# Documentation/Calc Functions/WEIBULL

Jump to navigation Jump to search

WEIBULL

## Category:

Statistical Analysis

## Summary:

Calculates values for the probability density function or the cumulative distribution function for the two-parameter Weibull distribution. The two-parameter Weibull distribution is a continuous probability distribution that is characterized by a shape parameter and a scale parameter, which are referred to as alpha and beta respectively within Calc but may have different designations in other sources. Depending on the settings of the shape and scale parameters, values of the probability density function may be greater than 1 for the two-parameter Weibull distribution.

## Syntax:

WEIBULL(Number; Alpha; Beta; C)

## Returns:

Returns a real number which is a value from the probability density function or the cumulative distribution function of the specified two-parameter Weibull distribution.

## Arguments:

Number is a non-negative real number or a reference to a cell containing that number which is the value at which to calculate the Weibull distribution.

Alpha is a positive real number or a reference to the cell containing that number which is the shape parameter of the Weibull distribution.

Beta is a positive real number or a reference to the cell containing that number which is the scale parameter of the Weibull distribution.

C is a logical value that determines the form of the function. C = 0 or False to calculate the probability density function. It can be any other value or True to calculate the cumulative distribution function.

• If Alpha or Beta is less than or equal to zero then the function returns an error value.
• If Number is less than zero then the function will return an error value.

## Additional details:

• The formula for WEIBULL is:

If C is 0, WEIBULL calculates the probability density function value

If C is 1, WEIBULL calculates the cumulative distribution function value

• WEIBULL will give the same result as an exponential distribution when the value of the Alpha parameter is 1. This will mean the Lambda parameter in EXPON.DIST and EXPONDIST will be equal to (1/β).

λ = (1/β)

• For more details on the Weibull distribution, visit Wikipedia.

## Examples:

Formula Description Returns
=WEIBULL(5.8;2.2;3.7;0) The function calculates the probability density function for the Weibull distribution for the given parameters. 0.069330557687019
=WEIBULL(5.8;2.2;3.7;1) The function calculates the cumulative distribution function for the Weibull distribution for the given parameters. 0.932012008181695
=WEIBULL(-5.8;2.2;3.7;1) The function returns an error value since Number is less than 0. Err:502
=WEIBULL(1,5,1,0) The function calculates the probability density function for the Weibull distribution for the given parameters. 1.83939720585721
=WEIBULL(5.8;0;3.7;1) The function returns an error value when either Alpha or Beta is less than or equal to 0. Err:502

WEIBULL