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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.
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.
The Weibull modulus is a dimensionless parameter of the Weibull distribution. It represents the width of a probability density function (PDF) in which a higher modulus is a characteristic of a narrower distribution of values.
Creator Development started First public release Latest stable version Stable release date Cost () License Notes ADMB: David Fournier, ADMB Project
If X is an exponential random variable with mean β, then X 1/γ is a Weibull (γ, β) random variable. The square of a standard normal random variable has a chi-squared distribution with one degree of freedom. If X is a Student’s t random variable with ν degree of freedom, then X 2 is an F (1,ν) random variable.
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