The WEIBULL.DIST function returns the Weibull Probability Density Function or the Weibull Cumulative Distribution Function for a supplied set of parameters.

  • This function was introduced in Excel 2010 and so is not available in earlier versions.
  • The WEIBULL.DIST function replaces the WEIBULL function included in earlier versions of Excel.

Syntax

=WEIBULL.DIST(x,alpha,beta,cumulative)

Arguments

Argument Description
x The value at which the function is to be calculated – must be ≥ 0
alpha The shape parameter to the distribution – must be > 0
beta The scale parameter to the distribution – must be > 0
cumulative A logical argument which denotes the type of distribution to be used

  TRUE Weibull Cumulative Distribution Function
  FALSE Weibull Probability Density Function

Examples

  A B C D
1 Data Description    
2 104 Value at which to evaluate the function    
3 20 Alpha parameter to the distribution    
4 100 Beta parameter to the distribution    
5        
6 Forumla Result Notes
7 =WEIBULL.DIST(A2,A3,A4,TRUE) 0.888208879 Weibull cumulative distribution function for the terms above
8 =WEIBULL.DIST(A2,A3,A4,FALSE) 0.047105406 Weibull probability density function for the terms above

Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if either of the supplied alpha or beta arguments are non-numeric
#NUM! Occurs if either:

  the supplied x value is < 0
  the supplied alpha or the supplied beta argument is ≤ 0

The Weibull distribution is a probability distribution that is frequently used in engineering.

The equation for the Weibull cumulative distribution function is:    

    \[    f(x;\alpha,\beta) = 1 - e^{ -(x/\beta)^\alpha }    \]

The equation for the Weibull probability density function is:

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

where x is the independent variable, \alpha is the shape parameter, and \beta is the scale parameter.

See Wikipedia for more information on Weibull distribution.