This study investigates the application of the two-parameter Weibull distribution in modeling state holding times within HIV/AIDS progression dynamics. By comparing the performance of the Weibull-based Accelerated Fai...This study investigates the application of the two-parameter Weibull distribution in modeling state holding times within HIV/AIDS progression dynamics. By comparing the performance of the Weibull-based Accelerated Failure Time (AFT) model, Cox Proportional Hazards model, and Survival model, we assess the effectiveness of these models in capturing survival rates across varying gender, age groups, and treatment categories. Simulated data was used to fit the models, with model identification criteria (AIC, BIC, and R2) applied for evaluation. Results indicate that the AFT model is particularly sensitive to interaction terms, showing significant effects for older age groups (50 - 60 years) and treatment interaction, while the Cox model provides a more stable fit across all age groups. The Survival model displayed variability, with its performance diminishing when interaction terms were introduced, particularly in older age groups. Overall, while the AFT model captures the complexities of interactions in the data, the Cox model’s stability suggests it may be better suited for general analyses without strong interaction effects. The findings highlight the importance of model selection in survival analysis, especially in complex disease progression scenarios like HIV/AIDS.展开更多
This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique.We refer to the new model as modified alpha p...This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique.We refer to the new model as modified alpha power transformed Weibull distribution.The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions,which are quite familiar in environmental investigations.Its hazard rate function can be decreasing,increasing,bathtub and upside-down then bathtub shaped.Diverse structural properties of the proposed model are acquired including quantile function,moments,entropies,order statistics,residual life and reversed failure rate function.The parameters of the distribution were estimated using the maximum likelihood function.The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed.Via a simulation study,the performance of the point and interval estimates are compared using different criteria.Employing real lifetime data sets,we verify that the offered model furnishes a better fit than some other lifetime models including Weibull,gamma and alpha powerWeibull models.展开更多
The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of...The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of fields,including reliability,economics,engineering,biomedical science,biological research,environmental studies,and finance.For modeling real data,several expanded classes of distributions have been established.The modified alpha power transformed approach is used to implement the new model.The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models.It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters.Precise expressions for quantiles,moments,incomplete moments,moment generating function,characteristic generating function,and entropy expression are among the determined attributes of the new distribution.The point and interval estimates are studied using the maximum likelihood method.Simulation research is conducted to illustrate the correctness of the theoretical results.Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.展开更多
In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditiona...In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.展开更多
Aim To quantitatively study three characteristics of the Weibull distribution. Methods Theoritical analysis of the three characteristics of parameters of the Weibull distribution was done and mathematics software wa...Aim To quantitatively study three characteristics of the Weibull distribution. Methods Theoritical analysis of the three characteristics of parameters of the Weibull distribution was done and mathematics software was used to make some chart analysis. Results 17 equations and 7 figures were made. Conclusion Under the standard form, the class of the Weibull probable density founction(pdf) curves appear double peak shape. Under the standard form, the maximum value point curve of the Weibull pdf takes line t =0 and t=1 as asymptotes. When β = 3 30-3 40, the Weibull distribution is the most similar to the normal distribution.展开更多
文摘This study investigates the application of the two-parameter Weibull distribution in modeling state holding times within HIV/AIDS progression dynamics. By comparing the performance of the Weibull-based Accelerated Failure Time (AFT) model, Cox Proportional Hazards model, and Survival model, we assess the effectiveness of these models in capturing survival rates across varying gender, age groups, and treatment categories. Simulated data was used to fit the models, with model identification criteria (AIC, BIC, and R2) applied for evaluation. Results indicate that the AFT model is particularly sensitive to interaction terms, showing significant effects for older age groups (50 - 60 years) and treatment interaction, while the Cox model provides a more stable fit across all age groups. The Survival model displayed variability, with its performance diminishing when interaction terms were introduced, particularly in older age groups. Overall, while the AFT model captures the complexities of interactions in the data, the Cox model’s stability suggests it may be better suited for general analyses without strong interaction effects. The findings highlight the importance of model selection in survival analysis, especially in complex disease progression scenarios like HIV/AIDS.
基金funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project No.(PNURSP2022R50),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique.We refer to the new model as modified alpha power transformed Weibull distribution.The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions,which are quite familiar in environmental investigations.Its hazard rate function can be decreasing,increasing,bathtub and upside-down then bathtub shaped.Diverse structural properties of the proposed model are acquired including quantile function,moments,entropies,order statistics,residual life and reversed failure rate function.The parameters of the distribution were estimated using the maximum likelihood function.The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed.Via a simulation study,the performance of the point and interval estimates are compared using different criteria.Employing real lifetime data sets,we verify that the offered model furnishes a better fit than some other lifetime models including Weibull,gamma and alpha powerWeibull models.
基金funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project No. (PNURSP2022R50),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of fields,including reliability,economics,engineering,biomedical science,biological research,environmental studies,and finance.For modeling real data,several expanded classes of distributions have been established.The modified alpha power transformed approach is used to implement the new model.The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models.It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters.Precise expressions for quantiles,moments,incomplete moments,moment generating function,characteristic generating function,and entropy expression are among the determined attributes of the new distribution.The point and interval estimates are studied using the maximum likelihood method.Simulation research is conducted to illustrate the correctness of the theoretical results.Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.
文摘In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.
基金Supported by the National Natural Science Foundation of China(12171335,12301603)the Science Development Project of Sichuan University(2020SCUNL201)the Scientific Foundation of Nanjing University of Posts and Telecommunications(NY221026)。
文摘Aim To quantitatively study three characteristics of the Weibull distribution. Methods Theoritical analysis of the three characteristics of parameters of the Weibull distribution was done and mathematics software was used to make some chart analysis. Results 17 equations and 7 figures were made. Conclusion Under the standard form, the class of the Weibull probable density founction(pdf) curves appear double peak shape. Under the standard form, the maximum value point curve of the Weibull pdf takes line t =0 and t=1 as asymptotes. When β = 3 30-3 40, the Weibull distribution is the most similar to the normal distribution.
