12},
  abstract = {Transmutation of baseline distributions has gained popularity in the last decade and many authors have studied the some transmuted distributions such as exponential, Weilbul, gamma, Pareto, normal and many more. This article will focus on the transmutation of type I generalized logistic distribution using quadratic rank transmutation map to develop a transmuted type I generalized logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its parent model to enhance more flexibility in the analysis of data in various disciplines such as biological sciences, actuarial science, finance and insurance. The graphs of the probability density function (pdf) and cumulative distribution function (cdf) of the model for different values of parameters are illustrated respectively. The mathematical properties such as moment generating function, quantile, median and characteristic function of this distribution are discussed. The probability density functions of the minimum and maximum order statistics of the transmuted type I generalized 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 function of the transmuted type I generalized logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using the model to fit relevant data. The study is concluded by demonstrating the performance of transmuted type I generalized logistic distribution over its parent model.},
 year = {2019}
}

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TY  - JOUR
T1  - On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application
AU  - Femi Samuel Adeyinka
Y1  - 2019/09/16
PY  - 2019
N1  - https://doi.org/10.11648/j.ijtam.20190502.12
DO  - 10.11648/j.ijtam.20190502.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 31
EP  - 36
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20190502.12
AB  - Transmutation of baseline distributions has gained popularity in the last decade and many authors have studied the some transmuted distributions such as exponential, Weilbul, gamma, Pareto, normal and many more. This article will focus on the transmutation of type I generalized logistic distribution using quadratic rank transmutation map to develop a transmuted type I generalized logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its parent model to enhance more flexibility in the analysis of data in various disciplines such as biological sciences, actuarial science, finance and insurance. The graphs of the probability density function (pdf) and cumulative distribution function (cdf) of the model for different values of parameters are illustrated respectively. The mathematical properties such as moment generating function, quantile, median and characteristic function of this distribution are discussed. The probability density functions of the minimum and maximum order statistics of the transmuted type I generalized 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 function of the transmuted type I generalized logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using the model to fit relevant data. The study is concluded by demonstrating the performance of transmuted type I generalized logistic distribution over its parent model.
VL  - 5
IS  - 2
ER  -

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Author Information

Femi Samuel Adeyinka

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

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Plain Text BibTeX RIS

APA Style

Femi Samuel Adeyinka. (2019). On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application. International Journal of Theoretical and Applied Mathematics, 5(2), 31-36. https://doi.org/10.11648/j.ijtam.20190502.12

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ACS Style

Femi Samuel Adeyinka. On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application. Int. J. Theor. Appl. Math. 2019, 5(2), 31-36. doi: 10.11648/j.ijtam.20190502.12

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AMA Style

Femi Samuel Adeyinka. On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application. Int J Theor Appl Math. 2019;5(2):31-36. doi: 10.11648/j.ijtam.20190502.12

Copy | Download

@article{10.11648/j.ijtam.20190502.12,
  author = {Femi Samuel Adeyinka},
  title = {On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {5},
  number = {2},
  pages = {31-36},
  doi = {10.11648/j.ijtam.20190502.12},
  url = {https://doi.org/10.11648/j.ijtam.20190502.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20190502.12},
  abstract = {Transmutation of baseline distributions has gained popularity in the last decade and many authors have studied the some transmuted distributions such as exponential, Weilbul, gamma, Pareto, normal and many more. This article will focus on the transmutation of type I generalized logistic distribution using quadratic rank transmutation map to develop a transmuted type I generalized logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its parent model to enhance more flexibility in the analysis of data in various disciplines such as biological sciences, actuarial science, finance and insurance. The graphs of the probability density function (pdf) and cumulative distribution function (cdf) of the model for different values of parameters are illustrated respectively. The mathematical properties such as moment generating function, quantile, median and characteristic function of this distribution are discussed. The probability density functions of the minimum and maximum order statistics of the transmuted type I generalized 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 function of the transmuted type I generalized logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using the model to fit relevant data. The study is concluded by demonstrating the performance of transmuted type I generalized logistic distribution over its parent model.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application
AU  - Femi Samuel Adeyinka
Y1  - 2019/09/16
PY  - 2019
N1  - https://doi.org/10.11648/j.ijtam.20190502.12
DO  - 10.11648/j.ijtam.20190502.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 31
EP  - 36
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20190502.12
AB  - Transmutation of baseline distributions has gained popularity in the last decade and many authors have studied the some transmuted distributions such as exponential, Weilbul, gamma, Pareto, normal and many more. This article will focus on the transmutation of type I generalized logistic distribution using quadratic rank transmutation map to develop a transmuted type I generalized logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its parent model to enhance more flexibility in the analysis of data in various disciplines such as biological sciences, actuarial science, finance and insurance. The graphs of the probability density function (pdf) and cumulative distribution function (cdf) of the model for different values of parameters are illustrated respectively. The mathematical properties such as moment generating function, quantile, median and characteristic function of this distribution are discussed. The probability density functions of the minimum and maximum order statistics of the transmuted type I generalized 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 function of the transmuted type I generalized logistic distribution are considered. The parameter estimation is done by the method of maximum likelihood estimation. The flexibility of the model in statistical data analysis and its applicability is demonstrated by using the model to fit relevant data. The study is concluded by demonstrating the performance of transmuted type I generalized logistic distribution over its parent model.
VL  - 5
IS  - 2
ER  -

Copy | Download