Weibull Distribution

Two-parameter Weibull distribution with shape parameter k > 0 and scale parameter λ > 0 is described with probability density function:

Random values modeled by the inverse transform method, which enables the user (when a sample generator from standard continuous uniform distribution is available) to draw a sample of the Weibull distribution. The following property is used: if a random value U ~ U(0, 1) is uniformly distributed at the interval (0, 1), the random value X = λ(ln(U))1/k follows the Weibull distribution W(k, λ) with the parameters k and λ. The sample x1, …, xn is generated by executed the following operations:

  1. Generate the sample u1, …, un of pseudo-random values from standard continuous uniform distribution at the interval (0, 1).

  2. Based on the inverse function , and considering that the values U and 1 – U have the same distribution U(0, 1), calculate the sample from the target Weibull distribution following the formula:

See also:

IStatistics.Weibull | ISmWeibullDistribution | Library of Methods and Models