从概率论和统计学角度看,Weibull Distribution是连续性的概率分布,其概率密度为: 其中,x是随机变量,λ>0是比例参数(scale parameter),k>0是形状参数(shape parameter)。显然,它的累积分布函数是扩展的指数分布函数,而且,Weibull distribution与很多分布都有关系。如,当k=1,它是指数分布;k=2时,是Rayleigh distributi...
where k > 0 is the shape parameter and > 0 is the scale parameter of the distribution. (It is one of the rare cases where we use a shape parameter different from skewness and kurtosis.) Its complementary cumulative distribution function is a stretched exponential function. If the quantity x...
其中,x是随机变量,λ>0是比例参数(scale parameter),k>0是形状参数(shape parameter)。显然,它的累积分布函数是扩展的指数分布函数,而且,Weibull distribution与很多分布都有关系。如,当k=1,它是指数分布;k=2且时,是Rayleigh distribution(瑞利分布)。©...
TheWeibull Distributionis a continuous probability distribution that is used to analyze life data, model failure times, and assess the reliability of access products. This distribution is used in different fields to analyze data. Reliability Function:R(t) = e^-[{(t-γ)/α}^β] Where, β =...
Safdar, S. and E. Ahmed, 2014. Process capability indices for shape parameter of Weibull distribution. Open J. Stat., 4: 207‑219.Safdar, S.; Ahmed, E.: Process capability indices for shape ...
publicWeibullDistribution(doubleshape,doublescale) { if(shape<=0) thrownewArgumentOutOfRangeException( "Shape parameter must be positive"); if(scale<=0) thrownewArgumentOutOfRangeException( "Scale parameter must be positive"); DefineParameters(shape, scale); ...
This happens if there is an “aging” process, or parts that are more likely to fail as time goes on. An example would be products with a built-in weakness that fail soon after the warranty expires. In the field of materials science, the shape parameter k of a distribution of strength...
The Weibull distribution is widely used in reliability and life (failure rate) data analysis. The toolbox provides the two-parameter Weibull distribution y=abxb−1e−axb whereais the scale parameter andbis the shape parameter. Note that there are other Weibull distributions, but you must crea...
Correct estimation of the shape parameter of the Weibull distribution plays a central role in these areas of statistical analysis. Many different methods can be used to estimate this parameter, most of which utilize regression methods. In this paper, we presented various regression methods for ...
When you hold the shape and scale parameters constant, the threshold shifts the distribution left and right. In the probability distribution plot below, I show the threshold’seffectin action! Weibull Shape Parameter (β, k) Unsurprisingly, the shape parameter describes the shape of your data’s...