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In probability theory and statistics, the Weibull distribution / ˈ w aɪ b ʊ l / is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.
Despite this, the GEV distribution is often used as an approximation to model the maxima of long (finite) sequences of random variables. In some fields of application the generalized extreme value distribution is known as the Fisher–Tippett distribution, named after R.A. Fisher and L.H.C. Tippett who recognised three different forms outlined ...
CDF of a bimodal Weibull distribution with Weibull Moduli of 4 and 10 and characteristic strengths of 40 and 120 MPa Examples of a bimodal Weibull PDF and CDF are plotted in the figures of this article with values of the characteristic strength being 40 and 120 MPa, the Weibull moduli being 4 and 10, and the value of Φ is 0.5, corresponding to ...
When the larger values tend to be farther away from the mean than the smaller values, one has a skew distribution to the right (i.e. there is positive skewness), one may for example select the log-normal distribution (i.e. the log values of the data are normally distributed), the log-logistic distribution (i.e. the log values of the data follow ...
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
[6] [8] Let the probability distribution function of the yield strength be given as (). Similarly, the applied load or predicted load can also only be known to a certain precision, and the range of stress which the material will undergo is unknown as well. Let this probability distribution be given as ().
The Fréchet distribution, also known as inverse Weibull distribution, [2] [3] is a special case of the generalized extreme value distribution. It has the cumulative distribution function ( ) = > . where α > 0 is a shape parameter.
The Poisson distribution is often used to model the number of rare event occurrences during a fixed period of time. 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 ...