pdfWeibull#

Purpose#

Computes the probability density function of a Weibull random variable.

Format#

p = pdfWeibull(x, k, lambda)#
Parameters:

  • x (NxK matrix, Nx1 vector or scalar) – x must be greater than 0.

  • k (NxK matrix, Nx1 vector or scalar) – Shape parameter, ExE conformable with x. k must be greater than 0.

  • lambda (NxK matrix, Nx1 vector or scalar) – Scale parameter, may be matrix, ExE conformable with x. lambda must be greater than 0.

Returns:

p (NxK matrix, Nx1 vector or scalar) – the probability density function of a Weibull random variable evaluated at x.

Remarks#

The probability density function of a Weibull random variable is defined as

\[\begin{split}f(x, \lambda, k) = \begin{cases} \frac{k}{\lambda} \big(\frac{x}{\lambda}\big)^{k-1} e^{-(x/\lambda)k}, & x \geq 0\\ 0, & x < 0 \end{cases}\end{split}\]

Examples#

// Data points
x = { 0.5, 1, 2, 3 };

// Weibull PDF with shape = 2, scale = 1
p = pdfWeibull(x, 2, 1);
print p;

After the code above, p is equal to:

   0.77880078
   0.73575888
  0.073262556
0.00074045882

See also

Functions cdfWeibull(), cdfWeibullInv()

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