article · Innovation in Statistics and Probability
A new family of statistical distributions, termed the new odd reparameterized exponential transformed-X family of distributions, has been developed. The method uses an exponential distribution with a constant scale parameter as a transformer alongside an odd function of a baseline distribution as a generalizer. This framework was applied to extend the traditional Weibull distribution. Mathematical characteristics of this extended model were analysed, including quantile functions, moments, moment generating functions, mean residual life, order statistics, entropy, and extropy. Both Bayesian and non-Bayesian methods were employed for parameter estimation, supported by Monte Carlo simulations across four distinct scenarios. When applied to real-world public health datasets for HIV/AIDS and COVID-19, the newly introduced distribution demonstrated superior fitting performance compared to the standard Weibull model and other related distributions, achieving probability values of 0.9959 and 0.7086 respectively.
Accurate statistical models are essential for interpreting complex trends in healthcare. By extending standard distributions to capture real-world variability better, this approach enhances analytical precision in epidemiological and clinical research. Demonstrating superior fits to HIV/AIDS and COVID-19 data shows how refined mathematical tools can help researchers and health authorities better represent and evaluate disease patterns.
This early-stage theoretical and applied research is relevant to biostatisticians, health data scientists, and developers of analytical software. The extended distribution could be incorporated into statistical computing packages used for epidemiological analysis and risk forecasting. At present, the model sits at an applied research stage, demonstrated on specific public health datasets, and requires implementation into accessible software libraries before direct deployment by commercial or public health organisations.
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In this study, we designed a new family of distributions called new odd reparameterized exponential transformed-X family of distributions. This was achieved by utilizing an exponential distribution with a constant scale parameter as the transformer and then the odd function of the baseline distribution as the generalizer. The new family was used to extend the classical Weibull distribution. We further studied the characteristics of the new extended Weibull distribution which include the quantile function, moment, moment generating function, mean residual life function, order statistic, entropy and extropy. Again, the parameters were estimated using both non-Bayesian and Bayesian approaches. A comprehensive Monte Carlo simulation was conducted under four different scenarios. The proposed distribution was fitted to HIV/AIDS and COVID-19 data and then compared with the baseline distribution (Weibull) and other related models. The new distribution commands superior fit with a probability value of 0.9959 and 0.7086 in the two datasets respectively.
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DOI: 10.64389/isp.2025.01107
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