The Modified Kies-Weibull Distribution: A Flexible Model for Survival Analysis

Sultana Begum; Md Rezaul Karim

doi:doi:10.11648/j.ijdsa.20251101.12

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The Modified Kies-Weibull Distribution: A Flexible Model for Survival Analysis

Sultana Begum

, Md Rezaul Karim^*

Published in International Journal of Data Science and Analysis (Volume 11, Issue 1)

Received: 25 March 2025 Accepted: 2 April 2025 Published: 10 April 2025

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Abstract

This paper introduces the Modified Kies-Weibull (MKW) distribution, a novel and flexible probability model that generalizes the Weibull distribution to better accommodate various hazard rate structures. The MKW distribution is derived by incorporating the Weibull distribution into the Modified Kies Generalized (MKi-G) family, enhancing its adaptability for reliability analysis and survival modeling. Key statistical properties, including the cumulative distribution function, probability density function, moments, and order statistics, are derived. Three estimation methods: (i) Maximum Likelihood Estimation (ML), (ii) Maximum Product Spacing (MPS), and (iii) Least Squares (LS) are examined and compared through simulation studies. The results demonstrate that LS estimation outperforms ML and MPS, particularly in small samples, exhibiting lower bias and greater stability. Furthermore, the empirical application of the MKW distribution to a bladder cancer remission dataset reveals superior model fit compared to existing Weibull-based models, as confirmed by information criteria and goodness-of-fit tests. The MKW distribution proves to be an effective tool for modeling lifetime data, offering enhanced flexibility for applications in medicine, engineering, and reliability studies.

Published in	International Journal of Data Science and Analysis (Volume 11, Issue 1)
DOI	10.11648/j.ijdsa.20251101.12
Page(s)	6-16
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), 2025. Published by Science Publishing Group

Keywords

Modified Kies-Weibull Distribution, Survival Analysis, Parameter Estimation, Reliability Modeling, Hazard Rate, Goodness-of-fit

References

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[2]	Kumar, C. S.; Dharmaja, S. H. S. (2013). On reduced Kies distribution. In Collection of Recent Statistical Methods and Applications, Kumar, C. S., Chacko, M., Sathar, E. I. A. (Eds.); Department of Statistics, University of Kerala Publishers: Trivandrum, India, pp. 111-123.
[3]	Kumar, C. S.; Dharmaja, S. H. S. (2017). The exponentiated reduced Kies distribution: Properties and applications. Communications in Statistics - Theory and Methods, 46, 8778-8790. https://doi.org/10.1080/03610926.2016.1252042
[4]	Shakhatreh, M. K., & Al-Babtain, A. A. (2021). Modeling engineering reliability data using the modified Kies distribution. Reliability Engineering & System Safety, 214, 107853. https://doi.org/10.1016/j.ress.2021.107853
[5]	Kumar, D., & Nassar, M. (2017). A generalized modified Kies distribution: Properties and estimation. Journal of Statistical Theory and Practice, 11(2), 302- 320. https://doi.org/10.1080/15598608.2017.1301842
[6]	Dey, S.; Nassar, M.; Kumar, D. (2019). Moments and estimation of reduced Kies distribution based on progressive type-II right censored order statistics. Hacettepe Journal of Mathematics and Statistics, 48, 332-350. https://doi.org/10.15672/HJMS.2019.569
[7]	Ferreira, A. A., & Cordeiro, G. M. (2024). The modified Kies flexible generalized family: Properties, simulations, and applications. Austrian Journal of Statistics, 53(4), 25-42. https://doi.org/10.17713/ajs.v53i4.318
[8]	Al-Babtain, A. A., Shakhatreh, M. K., Nassar, M., & Afify, A. Z. (2020). A new modified Kies family: Properties, estimation under complete and type-II censored samples, and engineering applications. Mathematics, 8(8), 1345–1368. https://doi.org/10.3390/math8081345
[9]	Bowley, A. (1920). Elements of Statistics (4th ed.). Charles Scribner.
[10]	Moors, J. J. A. (1998). A quantile alternative for kurtosis. The Statistician, 37, 25–32. https://doi.org/10.1111/1467-9884.00127
[11]	Cheng, R. C. H., & Amin, N. A. K. (1983). Estimating parameters in continuous univariate distribution with a shifted origin. Journal of the Royal Statistical Society, 45, 394–403. https://doi.org/10.1111/j.2517-6161.1983.tb01268.x
[12]	Lee, E. T., & Wang, J. W. (2003). Statistical methods for survival data analysis (3rd ed.). Wiley. ISBN: 978-0- 471-29821-1
[13]	Weibull, W. (1951). A statistical distribution function of wide applicability. Journal of Applied Mechanics, 18, 293–297. https://doi.org/10.1115/1.4010337
[14]	Dawlah Al-Sulami. (2020). Exponentiated exponential Weibull distribution: Mathematical properties and application. American Journal of Applied Sciences, 17, 188–195. https://doi.org/10.3844/ajassp.2020.188.195
[15]	Akgül, F. G., Senoglu, B., & Arslan, T. (2016). An alternative distribution to Weibull for modeling the wind speed data: Inverse Weibull distribution. Energy Conversion and Management, 114, 234–240. https://doi.org/10.1016/j.enconman.2016.02.026

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APA Style

S. B., Karim, M. R. (2025). The Modified Kies-Weibull Distribution: A Flexible Model for Survival Analysis. International Journal of Data Science and Analysis, 11(1), 6-16. https://doi.org/10.11648/j.ijdsa.20251101.12

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ACS Style

S. B.; Karim, M. R. The Modified Kies-Weibull Distribution: A Flexible Model for Survival Analysis. Int. J. Data Sci. Anal. 2025, 11(1), 6-16. doi: 10.11648/j.ijdsa.20251101.12

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AMA Style

SB, Karim MR. The Modified Kies-Weibull Distribution: A Flexible Model for Survival Analysis. Int J Data Sci Anal. 2025;11(1):6-16. doi: 10.11648/j.ijdsa.20251101.12

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@article{10.11648/j.ijdsa.20251101.12,
  author = {Sultana Begum and Md Rezaul Karim},
  title = {The Modified Kies-Weibull Distribution: A Flexible Model for Survival Analysis},
  journal = {International Journal of Data Science and Analysis},
  volume = {11},
  number = {1},
  pages = {6-16},
  doi = {10.11648/j.ijdsa.20251101.12},
  url = {https://doi.org/10.11648/j.ijdsa.20251101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20251101.12},
  abstract = {This paper introduces the Modified Kies-Weibull (MKW) distribution, a novel and flexible probability model that generalizes the Weibull distribution to better accommodate various hazard rate structures. The MKW distribution is derived by incorporating the Weibull distribution into the Modified Kies Generalized (MKi-G) family, enhancing its adaptability for reliability analysis and survival modeling. Key statistical properties, including the cumulative distribution function, probability density function, moments, and order statistics, are derived. Three estimation methods: (i) Maximum Likelihood Estimation (ML), (ii) Maximum Product Spacing (MPS), and (iii) Least Squares (LS) are examined and compared through simulation studies. The results demonstrate that LS estimation outperforms ML and MPS, particularly in small samples, exhibiting lower bias and greater stability. Furthermore, the empirical application of the MKW distribution to a bladder cancer remission dataset reveals superior model fit compared to existing Weibull-based models, as confirmed by information criteria and goodness-of-fit tests. The MKW distribution proves to be an effective tool for modeling lifetime data, offering enhanced flexibility for applications in medicine, engineering, and reliability studies.},
 year = {2025}
}

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TY  - JOUR
T1  - The Modified Kies-Weibull Distribution: A Flexible Model for Survival Analysis
AU  - Sultana Begum
AU  - Md Rezaul Karim
Y1  - 2025/04/10
PY  - 2025
N1  - https://doi.org/10.11648/j.ijdsa.20251101.12
DO  - 10.11648/j.ijdsa.20251101.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 6
EP  - 16
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20251101.12
AB  - This paper introduces the Modified Kies-Weibull (MKW) distribution, a novel and flexible probability model that generalizes the Weibull distribution to better accommodate various hazard rate structures. The MKW distribution is derived by incorporating the Weibull distribution into the Modified Kies Generalized (MKi-G) family, enhancing its adaptability for reliability analysis and survival modeling. Key statistical properties, including the cumulative distribution function, probability density function, moments, and order statistics, are derived. Three estimation methods: (i) Maximum Likelihood Estimation (ML), (ii) Maximum Product Spacing (MPS), and (iii) Least Squares (LS) are examined and compared through simulation studies. The results demonstrate that LS estimation outperforms ML and MPS, particularly in small samples, exhibiting lower bias and greater stability. Furthermore, the empirical application of the MKW distribution to a bladder cancer remission dataset reveals superior model fit compared to existing Weibull-based models, as confirmed by information criteria and goodness-of-fit tests. The MKW distribution proves to be an effective tool for modeling lifetime data, offering enhanced flexibility for applications in medicine, engineering, and reliability studies.
VL  - 11
IS  - 1
ER  -

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Author Information

Sultana Begum

Department of Statistics and Data Science, Jahangirnagar University, Savar, Dhaka, Bangladesh

Contact Email

http://orcid.org/0009-0000-1261-4913
Md Rezaul Karim

Department of Statistics and Data Science, Jahangirnagar University, Savar, Dhaka, Bangladesh

Contact Email

http://orcid.org/0000-0002-8453-1604

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Plain Text BibTeX RIS

APA Style

S. B., Karim, M. R. (2025). The Modified Kies-Weibull Distribution: A Flexible Model for Survival Analysis. International Journal of Data Science and Analysis, 11(1), 6-16. https://doi.org/10.11648/j.ijdsa.20251101.12

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ACS Style

S. B.; Karim, M. R. The Modified Kies-Weibull Distribution: A Flexible Model for Survival Analysis. Int. J. Data Sci. Anal. 2025, 11(1), 6-16. doi: 10.11648/j.ijdsa.20251101.12

Copy | Download

AMA Style

SB, Karim MR. The Modified Kies-Weibull Distribution: A Flexible Model for Survival Analysis. Int J Data Sci Anal. 2025;11(1):6-16. doi: 10.11648/j.ijdsa.20251101.12

Copy | Download

@article{10.11648/j.ijdsa.20251101.12,
  author = {Sultana Begum and Md Rezaul Karim},
  title = {The Modified Kies-Weibull Distribution: A Flexible Model for Survival Analysis},
  journal = {International Journal of Data Science and Analysis},
  volume = {11},
  number = {1},
  pages = {6-16},
  doi = {10.11648/j.ijdsa.20251101.12},
  url = {https://doi.org/10.11648/j.ijdsa.20251101.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20251101.12},
  abstract = {This paper introduces the Modified Kies-Weibull (MKW) distribution, a novel and flexible probability model that generalizes the Weibull distribution to better accommodate various hazard rate structures. The MKW distribution is derived by incorporating the Weibull distribution into the Modified Kies Generalized (MKi-G) family, enhancing its adaptability for reliability analysis and survival modeling. Key statistical properties, including the cumulative distribution function, probability density function, moments, and order statistics, are derived. Three estimation methods: (i) Maximum Likelihood Estimation (ML), (ii) Maximum Product Spacing (MPS), and (iii) Least Squares (LS) are examined and compared through simulation studies. The results demonstrate that LS estimation outperforms ML and MPS, particularly in small samples, exhibiting lower bias and greater stability. Furthermore, the empirical application of the MKW distribution to a bladder cancer remission dataset reveals superior model fit compared to existing Weibull-based models, as confirmed by information criteria and goodness-of-fit tests. The MKW distribution proves to be an effective tool for modeling lifetime data, offering enhanced flexibility for applications in medicine, engineering, and reliability studies.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - The Modified Kies-Weibull Distribution: A Flexible Model for Survival Analysis
AU  - Sultana Begum
AU  - Md Rezaul Karim
Y1  - 2025/04/10
PY  - 2025
N1  - https://doi.org/10.11648/j.ijdsa.20251101.12
DO  - 10.11648/j.ijdsa.20251101.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 6
EP  - 16
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20251101.12
AB  - This paper introduces the Modified Kies-Weibull (MKW) distribution, a novel and flexible probability model that generalizes the Weibull distribution to better accommodate various hazard rate structures. The MKW distribution is derived by incorporating the Weibull distribution into the Modified Kies Generalized (MKi-G) family, enhancing its adaptability for reliability analysis and survival modeling. Key statistical properties, including the cumulative distribution function, probability density function, moments, and order statistics, are derived. Three estimation methods: (i) Maximum Likelihood Estimation (ML), (ii) Maximum Product Spacing (MPS), and (iii) Least Squares (LS) are examined and compared through simulation studies. The results demonstrate that LS estimation outperforms ML and MPS, particularly in small samples, exhibiting lower bias and greater stability. Furthermore, the empirical application of the MKW distribution to a bladder cancer remission dataset reveals superior model fit compared to existing Weibull-based models, as confirmed by information criteria and goodness-of-fit tests. The MKW distribution proves to be an effective tool for modeling lifetime data, offering enhanced flexibility for applications in medicine, engineering, and reliability studies.
VL  - 11
IS  - 1
ER  -

Copy | Download