Generating New Lifetime Distributions Using Parsimonious Transformation: Properties and Applications

Santanu Dutta; Aditya Kumar Yadav

doi:doi:10.11648/j.ijsda.20251102.16

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Generating New Lifetime Distributions Using Parsimonious Transformation: Properties and Applications

Santanu Dutta, Aditya Kumar Yadav^*

Published in International Journal of Statistical Distributions and Applications (Volume 11, Issue 2)

Received: 18 May 2025 Accepted: 3 June 2025 Published: 21 June 2025

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Abstract

In this paper, we propose a new parsimonious transformation for obtaining lifetime distributions, and as special cases, we obtain two new lifetime distributions using exponential and Weibull distributions as baselines in the transformation. We study the mathematical properties of the transformation, and for the two new lifetime distributions, we obtain survival functions, hazard functions, moments, moment-generating functions, mean deviation, Rényi entropy, and quantile function. We estimate the parameters of the new lifetime distributions using the maximum likelihood (ML) estimation method, and the Monte Carlo simulations are used to assess the consistency of the ML estimators of the parameters. The proposed new lifetime distributions provide a better fit in terms of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) scores in comparison to the baseline distributions and other competing models, based on two real datasets, namely the exceedance of the flood peaks of the Wheaton River, and the failure times of 50 items.

Published in	International Journal of Statistical Distributions and Applications (Volume 11, Issue 2)
DOI	10.11648/j.ijsda.20251102.16
Page(s)	74-84
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

Lifetime Distribution, Parsimonious Transformation, Exponential Distribution, Weibull Distribution

References

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[7]	Kumar, D., Singh, U., & Singh, S. K. (2015). A new distribution using sine function-its application to bladder cancer patients data. Journal of Statistics Applications & Probability, 4(3), 417.
[8]	Lawless, J. F. (2011). Statistical models and methods for lifetime data. John Wiley & Sons.
[9]	Lee, E. T., & Wang, J. (2003). Statistical methods for survival data analysis. John Wiley & Sons.
[10]	Marshall, A. W., & Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84(3), 641-652.
[11]	Maurya, S. K., Kaushik, A., Singh, S. K., & Singh, U. (2017). A new class of distribution having decreasing, increasing, and bathtub-shaped failure rate. Communications in Statistics-Theory and Methods, 46(20), 10359-10372.
[12]	Murthy, D.N.P., Xie, M. & Jiang, R. (2004). Weibull Models. John Wiley & Sons, New York.
[13]	Renyi, A. (1961). On measures of entropy and information. In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume1: Contributions to the Theory of Statistics, volume 4, pages 547-562. University of California Press.
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[17]	Sule, I., Ismail, K. A., & Bello, O. A. (2023). On The Modeling of Biomedical Data Sets with a New Generalized Exponentiated Expo-nential Distribution. Journal of Biostatistics and Epidemiology, 9(4), 484-499.

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APA Style

Dutta, S., Yadav, A. K. (2025). Generating New Lifetime Distributions Using Parsimonious Transformation: Properties and Applications. International Journal of Statistical Distributions and Applications, 11(2), 74-84. https://doi.org/10.11648/j.ijsda.20251102.16

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ACS Style

Dutta, S.; Yadav, A. K. Generating New Lifetime Distributions Using Parsimonious Transformation: Properties and Applications. Int. J. Stat. Distrib. Appl. 2025, 11(2), 74-84. doi: 10.11648/j.ijsda.20251102.16

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AMA Style

Dutta S, Yadav AK. Generating New Lifetime Distributions Using Parsimonious Transformation: Properties and Applications. Int J Stat Distrib Appl. 2025;11(2):74-84. doi: 10.11648/j.ijsda.20251102.16

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@article{10.11648/j.ijsda.20251102.16,
  author = {Santanu Dutta and Aditya Kumar Yadav},
  title = {Generating New Lifetime Distributions Using Parsimonious Transformation: Properties and Applications},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {11},
  number = {2},
  pages = {74-84},
  doi = {10.11648/j.ijsda.20251102.16},
  url = {https://doi.org/10.11648/j.ijsda.20251102.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsda.20251102.16},
  abstract = {In this paper, we propose a new parsimonious transformation for obtaining lifetime distributions, and as special cases, we obtain two new lifetime distributions using exponential and Weibull distributions as baselines in the transformation. We study the mathematical properties of the transformation, and for the two new lifetime distributions, we obtain survival functions, hazard functions, moments, moment-generating functions, mean deviation, Rényi entropy, and quantile function. We estimate the parameters of the new lifetime distributions using the maximum likelihood (ML) estimation method, and the Monte Carlo simulations are used to assess the consistency of the ML estimators of the parameters. The proposed new lifetime distributions provide a better fit in terms of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) scores in comparison to the baseline distributions and other competing models, based on two real datasets, namely the exceedance of the flood peaks of the Wheaton River, and the failure times of 50 items.},
 year = {2025}
}

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TY  - JOUR
T1  - Generating New Lifetime Distributions Using Parsimonious Transformation: Properties and Applications
AU  - Santanu Dutta
AU  - Aditya Kumar Yadav
Y1  - 2025/06/21
PY  - 2025
N1  - https://doi.org/10.11648/j.ijsda.20251102.16
DO  - 10.11648/j.ijsda.20251102.16
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  - 74
EP  - 84
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsda.20251102.16
AB  - In this paper, we propose a new parsimonious transformation for obtaining lifetime distributions, and as special cases, we obtain two new lifetime distributions using exponential and Weibull distributions as baselines in the transformation. We study the mathematical properties of the transformation, and for the two new lifetime distributions, we obtain survival functions, hazard functions, moments, moment-generating functions, mean deviation, Rényi entropy, and quantile function. We estimate the parameters of the new lifetime distributions using the maximum likelihood (ML) estimation method, and the Monte Carlo simulations are used to assess the consistency of the ML estimators of the parameters. The proposed new lifetime distributions provide a better fit in terms of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) scores in comparison to the baseline distributions and other competing models, based on two real datasets, namely the exceedance of the flood peaks of the Wheaton River, and the failure times of 50 items.
VL  - 11
IS  - 2
ER  -

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Author Information

Santanu Dutta

Department of Mathematical Sciences, Tezpur University, Assam, India

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Aditya Kumar Yadav

Department of Mathematical Sciences, Tezpur University, Assam, India

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APA Style

Dutta, S., Yadav, A. K. (2025). Generating New Lifetime Distributions Using Parsimonious Transformation: Properties and Applications. International Journal of Statistical Distributions and Applications, 11(2), 74-84. https://doi.org/10.11648/j.ijsda.20251102.16

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ACS Style

Dutta, S.; Yadav, A. K. Generating New Lifetime Distributions Using Parsimonious Transformation: Properties and Applications. Int. J. Stat. Distrib. Appl. 2025, 11(2), 74-84. doi: 10.11648/j.ijsda.20251102.16

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AMA Style

Dutta S, Yadav AK. Generating New Lifetime Distributions Using Parsimonious Transformation: Properties and Applications. Int J Stat Distrib Appl. 2025;11(2):74-84. doi: 10.11648/j.ijsda.20251102.16

Copy | Download

@article{10.11648/j.ijsda.20251102.16,
  author = {Santanu Dutta and Aditya Kumar Yadav},
  title = {Generating New Lifetime Distributions Using Parsimonious Transformation: Properties and Applications},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {11},
  number = {2},
  pages = {74-84},
  doi = {10.11648/j.ijsda.20251102.16},
  url = {https://doi.org/10.11648/j.ijsda.20251102.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsda.20251102.16},
  abstract = {In this paper, we propose a new parsimonious transformation for obtaining lifetime distributions, and as special cases, we obtain two new lifetime distributions using exponential and Weibull distributions as baselines in the transformation. We study the mathematical properties of the transformation, and for the two new lifetime distributions, we obtain survival functions, hazard functions, moments, moment-generating functions, mean deviation, Rényi entropy, and quantile function. We estimate the parameters of the new lifetime distributions using the maximum likelihood (ML) estimation method, and the Monte Carlo simulations are used to assess the consistency of the ML estimators of the parameters. The proposed new lifetime distributions provide a better fit in terms of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) scores in comparison to the baseline distributions and other competing models, based on two real datasets, namely the exceedance of the flood peaks of the Wheaton River, and the failure times of 50 items.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - Generating New Lifetime Distributions Using Parsimonious Transformation: Properties and Applications
AU  - Santanu Dutta
AU  - Aditya Kumar Yadav
Y1  - 2025/06/21
PY  - 2025
N1  - https://doi.org/10.11648/j.ijsda.20251102.16
DO  - 10.11648/j.ijsda.20251102.16
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  - 74
EP  - 84
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsda.20251102.16
AB  - In this paper, we propose a new parsimonious transformation for obtaining lifetime distributions, and as special cases, we obtain two new lifetime distributions using exponential and Weibull distributions as baselines in the transformation. We study the mathematical properties of the transformation, and for the two new lifetime distributions, we obtain survival functions, hazard functions, moments, moment-generating functions, mean deviation, Rényi entropy, and quantile function. We estimate the parameters of the new lifetime distributions using the maximum likelihood (ML) estimation method, and the Monte Carlo simulations are used to assess the consistency of the ML estimators of the parameters. The proposed new lifetime distributions provide a better fit in terms of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) scores in comparison to the baseline distributions and other competing models, based on two real datasets, namely the exceedance of the flood peaks of the Wheaton River, and the failure times of 50 items.
VL  - 11
IS  - 2
ER  -

Copy | Download