The Excel WEIBULL.DIST Function

Weibull Distribution

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

The Weibull probability density function is given by the equation :

Weibull Probability Density Function

where x is the independent variable, α is the shape parameter, and β is the scale parameter.

The Weibull cumulative distribution function is :

Weibull Cumulative Distribution Function

More information on the Weibull Distribution is given on the Wikipedia Weibull Distribution Page


Basic Description

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

Although the function is new in Excel 2010, it is simply a renamed version of the Weibull function, which is available in Excel 2007 and earlier.

The format of the Weibull.Dist function is :

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

Where the function arguments are:


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


Weibull.Dist Function Examples

Example 1 - Weibull Probability Density Function

The chart on the right shows the Weibull Probability Density Function with the shape parameter, α = 3 and the scale parameter, β = 1.

If you want to calculate the value of this function at x = 1, this can be done with the Weibull.Dist function, as follows:

=WEIBULL.DIST( 1, 3, 1, FALSE )

This gives the result 1.10363832351433.
Plot of Weibull Probability Density Function with Alpha=3 and Beta=1

Weibull Probability Density Function with α = 3 and β = 1

Example 2 - Weibull Cumulative Distribution Function

The chart on the right shows the the Weibull Cumulative Distribution Function with the shape parameter, α = 5 and the scale parameter, β = 1.5.

If you want to calculate the value of this function at x = 2, this can be done with the Weibull.Dist function, as follows:

=WEIBULL.DIST( 2, 5, 1.5, TRUE )

This gives the result 0.985212776817482.
Plot of Weibull Cumulative Distribution Function with Alpha=5 and Beta=1.5

Weibull Cumulative Distribution Function with α = 5 and β = 1.5

The Excel Weibull.Dist function is described further on the Microsoft Office website.


Weibull.Dist Function Errors

If you get an error from the Excel Weibull.Dist function this is likely to be one of the following :

Common Errors
#NUM! - Occurs if either:
- the supplied x value is < 0
or
- the supplied alpha or the supplied beta argument is ≤ 0
#VALUE! - Occurs when either of the supplied alpha or beta arguments are non-numeric
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