For β = 1 the Weibull distribution coincides with the exponential distribution with mean α. In general, α represents the .632-quantile of the Weibull distribution regardless of the value of β since Fα,β(α) = 1 − exp(−1) ≈ .632 for all β > 0. Figure 1 shows a representative collection of Weibull densities. Note that the spread of the Weibull distributions around α gets smaller as β increases. Th...

We derive a closed form solution for the Kullback-Leibler divergence between two Weibull distributions. These notes are meant as reference material and intended to provide a guided tour towards a result that is often mentioned but seldom made explicit in the literature. 1 The Weibull Distribution TheWeibull distribution is the type III extreme value distribution; its probability density functio...

ISO 9001 (ISO 1987) certification issues are bringing-out calibration anxieties. The rush to document calibration intervals for certification purposes is often driving-up costs. Both instrument manufactures and calibration services are benefiting financially from calibration anxiety brought on by “ISO systems requiring you to say what you do and do what you say to meet the ISO specifications”. ...

purpose: to evaluate the effect of age, sex, type of surgery, extent of retinal detachment (rd), vitreous incarceration in wound, and myopic degeneration on the rate of retinal redetachment following rd surgery using eternal weibull regression analysis. methods: we performed a survival analysis on a multi-center randomized controlled trial conducted on patients with pseudophakic or aphakic rd t...

Annotation: In this papre We propose a neural network optimization algorithm for independent component analysis(ICA) which can separate mixtures of suband superGaussian source signals with self-adaptive nonlinearities. The ICA algorithem in the framework of natural Riemannian gradient, is derived using the parameterized Weibull density model. The nonlinear function in ICA algorithem is self-ada...

Recent third-order likelihood analysis theory is applied to obtain improved confidence intervals for scalar component interest parameters of the Weibull model. This theory involves implicit but appropriate conditioning and marginalization. Both the censored and complete Weibull models are examined where primary interest is focussed on assessing the shape, scale or median parameter. The simulati...

background and objectives: survival models are statistical technique to estimate or predict the overall time up to specific events. prediction is important in medical science and the accuracy of prediction is determined by a measurement, generally based on loss functions, called prediction error. the aim of this study is using parametric models to determine the factors influencing predicted sur...

We propose the Weibull negative binomial distribution that is a quite flexible model to analyze positive data, and includes as special submodels the Weibull, Weibull Poisson and Weibull geometric distributions. Some of its structural properties follow from the fact that its density function can be expressed as a mixture of Weibull densities. We provide explicit expressions for moments, generati...

Objective: This study investigated the Weibull parameters and 5% fracture probability of direct, indirect composites, and CAD/CAM composites. Material and Methods: Discshaped (12 mm diameter x 1 mm thick) specimens were prepared for a direct composite [Z100 (ZO), 3M-ESPE], an indirect laboratory composite [Ceramage (CM), Shofu], and two CAD/CAM composites [Lava Ultimate (LU), 3M ESPE; Vita En...