On Modelling of Infant Mortality Rate in Nigeria with Exponentiated Cubic Transmuted Exponential Distribution

Femi Samuel Adeyinka

doi:doi:10.11648/j.ijdst.20200601.13

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On Modelling of Infant Mortality Rate in Nigeria with Exponentiated Cubic Transmuted Exponential Distribution

Femi Samuel Adeyinka

Published in International Journal on Data Science and Technology (Volume 6, Issue 1)

Received: 11 December 2019 Accepted: 25 December 2019 Published: 6 January 2020

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Abstract

The idea of introducing extra parameters into the existing model in enhancing more flexibility is a giant stride in research. Transmutation map technique is one of the recent methods of introducing additional properties such as skewness, kurtosis and bimodality into the baseline distribution. In this article, a new exponentiated exponential distribution is developed using transmutation map. This model is referred to as exponentiated cubic transmuted exponential distribution (ECTED). The mathematical properties of the model which include survival function, hazard function, central and non- central moments, moment generating function and order statistics are established. The inherent parameters in the model are estimated using method of maximum likelihood estimation (MLE). The system of equations obtained is non-linear in parameters therefore non-linear optimization algorithms are implemented in R package. The distribution is used to model data on infant mortality rate in Nigeria. The performance of the subject model is compared with its baseline exponential distribution (ED), transmuted exponential distribution (TED), exponentiated transmuted exponential distribution (ETED) and cubic transmuted exponential distribution (CTED) using Akaike Information criterion (AIC), Corrected Akaike Information criterion (AICC) and Bayesian Information criterion (BIC). It is hope that this will serve as an alternative distribution in modelling complex real life data arising from various fields of human endeavors.

Published in	International Journal on Data Science and Technology (Volume 6, Issue 1)
DOI	10.11648/j.ijdst.20200601.13
Page(s)	16-22
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), 2020. Published by Science Publishing Group

Keywords

Exponentiated, Cubic, Infant Mortality, Reliability Function, Hazard Rate Function, Parameter Estimation, Order Statistics, Transmutation

References

[1]	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.
[2]	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.
[3]	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.
[4]	Aryal, G. R. (2013). Transmuted log-logistic distribution. Journal of Statistics Applications and probability. 2 (1), 11-20.
[5]	Merovci, F., Alizadeh, M., and Hamedani, G. (2016). Another Generalized Transmuted Family of Distributions: Properties and Applications. Austrian Journal of Statistics. 45, 71-93.
[6]	Merovci, F., Elbatal, I. (2014). Transmuted Lindley-geometric Distribution and its Applications. Journal of Statistics Applications and Probability. 3 (1), 77-91.
[7]	Merovci, F. (2014). Transmuted Generalized Rayleigh Distribution. Journal of Statistics Applications and Probability. 3 (1), 9-20.
[8]	Merovci, F., Puka, L. (2014). Transmuted Pareto Distribution. Probstat. 7, 1-11.
[9]	Merovci, F. (2013). Transmuted Lindley Distribution. International Journal of open Problems in Computer Science and Mathematics. 6 (2), 63-72.
[10]	AL-Kadim, K. A. and Mohammed, M. H. (2017). The cubic transmuted Weibull distribution. Journal of University of Babylon, 3: 862876.
[11]	Granzoto, D. C. T., Louzada, F., and Balakrishnan, N. (2017). Cubic rank transmuted distributions: Inferential issues and applications. Journal of statistical Computation and Simulation.
[12]	Rahman M. M, Al-Zahrani B, Shahbaz M. Q (2018). A general transmuted family of distributions. Pak J Stat Oper Res 14: 451-469.
[13]	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.
[14]	Adeyinka F. S, and Olapade A. K. (2019). A Study on Transmuted Half Logistic Distribution: Properties and Application. International Journal of Statistical Distributions and Applications. 5 (3): 54-59.
[15]	Adeyinka F. S, and Olapade, A. K. (2019). On the Flexibility of a Transmuted Type I Generalized Half-Logistic Distribution with Application. Engineering Mathematics. 3 (1): 13-18.
[16]	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.
[17]	Adeyinka, F. S. (2019). On the Tractability of Transmuted Type I Generalized Logistic Distribution with Application. International Journal of Theoretical and Applied Mathematics. 5 (2): 31-36.
[18]	Ebraheim, A. E. N. (2014). Exponentiated transmuted weibull distribution. International Scholarly and Scientific Research & Innovation, 8 (6), 903-911.
[19]	Al-Kadim K. A, Mahdi A. A. (2018). Exponentiated transmuted exponential distribution. Journal of Babylon University/Pure and Applied Sciences, 26 (2), 78-90.
[20]	David, H. A. (1970) Order Statistics. New York: Wiley Inter-science series.

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Femi Samuel Adeyinka. (2020). On Modelling of Infant Mortality Rate in Nigeria with Exponentiated Cubic Transmuted Exponential Distribution. International Journal on Data Science and Technology, 6(1), 16-22. https://doi.org/10.11648/j.ijdst.20200601.13

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ACS Style

Femi Samuel Adeyinka. On Modelling of Infant Mortality Rate in Nigeria with Exponentiated Cubic Transmuted Exponential Distribution. Int. J. Data Sci. Technol. 2020, 6(1), 16-22. doi: 10.11648/j.ijdst.20200601.13

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AMA Style

Femi Samuel Adeyinka. On Modelling of Infant Mortality Rate in Nigeria with Exponentiated Cubic Transmuted Exponential Distribution. Int J Data Sci Technol. 2020;6(1):16-22. doi: 10.11648/j.ijdst.20200601.13

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@article{10.11648/j.ijdst.20200601.13,
  author = {Femi Samuel Adeyinka},
  title = {On Modelling of Infant Mortality Rate in Nigeria with Exponentiated Cubic Transmuted Exponential Distribution},
  journal = {International Journal on Data Science and Technology},
  volume = {6},
  number = {1},
  pages = {16-22},
  doi = {10.11648/j.ijdst.20200601.13},
  url = {https://doi.org/10.11648/j.ijdst.20200601.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdst.20200601.13},
  abstract = {The idea of introducing extra parameters into the existing model in enhancing more flexibility is a giant stride in research. Transmutation map technique is one of the recent methods of introducing additional properties such as skewness, kurtosis and bimodality into the baseline distribution. In this article, a new exponentiated exponential distribution is developed using transmutation map. This model is referred to as exponentiated cubic transmuted exponential distribution (ECTED). The mathematical properties of the model which include survival function, hazard function, central and non- central moments, moment generating function and order statistics are established. The inherent parameters in the model are estimated using method of maximum likelihood estimation (MLE). The system of equations obtained is non-linear in parameters therefore non-linear optimization algorithms are implemented in R package. The distribution is used to model data on infant mortality rate in Nigeria. The performance of the subject model is compared with its baseline exponential distribution (ED), transmuted exponential distribution (TED), exponentiated transmuted exponential distribution (ETED) and cubic transmuted exponential distribution (CTED) using Akaike Information criterion (AIC), Corrected Akaike Information criterion (AICC) and Bayesian Information criterion (BIC). It is hope that this will serve as an alternative distribution in modelling complex real life data arising from various fields of human endeavors.},
 year = {2020}
}

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TY  - JOUR
T1  - On Modelling of Infant Mortality Rate in Nigeria with Exponentiated Cubic Transmuted Exponential Distribution
AU  - Femi Samuel Adeyinka
Y1  - 2020/01/06
PY  - 2020
N1  - https://doi.org/10.11648/j.ijdst.20200601.13
DO  - 10.11648/j.ijdst.20200601.13
T2  - International Journal on Data Science and Technology
JF  - International Journal on Data Science and Technology
JO  - International Journal on Data Science and Technology
SP  - 16
EP  - 22
PB  - Science Publishing Group
SN  - 2472-2235
UR  - https://doi.org/10.11648/j.ijdst.20200601.13
AB  - The idea of introducing extra parameters into the existing model in enhancing more flexibility is a giant stride in research. Transmutation map technique is one of the recent methods of introducing additional properties such as skewness, kurtosis and bimodality into the baseline distribution. In this article, a new exponentiated exponential distribution is developed using transmutation map. This model is referred to as exponentiated cubic transmuted exponential distribution (ECTED). The mathematical properties of the model which include survival function, hazard function, central and non- central moments, moment generating function and order statistics are established. The inherent parameters in the model are estimated using method of maximum likelihood estimation (MLE). The system of equations obtained is non-linear in parameters therefore non-linear optimization algorithms are implemented in R package. The distribution is used to model data on infant mortality rate in Nigeria. The performance of the subject model is compared with its baseline exponential distribution (ED), transmuted exponential distribution (TED), exponentiated transmuted exponential distribution (ETED) and cubic transmuted exponential distribution (CTED) using Akaike Information criterion (AIC), Corrected Akaike Information criterion (AICC) and Bayesian Information criterion (BIC). It is hope that this will serve as an alternative distribution in modelling complex real life data arising from various fields of human endeavors.
VL  - 6
IS  - 1
ER  -

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Author Information

Femi Samuel Adeyinka

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

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APA Style

Femi Samuel Adeyinka. (2020). On Modelling of Infant Mortality Rate in Nigeria with Exponentiated Cubic Transmuted Exponential Distribution. International Journal on Data Science and Technology, 6(1), 16-22. https://doi.org/10.11648/j.ijdst.20200601.13

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ACS Style

Femi Samuel Adeyinka. On Modelling of Infant Mortality Rate in Nigeria with Exponentiated Cubic Transmuted Exponential Distribution. Int. J. Data Sci. Technol. 2020, 6(1), 16-22. doi: 10.11648/j.ijdst.20200601.13

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AMA Style

Femi Samuel Adeyinka. On Modelling of Infant Mortality Rate in Nigeria with Exponentiated Cubic Transmuted Exponential Distribution. Int J Data Sci Technol. 2020;6(1):16-22. doi: 10.11648/j.ijdst.20200601.13

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@article{10.11648/j.ijdst.20200601.13,
  author = {Femi Samuel Adeyinka},
  title = {On Modelling of Infant Mortality Rate in Nigeria with Exponentiated Cubic Transmuted Exponential Distribution},
  journal = {International Journal on Data Science and Technology},
  volume = {6},
  number = {1},
  pages = {16-22},
  doi = {10.11648/j.ijdst.20200601.13},
  url = {https://doi.org/10.11648/j.ijdst.20200601.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdst.20200601.13},
  abstract = {The idea of introducing extra parameters into the existing model in enhancing more flexibility is a giant stride in research. Transmutation map technique is one of the recent methods of introducing additional properties such as skewness, kurtosis and bimodality into the baseline distribution. In this article, a new exponentiated exponential distribution is developed using transmutation map. This model is referred to as exponentiated cubic transmuted exponential distribution (ECTED). The mathematical properties of the model which include survival function, hazard function, central and non- central moments, moment generating function and order statistics are established. The inherent parameters in the model are estimated using method of maximum likelihood estimation (MLE). The system of equations obtained is non-linear in parameters therefore non-linear optimization algorithms are implemented in R package. The distribution is used to model data on infant mortality rate in Nigeria. The performance of the subject model is compared with its baseline exponential distribution (ED), transmuted exponential distribution (TED), exponentiated transmuted exponential distribution (ETED) and cubic transmuted exponential distribution (CTED) using Akaike Information criterion (AIC), Corrected Akaike Information criterion (AICC) and Bayesian Information criterion (BIC). It is hope that this will serve as an alternative distribution in modelling complex real life data arising from various fields of human endeavors.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - On Modelling of Infant Mortality Rate in Nigeria with Exponentiated Cubic Transmuted Exponential Distribution
AU  - Femi Samuel Adeyinka
Y1  - 2020/01/06
PY  - 2020
N1  - https://doi.org/10.11648/j.ijdst.20200601.13
DO  - 10.11648/j.ijdst.20200601.13
T2  - International Journal on Data Science and Technology
JF  - International Journal on Data Science and Technology
JO  - International Journal on Data Science and Technology
SP  - 16
EP  - 22
PB  - Science Publishing Group
SN  - 2472-2235
UR  - https://doi.org/10.11648/j.ijdst.20200601.13
AB  - The idea of introducing extra parameters into the existing model in enhancing more flexibility is a giant stride in research. Transmutation map technique is one of the recent methods of introducing additional properties such as skewness, kurtosis and bimodality into the baseline distribution. In this article, a new exponentiated exponential distribution is developed using transmutation map. This model is referred to as exponentiated cubic transmuted exponential distribution (ECTED). The mathematical properties of the model which include survival function, hazard function, central and non- central moments, moment generating function and order statistics are established. The inherent parameters in the model are estimated using method of maximum likelihood estimation (MLE). The system of equations obtained is non-linear in parameters therefore non-linear optimization algorithms are implemented in R package. The distribution is used to model data on infant mortality rate in Nigeria. The performance of the subject model is compared with its baseline exponential distribution (ED), transmuted exponential distribution (TED), exponentiated transmuted exponential distribution (ETED) and cubic transmuted exponential distribution (CTED) using Akaike Information criterion (AIC), Corrected Akaike Information criterion (AICC) and Bayesian Information criterion (BIC). It is hope that this will serve as an alternative distribution in modelling complex real life data arising from various fields of human endeavors.
VL  - 6
IS  - 1
ER  -

Copy | Download