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...

In this study, seven popular equations, including 3-parameter Weibull, 2-parameter Weibull, Gompertz, Logistic, Mitscherlich, Korf and R distribution, were used to model stand diameter distributions for exploring the relationship between the equations' inflection point attributes and model accuracy. A database comprised of 146 diameter frequency distributions of Chinese fir (Cunninghamia lanceo...

The function of a distribution that describes postpartum interval (PPI) under any experimental treatment is useful for simulation modeling, understanding the effects of stimuli on the endocrine system, and estimating the average PPI in experiments terminated before all animals have expressed estrus. This study was undertaken to compare the fit of three statistical distributions, the Weibull, th...

We study an integral formulation for the radiative transfer equation in anisotropic media with truncated approximation to scattering phase function. The consists of a coupl...

In this article, the analysis of left truncated and right censored competing risks data is carried out, under the assumption of the latent failure times model. It is assumed that there are two competing causes of failures, although most of the results can be extended for more than two causes of failures. The lifetimes corresponding to the competing causes of failures are assumed to follow Weibu...

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...

Left truncation and right censoring arise naturally in lifetime data. Left truncation arises because in many situations, failure of a unit is observed only if it fails after a certain period. Often, the units under study may not be followed until all of them fail and the experimenter may have to stop at a certain time when some of the units may still be working. This introduces right censoring ...

& Conclusion| We propose a sequential probability ratio test based on a two parameter Weibull distribution for IC failure analysis. The shape parameter of the Weibull distribution characterizes the decreasing, constant and the increasing failure rate regions in the bath tub model for ICs. The algorithm detects the operating region of the IC based on the observed failure times. Unlike the xed-le...

Frailty models are getting more and more popular to account for overdispersion and/or clustering in survival data. When the form of the baseline hazard is somehow known in advance, the parametric estimation approach can be used advantageously. Nonetheless, there is no unified widely available software that deals with the parametric frailty model. The new parfm package remedies that lack by prov...