Application of a 2 Parameter Weibull Distribution in Modeling of State Holding Time in HIV/AIDS Transition Dynamics

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.

Differential distribution of PINK1 and Parkin in the primate brain implies distinct roles

The vast majority of in vitro studies have demonstrated that PINK1 phosphorylates Parkin to work together in mitophagy to protect against neuronal degeneration.However,it remains largely unclear how PINK1 and Parkin are expressed in mammalian brains.This has been difficult to address because of the intrinsically low levels of PINK1 and undetectable levels of phosphorylated Parkin in small animals.Understanding this issue is critical for elucidating the in vivo roles of PINK1 and Parkin.Recently,we showed that the PINK1 kinase is selectively expressed as a truncated form(PINK1–55)in the primate brain.In the present study,we used multiple antibodies,including our recently developed monoclonal anti-PINK1,to validate the selective expression of PINK1 in the primate brain.We found that PINK1 was stably expressed in the monkey brain at postnatal and adulthood stages,which is consistent with the findings that depleting PINK1 can cause neuronal loss in developing and adult monkey brains.PINK1 was enriched in the membrane-bound fractionations,whereas Parkin was soluble with a distinguishable distribution.Immunofluorescent double staining experiments showed that PINK1 and Parkin did not colocalize under physiological conditions in cultured monkey astrocytes,though they did colocalize on mitochondria when the cells were exposed to mitochondrial stress.These findings suggest that PINK1 and Parkin may have distinct roles beyond their well-known function in mitophagy during mitochondrial damage.

Quantitative Study on Characteristics of the Weibull Distribution

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.

基于Weibull分布的煤矸石对混凝土断裂损伤特性的影响

为探索煤矸石质量取代率、粉煤灰质量取代率、水灰比对I型裂缝煤矸石混凝土荷载-裂缝张开位移、荷载-跨中挠度曲线、断裂韧性、断裂能的影响规律,对I型裂缝煤矸石混凝土进行三点弯曲试验,将所得结果结合损伤力学及Weibull分布函数建立煤矸石混凝土的断裂损伤本构模型。结果表明:煤矸石质量取代率对预制I型裂缝的煤矸石混凝土断裂性能影响最大,粉煤灰质量取代率对其断裂韧度影响较大,水灰比对其断裂能影响较大;提升煤矸石混凝土断裂时断裂韧度及断裂能的最佳组合的煤矸石质量取代率为25%、粉煤灰质量取代率为10%、水灰比为0.5;经对比可知,所得损伤本构模型对应的应力-应变曲线与试验曲线高度吻合。研究成果为煤矸石混凝土的制备及工程实际应用研究提供了参考。

基于Weibull混合分布的航空发动机零部件寿命建模

针对航空发动机在维修工作中存在重要零部件使用寿命及失效率难以估算的问题,搜集了发动机重要零部件燃油计量活门、整体驱动发电机、液压机械组件的使用寿命数据,并运用Weibull混合分布及单Weibull分布分别建立了上述重要零部件的寿命模型。在模型求解过程中采用了经典的三参数相关系数优化法,求出发动机重要零部件的可靠度、失效率及故障概率密度函数。通过计算得出Weibull混合分布模型的线性相关系数r_(g)比单Weibull分布模型的大;同时K-S假设检验结果显示,Weibull混合分布的统计量观测值D_(n)均小于临界值D_(30,0.1)。结果表明:相对于单Weibull分布,Weibull混合分布模型更精确地表征了发动机重要零部件的寿命数据,从而有效地提高寿命参数的估算精度;Weibull混合分布模型的可靠性有助于发动机管理工程师制定视情维修方案;并对航材备件的数量有指导意义,具有较高的推广应用价值。

基于Weibull分布的石砌体单轴受压损伤本构模型

石砌体的本构模型是石砌体力学计算和有限元数值模拟的重要基础和前提条件。为了深入研究石砌体单轴受压下的本构关系,基于损伤力学理论,应用双参数Weibull分布函数反映损伤变量,根据石砌体单轴受压应力-应变全过程曲线的特征条件确定其参数,推导并建立了石砌体单轴受压损伤本构模型,将已有试验数据验证本构模型的正确性,并将本构模型与典型的砌体本构模型进行对比分析,最后应用本构模型对已有石砌体拱桥试验进行有限元分析以验证本构模型的适用性。结果表明:所建模型与已有石砌体单轴受压试验结果吻合良好;所建模型验证了石砌体损伤演化的一般规律,符合典型的砌体本构模型的一般趋势;所建模型可应用于石砌体结构有限元分析计算,适用性良好。

基于Weibull分布的缺口件多轴疲劳寿命建模

针对多轴缺口件,引入Weibull分布建立考虑应力梯度效应的疲劳寿命预测方法.首先,将最大应变能密度定义为损伤参量,并结合坐标变换确定能反映裂纹萌生和扩展的临界面位置;其次,利用有限元方法提取临界面特定路径的应力分布,并对其进行归一化处理得到多轴等效应力梯度因子,进而基于GSP应变能密度模型得出应变能密度与实验寿命的线性关系;最后,结合等效应力梯度因子、应变能密度模型和Weibull分布,基于Von-Mises准则提出了新的疲劳寿命预测方法,并利用该方法分别求出失效概率10%、50%和90%对应的疲劳寿命.为验证该方法,将计算结果与SWT模型、FS模型和Manson-Coffin方程的计算结果进行对比,结果表明该方法的预测精度较高.

三参数Weibulldistribution场合下定数截尾矩估计

本文讨论了在定数截尾样本下三参数威布尔分布的矩估计问题,并改进了文[4]的结果。

Performance of Weibull function as a diameter distribution model for Pinus thunbergii stands in the eastern coast of South Korea

This study was carried out to determine the performance of percentile-based Weibull diameter distribution model for Pinus thunbergii stands thriving along the eastern coast of South Korea. The parameter recovery technique was used to estimate the three parameters of the Weibull model. The analysis demonstrated satisfactory results based on the following test statistics for the principal percentile models： fit index （FI） range from 0.501（minimum diameter） to 0.932 （50th diameter percentiles） and root mean square error （RMSE） range from 0.112 （quadratic mean diameter） to 3.572 （minimum diameter）. The developed model was further evaluated by determining the mean bias （E） in trees per ha （TPH） for each diameter class, and the results showed highest over-prediction in the 20 cm, and under-prediction in the x6 cm and 24 cm diameter classes. The goodness of fit tested by Kolmogorov- Smirnov （KS） test showed no significant differences （P〉0.05） between the observed and predicted diameter distributions for almost all plots. Using site index and aboveground biomass （AGB） models developed for P. thunbergii in South Korea, a model to predict the AGB per ha for each diameter class and subsequently the total AGB of the stand was created. An application guide was also created, which will serve as a decision-support tool for forest managers in quantifying the future total AGB in P. thunbergii stands located in the eastern coast of South Korea and, subsequently, the quantification of potential carbon stocks aside from being a vital input in designing efficient management and protection strategies for these stands.

A New Study on Combustion Behavior of Pine Sawdust Characterized by the Weibull Distribution

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.

基于Weibull分布的非均质隧洞围岩破裂碎胀FDEM数值模拟研究

岩石材料具有非均质特征,矿物颗粒和胶结材料强度在统计学上服从Weibull分布。基于有限元-离散元耦合数值模拟方法(FDEM)提出了三角形单元弹性模量和四边形节理单元强度服从Weibull分布的参数赋值流程,随后研究了非均质岩样在单轴压缩、三轴压缩和巴西劈裂下的力学特征和破坏行为,最后对非均质隧洞围岩在高应力下的破裂碎胀大变形机制进行了模拟研究。结果表明:提出的随机参数赋值方法可建立不同弹性模量三角形单元数目服从Weibull分布、且空间分布具有随机性的FDEM数值模型;非均质岩样单轴抗压强度、三轴抗压强度、巴西劈裂抗拉强度、等效粘聚力和等效内摩擦角随着非均质度m的增大,均呈指数增大,并向均质材料逼近;高应力非均质隧洞围岩随着m的增大,裂隙网络形态变化不大,均以共轭剪切破裂为主,并伴随少量拉伸裂隙,但围岩破坏程度和裂隙扩展范围呈指数降低。

Parameter Estimations for Some Modifications of the Weibull Distribution

Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibility, some modifications of the Weibull distribution have been made from several researches in order to best adjust the non-monotonic shapes. This paper gives a study on the performance of two specific modifications of the Weibull distribution which are the exponentiated Weibull distribution and the additive Weibull distribution.

Interval Estimation in a Two Parameter Weibull Distribution Based on Type-2 Censored Data

In this paper, we consider the construction of the approximate profile- 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 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.

Constant-step stress accelerated life test of VFD under Weibull distribution case

Constant-step stress accelerated life test of Vacuum Fluorescent Display (VFD) was conducted with increased cathode temperature. Statistical analysis was done by applying Weibull distribution for describing the life, and Least Square Method (LSM)for estimating Weibull parameters. Self-designed special software was used to predict the VFD life. Numerical results showed that the average life of VFD is over 30000 h, that the VFD life follows Weibull distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. Accurate calculation of the key parameter enabled rapid estimation of VFD life.

The Marshall-Olkin Right Truncated Fréchet-Inverted Weibull Distribution: Its Properties and Applications

In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are derived. The method of maximum likelihood is used to estimate the model parameters. The graphs of the reliability function and hazard rate function are plotted by taken some values of the parameters. Three real life applications are introduced to compare the behaviour of the new distribution with other distributions.

Application of the Weibull Distribution to Estimate the Volume of Water Pumping by a Windmill

Given the steady increase in use of alternative energy sources to supply part of the energy demand of the world, and considering that Mexico has enough wind resources to produce all the electricity required by the country, in this work, it is carried out the development of a system of wind resource assessment to determine the volume of water that a windmill pumping system can provide in a specific area. To this end, it has developed a computer program for wind resource assessment by measurements of wind speed, direction, temperature, barometric pressure and relative humidity. Measuring equipments were mounted in a wind measurement tower of 10 m high, within the premises of the University of Quintana Roo which is located along the coast. Until this day, there are records over a period of five months of the variables of wind speed, wind direction, temperature, relative humidity and atmospheric pressure. These variables were used for statistical calculations using the Weibull distributions. To give a better use of the calculated data, they were applied to the evaluation of a Pumping System.

由Chvátal定理引出的关于Weibull分布和Pareto分布的研究

受Chvátal定理的启发,本文研究了随机变量不超过其期望的概率的下确界问题.利用分析的方法,我们得到了当随机变量的分布为Weibull分布或Pareto分布时该随机变量不超过其期望的概率的下确界.

基于混合双参数Weibull分布的冬夏两季香港地区某地的行人风环境舒适度分析

城市的密集建筑会影响周边区域风环境,甚至产生行人风环境问题。研究了香港地区气象条件,对比了双参数Weibull分布和混合双参数Weibull分布,结果表明混合双参数Weibull分布更加适合香港地区的气象数据;根据夏季以及冬季不同的情况,分析了夏季与冬季的行人风环境。在夏季,一号和二号建筑之间的空地有不舒适的区域,在冬季,行人风环境舒适度整体较好。

Comparison of the Bayesian Methods on Interval-Censored Data for Weibull Distribution

This study considers the estimation of Maximum Likelihood Estimator and the Bayesian Estimator of the Weibull distribution with interval-censored data. The Bayesian estimation can’t be used to solve the parameters analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the scale and shape parameters are obtained via Metropolis-Hastings algorithm. Also Lindley’s approximation is used. The two methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the mean square error (MSE) to determine the best for estimating of the scale and shape parameters.

基于Weibull分布模型的不规则矿石颗粒强度分布

不规则矿石颗粒的强度分布决定其断裂行为与破碎产品粒度分布。本文采用不同形式的Weibull分布模型分别拟合不同尺寸的铜矿石颗粒和锡矿石颗粒的强度分布,并对不同模型中的参数进行比较分析。结果表明:两参数Weibull分布模型对两种矿石颗粒强度分布的拟合效果均较好,且在双对数坐标系下,两种矿石颗粒的模型参数(特征破碎强度σ_0和两参数Weibull分布模量m)都随着颗粒尺寸d的增加而线性减小;在两参数Weibull分布模型的基础上,通过引入权重因子w与强度阈值σ_(th)分别构建两段Weibull分布模型和三参数Weibull分布模型,发现两段Weibull分布模型可定量描述剪切破坏与张拉破坏在整个破碎过程中对不规则矿石颗粒的破坏程度,而三参数Weibull分布模型可对低应力强度数据偏离两参数Weibull分布模型拟合曲线得到解释并加以修正。研究成果为碎磨设备操作参数的确定与设备选型提供理论指导,进一步丰富了不规则颗粒强度分布理论与研究方法。