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
In random network models, sizes for pores and throats are distributed according to a truncated Weibull distribution. As a result, parameters defining the shape of the distribution are critical for the characteristic o...In random network models, sizes for pores and throats are distributed according to a truncated Weibull distribution. As a result, parameters defining the shape of the distribution are critical for the characteristic of the network. In this paper, an algorithm to distribute pores and throats in random network was established to more representatively describe the topology of porous media. First, relations between Weibull parameters and the distribution of dimensionless throat sizes were studied and a series of standard curves were obtained. Then, by analyzing the capillary pressure curve of the core sample, frequency distribution histogram of throat sizes was obtained. All the sizes were transformed to dimensionless numbers ranged from 0 to 1. Curves of the core were compared to the standard curves, and truncated Weibull parameters could be determined according an inverse algorithm. Finally, aspect ratio and average length of throats were adjusted to simultaneously fit the porosity and the capillary pressure curves and the whole network was established. The predicted relative permeability curves were in good agreement with the experimental data of cores, indicating the validity of the algorithm.展开更多
An isothermal operation is implemented by employing a thermogravimetric analyzer (TGA) for simulating the thermal decomposition behavior of 58μm pine sawdust in air atmosphere.An independent parallel reaction model i...An isothermal operation is implemented by employing a thermogravimetric analyzer (TGA) for simulating the thermal decomposition behavior of 58μm pine sawdust in air atmosphere.An independent parallel reaction model is adopted in this study to describe the thermal decomposition mechanism.The Weibull distribution function is used to record and analyze the weight loss during isothermal decomposition at different temperatures(500,600,700,and 800°C).The total weight loss of the pine sawdust is assumed as a linear combination of individual weight loss from three components,including the char and two volatile matters.The plot of the thermal decomposition rate curve leads to kinetic parameters such as the reaction rate constants and the reaction order.The results show that the Weibull distribution function successfully represents decomposition curves of three components,and fits the experimental data very well.Therefore,this study provides a simple way to evaluate the decomposition rate of biomass combustion in a real combustor.展开更多
In this paper, we consider the construction of the approximate profile-</span><span style="font-family:""> </span><span style="font-family:Verdana;">likelihood confiden...In this paper, we consider the construction of the approximate profile-</span><span style="font-family:""> </span><span style="font-family:Verdana;">likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution</span><span style="font-family:""> </span><span style="font-family:Verdana;">under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.展开更多
Statistical distributions play a prominent role in applied sciences,particularly in biomedical sciences.The medical data sets are generally skewed to the right,and skewed distributions can be used quite effectively to...Statistical distributions play a prominent role in applied sciences,particularly in biomedical sciences.The medical data sets are generally skewed to the right,and skewed distributions can be used quite effectively to model such kind of data sets.In the present study,therefore,we propose a new family of distributions suitable for modeling right-skewed medical data sets.The proposed family may be called a new generalized-X family.A special sub-model of the proposed family called a new generalized-Weibull distribution is discussed in detail.The maximum likelihood estimators of the model parameters are obtained.A brief Monte Carlo simulation study is conducted to evaluate the performance of these estimators.Finally,the proposed model is applied to the remission times of the stomach cancer patient’s data.The comparison of the goodness of fit results of the proposed model is made with the other competing models such as Weibull,Kumaraswamy Weibull,and exponentiated Weibull distributions.Certain analytical measures such as Akaike information criterion,Bayesian information criterion,Anderson Darling statistic,and Kolmogorov-Smirnov test statistic are considered to show which distribution provides the best fit to data.Based on these measures,it is showed that the proposed distribution is a reasonable candidate for modeling data in medical sciences and other related fields.展开更多
The purpose of this work is to assess wind potential on the Kanfarandé site (Guinea). The data used for this research covers a period of 6 years (2018 to 2023) and consists of in situ data (Boké meteorologic...The purpose of this work is to assess wind potential on the Kanfarandé site (Guinea). The data used for this research covers a period of 6 years (2018 to 2023) and consists of in situ data (Boké meteorological station) and satellite products via NASA Power Larc. The study is based on sorted hourly data (speed and direction). The treatments focus on the monthly, annual and seasonal average of speeds, by sector and their frequencies as well as the annual available powers. The obtained results made it possible, on the one hand, to assess wind potential and, on the other hand, to highlight the most favorable periods for wind energy exploitation. The analyzes show the months of July and August have the best average wind speeds with 5.01 m/s and 5.34 m/s respectively. Average wind speeds are higher during the day than at night with a peak observed at 6 p.m. The study also shows that the prevailing winds are oriented towards the South-West. The Weibull parameters determined for the site give an average of 4.5 m/s for the scale parameter and for the shape parameter 2.40 corresponding to an average power density of 65 w/m2 with an annual available power of 194.80 W/m2 and an annual available energy of 1706.45 kWh/m2.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.
文摘In random network models, sizes for pores and throats are distributed according to a truncated Weibull distribution. As a result, parameters defining the shape of the distribution are critical for the characteristic of the network. In this paper, an algorithm to distribute pores and throats in random network was established to more representatively describe the topology of porous media. First, relations between Weibull parameters and the distribution of dimensionless throat sizes were studied and a series of standard curves were obtained. Then, by analyzing the capillary pressure curve of the core sample, frequency distribution histogram of throat sizes was obtained. All the sizes were transformed to dimensionless numbers ranged from 0 to 1. Curves of the core were compared to the standard curves, and truncated Weibull parameters could be determined according an inverse algorithm. Finally, aspect ratio and average length of throats were adjusted to simultaneously fit the porosity and the capillary pressure curves and the whole network was established. The predicted relative permeability curves were in good agreement with the experimental data of cores, indicating the validity of the algorithm.
基金Supported by the Chung Yuan Christian University (CYCU-97-CR-CE)
文摘An isothermal operation is implemented by employing a thermogravimetric analyzer (TGA) for simulating the thermal decomposition behavior of 58μm pine sawdust in air atmosphere.An independent parallel reaction model is adopted in this study to describe the thermal decomposition mechanism.The Weibull distribution function is used to record and analyze the weight loss during isothermal decomposition at different temperatures(500,600,700,and 800°C).The total weight loss of the pine sawdust is assumed as a linear combination of individual weight loss from three components,including the char and two volatile matters.The plot of the thermal decomposition rate curve leads to kinetic parameters such as the reaction rate constants and the reaction order.The results show that the Weibull distribution function successfully represents decomposition curves of three components,and fits the experimental data very well.Therefore,this study provides a simple way to evaluate the decomposition rate of biomass combustion in a real combustor.
文摘In this paper, we consider the construction of the approximate profile-</span><span style="font-family:""> </span><span style="font-family:Verdana;">likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution</span><span style="font-family:""> </span><span style="font-family:Verdana;">under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.
基金School of Statistics,Shanxi University of Finance and Economics,Taiyuan china.(i)The National Social Science Fund of China(17BTJ010)and(ii)The Fund for Shanxi“1331 Project”Key Innovative ResearchTeam.
文摘Statistical distributions play a prominent role in applied sciences,particularly in biomedical sciences.The medical data sets are generally skewed to the right,and skewed distributions can be used quite effectively to model such kind of data sets.In the present study,therefore,we propose a new family of distributions suitable for modeling right-skewed medical data sets.The proposed family may be called a new generalized-X family.A special sub-model of the proposed family called a new generalized-Weibull distribution is discussed in detail.The maximum likelihood estimators of the model parameters are obtained.A brief Monte Carlo simulation study is conducted to evaluate the performance of these estimators.Finally,the proposed model is applied to the remission times of the stomach cancer patient’s data.The comparison of the goodness of fit results of the proposed model is made with the other competing models such as Weibull,Kumaraswamy Weibull,and exponentiated Weibull distributions.Certain analytical measures such as Akaike information criterion,Bayesian information criterion,Anderson Darling statistic,and Kolmogorov-Smirnov test statistic are considered to show which distribution provides the best fit to data.Based on these measures,it is showed that the proposed distribution is a reasonable candidate for modeling data in medical sciences and other related fields.
文摘The purpose of this work is to assess wind potential on the Kanfarandé site (Guinea). The data used for this research covers a period of 6 years (2018 to 2023) and consists of in situ data (Boké meteorological station) and satellite products via NASA Power Larc. The study is based on sorted hourly data (speed and direction). The treatments focus on the monthly, annual and seasonal average of speeds, by sector and their frequencies as well as the annual available powers. The obtained results made it possible, on the one hand, to assess wind potential and, on the other hand, to highlight the most favorable periods for wind energy exploitation. The analyzes show the months of July and August have the best average wind speeds with 5.01 m/s and 5.34 m/s respectively. Average wind speeds are higher during the day than at night with a peak observed at 6 p.m. The study also shows that the prevailing winds are oriented towards the South-West. The Weibull parameters determined for the site give an average of 4.5 m/s for the scale parameter and for the shape parameter 2.40 corresponding to an average power density of 65 w/m2 with an annual available power of 194.80 W/m2 and an annual available energy of 1706.45 kWh/m2.