Weibull distribution functions

PDFWeibull(x,alpha,beta)

PDFWeibull(x,alpha,beta) returns the probability density at the value x of the Weibull distribution with shape parameter alpha and scale parameter beta.

This equals the Excel function Weibull.DIST(x,alpha,beta,FALSE).

The equation for the Weibull probability density function is:

$$f(x;\alpha,\beta) = \frac{\alpha}{\beta^\alpha} x^{\alpha-1} \mathrm{e}^{-(x/\beta)^{\alpha}} $$

The following graph shows the PDFWeibull distribution function for different values of the shape parameter alpha with scale parameter beta=1

Weibull probability density function for different values of alpha.

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Function:

PDFWeibull(,,)

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CDFWeibull(x,alpha,beta)

CDFWeibull(x,alpha,beta) returns the value at x of the cumulative Weibull distribution with parameters alpha and beta.

This equals the Excel function Weibull.DIST(x,alpha,beta,TRUE).

The equation for the Weibull cumulative distribution function is:

$$ F(x;\alpha,\beta) = 1- \mathrm{e}^{-(x/\beta)^\alpha}\ $$

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Function:

CDFWeibull(,,)

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RndWeibull(alpha,beta)

RndWeibull(alpha,beta) returns a random number of the Weibull distribution with parameters alpha and beta.

Weibull distribution functions

PDFWeibull(x,alpha,beta)

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CDFWeibull(x,alpha,beta)

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RndWeibull(alpha,beta)

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See also