The distribution theory literature contains recent types of parametric distributional models that have been successfully used in the past and whose goodness of fit is sufficient only for certain datasets, suggesting further attention to accommodate a wider range of real-world datasets, for more adaptability, efficiency, and applications. This study aims to develop an extended Fréchet-G family of distributions and study their mathematical properties. The method of Alzaatreh is employed in developing a new lifetime continuous probability distribution called the new Generalized Odd Fréchet-G Family of Distribution. The developed distribution is flexible for studying positive real-life datasets. The statistical properties related to this family are obtained. The parameters of the family were estimated by using a technique of maximum likelihood. A New Generalized Odd Fréchet-Weibull model is introduced. This distribution was fitted with a set of lifetime data. A Monte Carlo simulation is applied to test the consistency of the estimated parameters of this distribution in terms of their bias and mean squared error with a comparison of M.L.E and the maximum product spacing (MPS). The findings of the Monte Carlo simulation show that the M.L.E method is the best technique for estimating the parameter of New Generalized Odd Frechet-Weibull distribution than the M.PS method. The findings of the application on the data set produce a higher flexibility than some of the competing distributions. In general, our new distributions serve as a viable alternative to other distributions available in the literature for modelling positive data.

A new lifetime continuous probability distribution called the new Generalized Odd Fréchet-Odd-Exponential-G Family of Distribution is developed using the principle of Alzaatreh. The developed distribution is flexible for studying positive real-life datasets. The statistical properties related to this family are obtained. The parameters of the family were estimated by using a technique of maximum likelihood. A NewGeneralized Odd Fréchet-Odd-Exponential-Weibull model is introduced. This distribution was fitted with a set of lifetime data. A Monte Carlo simulation is applied to test the consistency of the estimated parameters of this distribution in terms of their bias and mean squared error with a comparison of M.L.E and the maximum product spacing (MPS).The outcome of the Monte Carlo simulation shows that the M.L.E method is the best technique for estimating the parameter of the New Generalized Odd Frechet-Odd-Exponential-Weibull distribution and the New Generalized Odd Frechet-Odd-Exponential-Rayleigh distribution than the M.PS method. The outcomes of the application on the data set produce a higher flexibility than some of the competing distributions. The distributions serve as a viable alternative to other distributions available in the literature for modelling positive data.

The study examines the limitations of existing parametric distributional models in accommodating various real-world datasets and proposes an extension termed the New Generalized Odd Fréchet-Exponentiated-G (NGOF-Et-G) family. Building upon prior work, this new distribution model aims to enhance flexibility across datasets by employing the direct substitution method. Mathematical properties including moments, entropy, moment generating function (mgf), and order statistics of the NGOF-Et-G family are analyzed, while parameters are estimated using the maximum likelihood technique. Furthermore, the study introduces the NGOF-Et-Rayleigh and NGOF-Et-Weibull models, evaluating their performance using lifetime datasets. A Monte Carlo simulation is employed to assess the consistency and accuracy of parameter estimation methods, comparing maximum likelihood estimation (MLE) and maximum product spacing (MPS). Results indicate the superiority of MLE in estimating parameters for the introduced distribution, alongside the enhanced flexibility of the new models in fitting positive data compared to existing distributions. In conclusion, the research establishes the potential of the proposed NGOF-Et-G family and its variants as promising alternatives in modelling positive data, offering greater flexibility and improved parameter estimation accuracy, as evidenced by Monte Carlo simulations and real-world dataset applications.

Tuberculosis (TB) remains a significant global health burden, necessitating robust statistical models to understand survival dynamics and inform interventions. Most survival analyses rely on the Cox Proportional Hazards (Cox PH) model, which may not adequately capture the survival time distribution. This study focuses on data from the National Tuberculosis and Leprosy Center (NTLC), Zaria, Kaduna State, Nigeria, to identify factors influencing TB survival and assess alternative parametric survival models. The study aims to identify factors associated with TB mortality, assess their impact on survival outcomes, and compare the performance of Weibull, and Log-Logistic Accelerated Failure Time (AFT) models to determine the most suitable model for TB survival data from NTLC Zaria. This study compares the performance of two Accelerated Failure Time (AFT) models, the Weibull, and the Log-Logistic in analyzing TB survival data. The analysis evaluates model fit using p-values, log-likelihood, and Akaike Information Criterion (AIC). Results indicate that the Weibull AFT model outperforms the Log-logistic, with the highest log-likelihood (-228.6) and the lowest AIC (485.11), and the Log-Logistic AFT model (AIC: 492.02, log-likelihood: -232.0). The p-values for both models demonstrate statistical significance, highlighting their effectiveness in modelling TB survival data. However, the Weibull model's higher performance suggests it better captures survival time variability in TB patients. These findings emphasize the importance of selecting appropriate survival models for TB data analysis and support the application of the Weibull AFT model for future studies. Further research should explore integrating advanced statistical techniques and machine learning approaches to enhance predictive accuracy and improve TB management strategies. This study contributes to this growing field by applying parametric survival models, to analyse TB survival data from the National Tuberculosis and Leprosy Centre (NTLC) in Zaria, Nigeria.

Study’s Excerpt Full Abstract In this study, we introduce a novel statistical model termed the New Extension of Topp-Leone Distribution (NETD), constructed using a generalized logarithm function. The derivation of the cumulative density function (CDF) and the probability density function (PDF) for this new distribution is thoroughly detailed. A validity test was conducted to confirm the legitimacy of the proposed NETD, and the results affirm that it is indeed a valid probability distribution. We investigate several key mathematical and statistical properties of the NETD, including the quantile function, moments, Renyi entropy, probability-weighted moments, and order statistics. These properties provide a comprehensive understanding of the distribution's behaviour and characteristics. To estimate the parameters of the NETD, we applied the Maximum Likelihood Estimation (MLE) method, which is known for its efficiency and asymptotic properties. The flexibility, versatility, and performance of the NETD were evaluated using four diverse real-world datasets. Through the application of model selection criteria such as the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Corrected Akaike Information Criterion (CAIC), and Hannan-Quinn Information Criterion (HQIC), we demonstrated that the NETD exhibits superior goodness-of-fit compared to existing variants of the Topp-Leone distribution. Our findings suggest that the NETD is a robust and adaptable distribution, capable of effectively modelling a wide range of empirical data. This new extension not only broadens the applicability of the Topp-Leone family of distributions but also enhances the toolkit available for statistical analysis and modelling in various fields.