Research Article
A New Exponentiated Siya Distribution and Its Biomedical Application
Shiny Chulliparambil Raj*
,
Mani Vijayakumar
Issue:
Volume 11, Issue 1, March 2025
Pages:
11-19
Received:
12 February 2025
Accepted:
27 February 2025
Published:
13 March 2025
DOI:
10.11648/j.ijsda.20251001.12
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Abstract: This article introduces a new exponentiated distribution called the Siya Distribution by incorporating a new parameter into the existing two-parameter Gamma distribution. It is a versatile three-parameter model designed to capture various data behaviors encountered in biological and environmental studies. Siya distribution accounts for data that exhibit variable degrees of skewness and kurtosis, making it suitable for complex datasets such as medical measurements, reliability analysis, and survival times. We derive fundamental properties including the probability density function (PDF), moments, the cumulative distribution function (CDF), and moment generating function (MGF), along with the hazard function to allow comprehensive analytical exploration of the distribution’s behavior. Parameter estimation is conducted using Maximum Likelihood Estimation (MLE), providing robust estimators for real-world applications. Model performance is evaluated using two real datasets against three alternative existing parameter distributions using the Akaike Information Criterion (AIC), Corrected AIC (AICc), and Bayesian Information Criterion (BIC), demonstrating that the Siya Distribution consistently achieves a superior fit, especially with highly skewed data. Empirical applications to biological and medical data illustrate the model’s adaptability and potential to improve data representation in fields requiring precise distribution modelling. The Exponentiated Siya distribution thus offers a significant tool for advanced statistical analyses in applied sciences, supporting more accurate and nuanced interpretation of complex data trends.
Abstract: This article introduces a new exponentiated distribution called the Siya Distribution by incorporating a new parameter into the existing two-parameter Gamma distribution. It is a versatile three-parameter model designed to capture various data behaviors encountered in biological and environmental studies. Siya distribution accounts for data that ex...
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Research Article
The Additive Dhillon-Chen Distribution: Properties and Applications to Failure Time Data
Faisal Muhammad Amiru*,
Umar Usman,
Suleiman Shamsuddeen,
Umar Muhammad Adamu,
Badamasi Abba
Issue:
Volume 11, Issue 1, March 2025
Pages:
1-10
Received:
30 December 2024
Accepted:
16 January 2025
Published:
11 February 2025
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.
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 ...
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