Weibull Log Logistic {Exponential} Distribution: Some Properties and Application to Survival Data

Obalowu Job; Adeyinka Solomon Ogunsanya

doi:doi:10.11648/j.ijsd.20220801.11

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Weibull Log Logistic {Exponential} Distribution: Some Properties and Application to Survival Data

Obalowu Job, Adeyinka Solomon Ogunsanya

Published in International Journal of Statistical Distributions and Applications (Volume 8, Issue 1)

Received: 13 February 2022 Accepted: 8 March 2022 Published: 15 March 2022

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Abstract

A four-parameter continuous probability model called the Weibull log-logistic {Exponential} distribution (WLLED) was introduced and studied in this research using T-log-logistic {Exponential} distribution via T-R{Y} framework to extend the two-parameter log-logistic distribution. The objective of this research is to explore the versatility and flexibility of the log-logistic and Weibull distributions in modeling lifetime data. Some basic structural properties which include the reliability measures and hazard function, cumulative hazard function, Moment, Quantile, skewness, kurtosis, mixture representation, order statistics and asymptotic behavior of the WLLED were obtained and established. The shape of the new four parameter distribution is also investigated. A simulation study was conducted to evaluate the MLE estimates, bias, and standard error for various parameter combinations and different sample sizes. The efficiency of the WLLE distribution was compared with other related distribution from the literature using five goodness-of-fit statistics: AIC, CAIC and BIC, Anderson-Darling A* and Cramér-Von Mises W*, methods of comparison. The method of maximum likelihood estimation was proposed in estimating its parameters. An application to the survival times of 121 patients with breast cancer dataset was provided and the WLLED displays a good fit. Finally, it is recommended that the WLLED can be used for modeling positively skewed real-life data.

Published in	International Journal of Statistical Distributions and Applications (Volume 8, Issue 1)
DOI	10.11648/j.ijsd.20220801.11
Page(s)	1-13
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

Log-logistic Distribution, Censored Data, Lifetime Data, Mathematical Statistics, Maximum Likelihood Estimation

References

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[5]	Cordeiro, G. M., Alizadeh, M., Ozel, G., Hosseini, B., Ortega, E. M. M. and Altun, E. The generalized odd log-logistic family of distributions: properties, regression models and applications, Journal of Statistical Computation and Simulation 87, 908-932, (2017).
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APA Style

Obalowu Job, Adeyinka Solomon Ogunsanya. (2022). Weibull Log Logistic {Exponential} Distribution: Some Properties and Application to Survival Data. International Journal of Statistical Distributions and Applications, 8(1), 1-13. https://doi.org/10.11648/j.ijsd.20220801.11

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ACS Style

Obalowu Job; Adeyinka Solomon Ogunsanya. Weibull Log Logistic {Exponential} Distribution: Some Properties and Application to Survival Data. Int. J. Stat. Distrib. Appl. 2022, 8(1), 1-13. doi: 10.11648/j.ijsd.20220801.11

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AMA Style

Obalowu Job, Adeyinka Solomon Ogunsanya. Weibull Log Logistic {Exponential} Distribution: Some Properties and Application to Survival Data. Int J Stat Distrib Appl. 2022;8(1):1-13. doi: 10.11648/j.ijsd.20220801.11

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@article{10.11648/j.ijsd.20220801.11,
  author = {Obalowu Job and Adeyinka Solomon Ogunsanya},
  title = {Weibull Log Logistic {Exponential} Distribution: Some Properties and Application to Survival Data},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {8},
  number = {1},
  pages = {1-13},
  doi = {10.11648/j.ijsd.20220801.11},
  url = {https://doi.org/10.11648/j.ijsd.20220801.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20220801.11},
  abstract = {A four-parameter continuous probability model called the Weibull log-logistic {Exponential} distribution (WLLED) was introduced and studied in this research using T-log-logistic {Exponential} distribution via T-R{Y} framework to extend the two-parameter log-logistic distribution. The objective of this research is to explore the versatility and flexibility of the log-logistic and Weibull distributions in modeling lifetime data. Some basic structural properties which include the reliability measures and hazard function, cumulative hazard function, Moment, Quantile, skewness, kurtosis, mixture representation, order statistics and asymptotic behavior of the WLLED were obtained and established. The shape of the new four parameter distribution is also investigated. A simulation study was conducted to evaluate the MLE estimates, bias, and standard error for various parameter combinations and different sample sizes. The efficiency of the WLLE distribution was compared with other related distribution from the literature using five goodness-of-fit statistics: AIC, CAIC and BIC, Anderson-Darling A* and Cramér-Von Mises W*, methods of comparison. The method of maximum likelihood estimation was proposed in estimating its parameters. An application to the survival times of 121 patients with breast cancer dataset was provided and the WLLED displays a good fit. Finally, it is recommended that the WLLED can be used for modeling positively skewed real-life data.},
 year = {2022}
}

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TY  - JOUR
T1  - Weibull Log Logistic {Exponential} Distribution: Some Properties and Application to Survival Data
AU  - Obalowu Job
AU  - Adeyinka Solomon Ogunsanya
Y1  - 2022/03/15
PY  - 2022
N1  - https://doi.org/10.11648/j.ijsd.20220801.11
DO  - 10.11648/j.ijsd.20220801.11
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  - 1
EP  - 13
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20220801.11
AB  - A four-parameter continuous probability model called the Weibull log-logistic {Exponential} distribution (WLLED) was introduced and studied in this research using T-log-logistic {Exponential} distribution via T-R{Y} framework to extend the two-parameter log-logistic distribution. The objective of this research is to explore the versatility and flexibility of the log-logistic and Weibull distributions in modeling lifetime data. Some basic structural properties which include the reliability measures and hazard function, cumulative hazard function, Moment, Quantile, skewness, kurtosis, mixture representation, order statistics and asymptotic behavior of the WLLED were obtained and established. The shape of the new four parameter distribution is also investigated. A simulation study was conducted to evaluate the MLE estimates, bias, and standard error for various parameter combinations and different sample sizes. The efficiency of the WLLE distribution was compared with other related distribution from the literature using five goodness-of-fit statistics: AIC, CAIC and BIC, Anderson-Darling A* and Cramér-Von Mises W*, methods of comparison. The method of maximum likelihood estimation was proposed in estimating its parameters. An application to the survival times of 121 patients with breast cancer dataset was provided and the WLLED displays a good fit. Finally, it is recommended that the WLLED can be used for modeling positively skewed real-life data.
VL  - 8
IS  - 1
ER  -

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Author Information

Obalowu Job

Department of Statistics, University of Ilorin, Ilorin, Nigeria
Adeyinka Solomon Ogunsanya

Department of Statistics, University of Ilorin, Ilorin, Nigeria

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APA Style

Obalowu Job, Adeyinka Solomon Ogunsanya. (2022). Weibull Log Logistic {Exponential} Distribution: Some Properties and Application to Survival Data. International Journal of Statistical Distributions and Applications, 8(1), 1-13. https://doi.org/10.11648/j.ijsd.20220801.11

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ACS Style

Obalowu Job; Adeyinka Solomon Ogunsanya. Weibull Log Logistic {Exponential} Distribution: Some Properties and Application to Survival Data. Int. J. Stat. Distrib. Appl. 2022, 8(1), 1-13. doi: 10.11648/j.ijsd.20220801.11

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AMA Style

Obalowu Job, Adeyinka Solomon Ogunsanya. Weibull Log Logistic {Exponential} Distribution: Some Properties and Application to Survival Data. Int J Stat Distrib Appl. 2022;8(1):1-13. doi: 10.11648/j.ijsd.20220801.11

Copy | Download

@article{10.11648/j.ijsd.20220801.11,
  author = {Obalowu Job and Adeyinka Solomon Ogunsanya},
  title = {Weibull Log Logistic {Exponential} Distribution: Some Properties and Application to Survival Data},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {8},
  number = {1},
  pages = {1-13},
  doi = {10.11648/j.ijsd.20220801.11},
  url = {https://doi.org/10.11648/j.ijsd.20220801.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20220801.11},
  abstract = {A four-parameter continuous probability model called the Weibull log-logistic {Exponential} distribution (WLLED) was introduced and studied in this research using T-log-logistic {Exponential} distribution via T-R{Y} framework to extend the two-parameter log-logistic distribution. The objective of this research is to explore the versatility and flexibility of the log-logistic and Weibull distributions in modeling lifetime data. Some basic structural properties which include the reliability measures and hazard function, cumulative hazard function, Moment, Quantile, skewness, kurtosis, mixture representation, order statistics and asymptotic behavior of the WLLED were obtained and established. The shape of the new four parameter distribution is also investigated. A simulation study was conducted to evaluate the MLE estimates, bias, and standard error for various parameter combinations and different sample sizes. The efficiency of the WLLE distribution was compared with other related distribution from the literature using five goodness-of-fit statistics: AIC, CAIC and BIC, Anderson-Darling A* and Cramér-Von Mises W*, methods of comparison. The method of maximum likelihood estimation was proposed in estimating its parameters. An application to the survival times of 121 patients with breast cancer dataset was provided and the WLLED displays a good fit. Finally, it is recommended that the WLLED can be used for modeling positively skewed real-life data.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Weibull Log Logistic {Exponential} Distribution: Some Properties and Application to Survival Data
AU  - Obalowu Job
AU  - Adeyinka Solomon Ogunsanya
Y1  - 2022/03/15
PY  - 2022
N1  - https://doi.org/10.11648/j.ijsd.20220801.11
DO  - 10.11648/j.ijsd.20220801.11
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  - 1
EP  - 13
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20220801.11
AB  - A four-parameter continuous probability model called the Weibull log-logistic {Exponential} distribution (WLLED) was introduced and studied in this research using T-log-logistic {Exponential} distribution via T-R{Y} framework to extend the two-parameter log-logistic distribution. The objective of this research is to explore the versatility and flexibility of the log-logistic and Weibull distributions in modeling lifetime data. Some basic structural properties which include the reliability measures and hazard function, cumulative hazard function, Moment, Quantile, skewness, kurtosis, mixture representation, order statistics and asymptotic behavior of the WLLED were obtained and established. The shape of the new four parameter distribution is also investigated. A simulation study was conducted to evaluate the MLE estimates, bias, and standard error for various parameter combinations and different sample sizes. The efficiency of the WLLE distribution was compared with other related distribution from the literature using five goodness-of-fit statistics: AIC, CAIC and BIC, Anderson-Darling A* and Cramér-Von Mises W*, methods of comparison. The method of maximum likelihood estimation was proposed in estimating its parameters. An application to the survival times of 121 patients with breast cancer dataset was provided and the WLLED displays a good fit. Finally, it is recommended that the WLLED can be used for modeling positively skewed real-life data.
VL  - 8
IS  - 1
ER  -

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