The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data

Faisal Muhammad Amiru; Umar Usman; Suleiman Shamsuddeen; Umar Muhammad Adamu; Badamasi Abba

doi:doi:10.11648/j.ijsda.20251101.11

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The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data

Faisal Muhammad Amiru^*, Umar Usman, Suleiman Shamsuddeen, Umar Muhammad Adamu, Badamasi Abba

Published in International Journal of Statistical Distributions and Applications (Volume 11, Issue 1)

Received: 30 December 2024 Accepted: 16 January 2025 Published: 11 February 2025

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Abstract

To measure the average lifespan of systems and components, and to analyze lifetime data with a monotonic failure rate, distributions such as Weibull, Exponential, and Gamma are commonly used in reliability and survival studies. However, these distributions are not suitable for datasets with non-monotonic patterns like the bathtub curve. To address this, the Chen distribution, which accommodates increasing or bathtub-shaped failure rates, has been proposed. Yet, this model lacks a scale parameter. This article presents a new four parameter lifetime distribution with bathtub-shaped failure rate called Additive Dhillon-Chen (ADC) distribution. We applied the additive methodology to establish the model, for which the Dhillon distribution was considered as baseline distribution. Some statistical properties such as quartile function, mode, moment and moment generating function, order statistics and asymptotic behavior of the distribution are studied. Parameters of the distribution are estimated using the maximum likelihood estimation method. The ADC distribution is applied to two lifetime dataset and compared with an existing distribution in the literature. Model selection was carried out based on Log-likelihood, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Corrected Akaike Information Criterion (AICc). The results, based on parameter estimation from real-life data, demonstrate that the ADC distribution fits the data well and offers a valuable alternative for modeling datasets with non-monotonic behavior.

Published in	International Journal of Statistical Distributions and Applications (Volume 11, Issue 1)
DOI	10.11648/j.ijsda.20251101.11
Page(s)	1-10
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

Reliability, Survival, Bathtub-curve, Additive, Dhillon-Chen Distribution

References

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APA Style

Amiru, F. M., Usman, U., Shamsuddeen, S., Adamu, U. M., Abba, B. (2025). The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data. International Journal of Statistical Distributions and Applications, 11(1), 1-10. https://doi.org/10.11648/j.ijsda.20251101.11

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ACS Style

Amiru, F. M.; Usman, U.; Shamsuddeen, S.; Adamu, U. M.; Abba, B. The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data. Int. J. Stat. Distrib. Appl. 2025, 11(1), 1-10. doi: 10.11648/j.ijsda.20251101.11

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AMA Style

Amiru FM, Usman U, Shamsuddeen S, Adamu UM, Abba B. The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data. Int J Stat Distrib Appl. 2025;11(1):1-10. doi: 10.11648/j.ijsda.20251101.11

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@article{10.11648/j.ijsda.20251101.11,
  author = {Faisal Muhammad Amiru and Umar Usman and Suleiman Shamsuddeen and Umar Muhammad Adamu and Badamasi Abba},
  title = {The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {11},
  number = {1},
  pages = {1-10},
  doi = {10.11648/j.ijsda.20251101.11},
  url = {https://doi.org/10.11648/j.ijsda.20251101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsda.20251101.11},
  abstract = {To measure the average lifespan of systems and components, and to analyze lifetime data with a monotonic failure rate, distributions such as Weibull, Exponential, and Gamma are commonly used in reliability and survival studies. However, these distributions are not suitable for datasets with non-monotonic patterns like the bathtub curve. To address this, the Chen distribution, which accommodates increasing or bathtub-shaped failure rates, has been proposed. Yet, this model lacks a scale parameter. This article presents a new four parameter lifetime distribution with bathtub-shaped failure rate called Additive Dhillon-Chen (ADC) distribution. We applied the additive methodology to establish the model, for which the Dhillon distribution was considered as baseline distribution. Some statistical properties such as quartile function, mode, moment and moment generating function, order statistics and asymptotic behavior of the distribution are studied. Parameters of the distribution are estimated using the maximum likelihood estimation method. The ADC distribution is applied to two lifetime dataset and compared with an existing distribution in the literature. Model selection was carried out based on Log-likelihood, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Corrected Akaike Information Criterion (AICc). The results, based on parameter estimation from real-life data, demonstrate that the ADC distribution fits the data well and offers a valuable alternative for modeling datasets with non-monotonic behavior.},
 year = {2025}
}

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TY  - JOUR
T1  - The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data
AU  - Faisal Muhammad Amiru
AU  - Umar Usman
AU  - Suleiman Shamsuddeen
AU  - Umar Muhammad Adamu
AU  - Badamasi Abba
Y1  - 2025/02/11
PY  - 2025
N1  - https://doi.org/10.11648/j.ijsda.20251101.11
DO  - 10.11648/j.ijsda.20251101.11
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  - 10
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsda.20251101.11
AB  - To measure the average lifespan of systems and components, and to analyze lifetime data with a monotonic failure rate, distributions such as Weibull, Exponential, and Gamma are commonly used in reliability and survival studies. However, these distributions are not suitable for datasets with non-monotonic patterns like the bathtub curve. To address this, the Chen distribution, which accommodates increasing or bathtub-shaped failure rates, has been proposed. Yet, this model lacks a scale parameter. This article presents a new four parameter lifetime distribution with bathtub-shaped failure rate called Additive Dhillon-Chen (ADC) distribution. We applied the additive methodology to establish the model, for which the Dhillon distribution was considered as baseline distribution. Some statistical properties such as quartile function, mode, moment and moment generating function, order statistics and asymptotic behavior of the distribution are studied. Parameters of the distribution are estimated using the maximum likelihood estimation method. The ADC distribution is applied to two lifetime dataset and compared with an existing distribution in the literature. Model selection was carried out based on Log-likelihood, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Corrected Akaike Information Criterion (AICc). The results, based on parameter estimation from real-life data, demonstrate that the ADC distribution fits the data well and offers a valuable alternative for modeling datasets with non-monotonic behavior.
VL  - 11
IS  - 1
ER  -

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Author Information

Faisal Muhammad Amiru

Department of Mathematical Sciences, Bayero University, Kano, Nigeria

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Umar Usman

Department of Statistics, Usmanu Danfodio University, Sokoto, Nigeria

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Suleiman Shamsuddeen

Department of Statistics, Federal University Dutsin-ma, Katsina, Nigeria

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Umar Muhammad Adamu

Department of Mathematical Sciences, Bayero University, Kano, Nigeria

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Badamasi Abba

Department of Mathematics, North-West University, Kano, Nigeria

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APA Style

Amiru, F. M., Usman, U., Shamsuddeen, S., Adamu, U. M., Abba, B. (2025). The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data. International Journal of Statistical Distributions and Applications, 11(1), 1-10. https://doi.org/10.11648/j.ijsda.20251101.11

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ACS Style

Amiru, F. M.; Usman, U.; Shamsuddeen, S.; Adamu, U. M.; Abba, B. The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data. Int. J. Stat. Distrib. Appl. 2025, 11(1), 1-10. doi: 10.11648/j.ijsda.20251101.11

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AMA Style

Amiru FM, Usman U, Shamsuddeen S, Adamu UM, Abba B. The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data. Int J Stat Distrib Appl. 2025;11(1):1-10. doi: 10.11648/j.ijsda.20251101.11

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@article{10.11648/j.ijsda.20251101.11,
  author = {Faisal Muhammad Amiru and Umar Usman and Suleiman Shamsuddeen and Umar Muhammad Adamu and Badamasi Abba},
  title = {The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {11},
  number = {1},
  pages = {1-10},
  doi = {10.11648/j.ijsda.20251101.11},
  url = {https://doi.org/10.11648/j.ijsda.20251101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsda.20251101.11},
  abstract = {To measure the average lifespan of systems and components, and to analyze lifetime data with a monotonic failure rate, distributions such as Weibull, Exponential, and Gamma are commonly used in reliability and survival studies. However, these distributions are not suitable for datasets with non-monotonic patterns like the bathtub curve. To address this, the Chen distribution, which accommodates increasing or bathtub-shaped failure rates, has been proposed. Yet, this model lacks a scale parameter. This article presents a new four parameter lifetime distribution with bathtub-shaped failure rate called Additive Dhillon-Chen (ADC) distribution. We applied the additive methodology to establish the model, for which the Dhillon distribution was considered as baseline distribution. Some statistical properties such as quartile function, mode, moment and moment generating function, order statistics and asymptotic behavior of the distribution are studied. Parameters of the distribution are estimated using the maximum likelihood estimation method. The ADC distribution is applied to two lifetime dataset and compared with an existing distribution in the literature. Model selection was carried out based on Log-likelihood, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Corrected Akaike Information Criterion (AICc). The results, based on parameter estimation from real-life data, demonstrate that the ADC distribution fits the data well and offers a valuable alternative for modeling datasets with non-monotonic behavior.},
 year = {2025}
}

Copy | Download

TY  - JOUR
T1  - The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data
AU  - Faisal Muhammad Amiru
AU  - Umar Usman
AU  - Suleiman Shamsuddeen
AU  - Umar Muhammad Adamu
AU  - Badamasi Abba
Y1  - 2025/02/11
PY  - 2025
N1  - https://doi.org/10.11648/j.ijsda.20251101.11
DO  - 10.11648/j.ijsda.20251101.11
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  - 10
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsda.20251101.11
AB  - To measure the average lifespan of systems and components, and to analyze lifetime data with a monotonic failure rate, distributions such as Weibull, Exponential, and Gamma are commonly used in reliability and survival studies. However, these distributions are not suitable for datasets with non-monotonic patterns like the bathtub curve. To address this, the Chen distribution, which accommodates increasing or bathtub-shaped failure rates, has been proposed. Yet, this model lacks a scale parameter. This article presents a new four parameter lifetime distribution with bathtub-shaped failure rate called Additive Dhillon-Chen (ADC) distribution. We applied the additive methodology to establish the model, for which the Dhillon distribution was considered as baseline distribution. Some statistical properties such as quartile function, mode, moment and moment generating function, order statistics and asymptotic behavior of the distribution are studied. Parameters of the distribution are estimated using the maximum likelihood estimation method. The ADC distribution is applied to two lifetime dataset and compared with an existing distribution in the literature. Model selection was carried out based on Log-likelihood, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Corrected Akaike Information Criterion (AICc). The results, based on parameter estimation from real-life data, demonstrate that the ADC distribution fits the data well and offers a valuable alternative for modeling datasets with non-monotonic behavior.
VL  - 11
IS  - 1
ER  -

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