On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application

Adeyinka Femi Samuel; Olapade Akintayo Kehinde

doi:doi:10.11648/j.engmath.20190301.14

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On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application

Adeyinka Femi Samuel, Olapade Akintayo Kehinde

Published in Engineering Mathematics (Volume 3, Issue 1)

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

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Abstract

In this article we transmute the type I half logistic distribution using quadratic rank transmutation map to develop a transmuted type I half logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its 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 transmuted type I half logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the transmuted type I half 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 half 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 it to fit relevant data. The study is concluded by demonstrating that the transmuted type I half 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 the literature in fitting positive real data.

Published in	Engineering Mathematics (Volume 3, Issue 1)
DOI	10.11648/j.engmath.20190301.14
Page(s)	13-18
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

Half logistic Distribution, Reliability Function, Hazard Rate Function, Parameter Estimation, Order Statistics, Transmutation

References

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[2]	Balakrishnan, N., and Puthenpura, S. (1986). Best linear unbiased estimators of location and scale parameters of the half logistic distribution. Journal of Statistical Computation and Simulation. Vol 4. Pp 193-204.
[3]	Olapade, A. K. (2014), The Type I Generalized Half Logistic Distribution. JIRSS. Vol. 13, No. 1, pp 69-82.
[4]	David, H. A. (1970) Order Statistics. New York: Wiley Inter-science series.
[5]	Usman, R. M, Haq, M. A and Talib, J (2017). Kumaraswamy Half-Logistic Distribution: Properties and Applications. Journal of Statistics Applications and Probability. No 3, 597-609.
[6]	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.
[7]	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.
[8]	Bjerkedal, T (1960). Acquisition of Resistance in Guinea Pigs infected with Different Doses of Virulent Tubercle Bacilli, American Journal of Hygiene, 72, 130-148.
[9]	Haq, M. A, (2016). Kumaraswamy Exponentiated Inverse Rayleigh Distribution, Mathematical Theory and Modeling, 6, 93-104.
[10]	Merovci, F., Alizadeh, M., and Hamedani, G. (2016). Another Generalized Transmuted Family of Distributions: Properties and Applications. Austrian Journal of Statistics. 45, 71-93.
[11]	Merovci, F. (2014). Transmuted Generalized Rayleigh Distribution. Journal of Statistics Applications and Probability. 3(1), 9-20.
[12]	Merovci, F., Elbatal, I. (2014). Transmuted Lindley-geometric Distribution and its Applications. Journal of Statistics Applications and Probability. 3(1), 77-91.
[13]	Merovci, F., Puka, L. (2014). Transmuted Pareto Distribution. Probstat. 7, 1-11.
[14]	Olapade, A. K. (2003), On Characterizations of the Half Logistic Distri-bution. InterStat, February Issue, 2, http://interstat.stat.vt.edu/InterStat/ARTICLES/2003articles/F06002.pdf.
[15]	Rahman M. M, Al-Zahrani B, Shahbaz M. Q (2018). A general transmuted family of distributions. Pak J Stat Oper Res 14: 451-469.
[16]	Shaw, W. T, and Buckley, I. R. (2009). Alchemy of Probability Distributions: Beyond Gram-Charlier and Cornish -Fisher Expansions, and Skewed- kurtotic Normal Distribution from a Rank Transmutation Map. arxivpreprint arxiv: 0901.0434.

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Adeyinka Femi Samuel, Olapade Akintayo Kehinde. (2019). On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application. Engineering Mathematics, 3(1), 13-18. https://doi.org/10.11648/j.engmath.20190301.14

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Adeyinka Femi Samuel; Olapade Akintayo Kehinde. On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application. Eng. Math. 2019, 3(1), 13-18. doi: 10.11648/j.engmath.20190301.14

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AMA Style

Adeyinka Femi Samuel, Olapade Akintayo Kehinde. On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application. Eng Math. 2019;3(1):13-18. doi: 10.11648/j.engmath.20190301.14

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@article{10.11648/j.engmath.20190301.14,
  author = {Adeyinka Femi Samuel and Olapade Akintayo Kehinde},
  title = {On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application},
  journal = {Engineering Mathematics},
  volume = {3},
  number = {1},
  pages = {13-18},
  doi = {10.11648/j.engmath.20190301.14},
  url = {https://doi.org/10.11648/j.engmath.20190301.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.engmath.20190301.14},
  abstract = {In this article we transmute the type I half logistic distribution using quadratic rank transmutation map to develop a transmuted type I half logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its 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 transmuted type I half logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the transmuted type I half 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 half 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 it to fit relevant data. The study is concluded by demonstrating that the transmuted type I half 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 the literature in fitting positive real data.},
 year = {2019}
}

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TY  - JOUR
T1  - On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application
AU  - Adeyinka Femi Samuel
AU  - Olapade Akintayo Kehinde
Y1  - 2019/07/16
PY  - 2019
N1  - https://doi.org/10.11648/j.engmath.20190301.14
DO  - 10.11648/j.engmath.20190301.14
T2  - Engineering Mathematics
JF  - Engineering Mathematics
JO  - Engineering Mathematics
SP  - 13
EP  - 18
PB  - Science Publishing Group
SN  - 2640-088X
UR  - https://doi.org/10.11648/j.engmath.20190301.14
AB  - In this article we transmute the type I half logistic distribution using quadratic rank transmutation map to develop a transmuted type I half logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its 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 transmuted type I half logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the transmuted type I half 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 half 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 it to fit relevant data. The study is concluded by demonstrating that the transmuted type I half 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 the literature in fitting positive real data.
VL  - 3
IS  - 1
ER  -

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Author Information

Adeyinka Femi Samuel

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

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

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APA Style

Adeyinka Femi Samuel, Olapade Akintayo Kehinde. (2019). On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application. Engineering Mathematics, 3(1), 13-18. https://doi.org/10.11648/j.engmath.20190301.14

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ACS Style

Adeyinka Femi Samuel; Olapade Akintayo Kehinde. On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application. Eng. Math. 2019, 3(1), 13-18. doi: 10.11648/j.engmath.20190301.14

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AMA Style

Adeyinka Femi Samuel, Olapade Akintayo Kehinde. On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application. Eng Math. 2019;3(1):13-18. doi: 10.11648/j.engmath.20190301.14

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@article{10.11648/j.engmath.20190301.14,
  author = {Adeyinka Femi Samuel and Olapade Akintayo Kehinde},
  title = {On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application},
  journal = {Engineering Mathematics},
  volume = {3},
  number = {1},
  pages = {13-18},
  doi = {10.11648/j.engmath.20190301.14},
  url = {https://doi.org/10.11648/j.engmath.20190301.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.engmath.20190301.14},
  abstract = {In this article we transmute the type I half logistic distribution using quadratic rank transmutation map to develop a transmuted type I half logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its 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 transmuted type I half logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the transmuted type I half 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 half 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 it to fit relevant data. The study is concluded by demonstrating that the transmuted type I half 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 the literature in fitting positive real data.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - On the Flexibility of a Transmuted Type I Generalized Half Logistic Distribution with Application
AU  - Adeyinka Femi Samuel
AU  - Olapade Akintayo Kehinde
Y1  - 2019/07/16
PY  - 2019
N1  - https://doi.org/10.11648/j.engmath.20190301.14
DO  - 10.11648/j.engmath.20190301.14
T2  - Engineering Mathematics
JF  - Engineering Mathematics
JO  - Engineering Mathematics
SP  - 13
EP  - 18
PB  - Science Publishing Group
SN  - 2640-088X
UR  - https://doi.org/10.11648/j.engmath.20190301.14
AB  - In this article we transmute the type I half logistic distribution using quadratic rank transmutation map to develop a transmuted type I half logistic distribution. The quadratic rank transmutation map enables the introduction of extra parameter into its 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 transmuted type I half logistic distribution are obtained. The probability density functions of the minimum and maximum order statistics of the transmuted type I half 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 half 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 it to fit relevant data. The study is concluded by demonstrating that the transmuted type I half 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 the literature in fitting positive real data.
VL  - 3
IS  - 1
ER  -

Copy | Download