Search results
Results From The WOW.Com Content Network
for and (;,,) = for <, where > is the shape parameter, > is the scale parameter and is the location parameter of the distribution. θ {\displaystyle \theta } value sets an initial failure-free time before the regular Weibull process begins.
In probability theory and statistics, a shape parameter (also known as form parameter) [1] is a kind of numerical parameter of a parametric family of probability distributions [2] that is neither a location parameter nor a scale parameter (nor a function of these, such as a rate parameter).
This arises because the ordinary Weibull distribution is used for cases that deal with data minima rather than data maxima. The distribution here has an addition parameter compared to the usual form of the Weibull distribution and, in addition, is reversed so that the distribution has an upper bound rather than a lower bound.
If we denote the location parameter by , and the scale parameter by , then we require that (;,,) = (() /;,,) where (,,,) is the cmd for the parametrized family. [1] This modification is necessary in order for the standard deviation of a non-central Gaussian to be a scale parameter, since otherwise the mean would change when we rescale x ...
It is characterized by a single parameter, λ, which is both the mean and variance of the distribution. The discrete Weibull distribution, on the other hand, is more flexible and can handle both over- and under-dispersion in count data. It has two parameters, q and β, which influence the shape and scale of the distribution.
However, it is important to note that the Weibull modulus is a fitting parameter from strength data, and therefore the reported value may vary from source to source. It also is specific to the sample preparation and testing method, and subject to change if the analysis or manufacturing process changes.
In statistics, the exponentiated Weibull family of probability distributions was introduced by Mudholkar and Srivastava (1993) as an extension of the Weibull family obtained by adding a second shape parameter. The cumulative distribution function for the exponentiated Weibull distribution is
The Kaniadakis κ-Weibull distribution is exhibits power-law right tails, and it has the following probability density function: [3] = + ()valid for , where | | < is the entropic index associated with the Kaniadakis entropy, > is the scale parameter, and > is the shape parameter or Weibull modulus.