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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.
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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 ...
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The q-Weibull is a generalization of the Weibull, as it extends this distribution to the cases of finite support (q < 1) and to include heavy-tailed distributions (+ +). The q -Weibull is a generalization of the Lomax distribution (Pareto Type II), as it extends this distribution to the cases of finite support and adds the κ {\displaystyle ...
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.
Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic density, the normal density, and Student's t probability density functions. The logistic sigmoid function is invertible, and its inverse is the logit function.
The Gumbel distribution is a particular case of the generalized extreme value distribution (also known as the Fisher–Tippett distribution). It is also known as the log-Weibull distribution and the double exponential distribution (a term that is alternatively sometimes used to refer to the Laplace distribution).