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Excel - WEIBULL.DIST Function
WEIBULL.DIST Function
The Excel WEBULL.DIST function is listed under the Statistical function and generates the Weibull distribution. Manually calculating the mathematical equation of the WEIBULL distribution in the massive dataset gives inaccurate results and wastes the user's precious time.
This function is used in various scenarios, such as reliability and electrical engineering, general insurance, radar systems, duration modeling, event analysis, etc.
Three properties of the WEIBULL.DIST are −
- Probability Density Function
- Cumulative Distribution Function
- Moment Generating Function
Compatibility
This advanced Excel function is compatible with the following versions of MS Excel −
- Excel for Microsoft 365
- Excel for Microsoft 365 for Mac
- Excel for the web
- Excel 2024
- Excel 2024 for Mac
- Excel 2021
- Excel 2021 for Mac
- Excel 2019
- Excel 2016
- Excel 2013
- Excel 2010
Syntax
The formula of the WEIBULL.DIST function is given below −
=WEIBULL.DIST(x,alpha,beta,cumulative)
Arguments
You can use the following arguments with the WEIBULL.DIST function −
| Argument | Description | Required/Optional |
|---|---|---|
| X | A numeric value to compute the function. | Required |
| Alpha | A shape parameter | Required |
| Beta | Another scale parameter. | Required |
| Cumulative | A Boolean value to identify the function's form. | Required |
Points to Remember
- The mathematical equation for the Weibull cumulative distribution function is −
$$\mathrm{F\left ( x;\alpha ,\:\beta \right )\:=\:1\:-\:e^{-\left ( X/\beta \right )^\alpha}}$$
- The mathematical equation for the Weibull probability density function is −
$$\mathrm{F\left ( x;\alpha ,\:\beta \right )\:=\:\frac{\alpha }{\beta^a }x^{a-1}e^{\left ( -x/\beta \right )^\alpha }}$$
- If the alpha is equal to 1, then the WEIBULL.DIST function receives the exponential distribution with −
$$\mathrm{\lambda \:=\:\frac{1}{\beta }}$$
- If x, alpha, or beta argument contains a value other than numeric, WEIBULL.DIST returns the #VALUE! Error.
- If the x argument contains the negative value, the WEIBULL.DIST function retrieves the #NUM! error.
- If alpha ≤ 0 or if beta ≤ 0, then the WEIBULL.DIST function retrieves the #NUM! error.
Examples of WEIBULL.DIST Function
Practice the following examples to learn the use of the WEIBULL.DIST function in Excel.
Example 1: How to use the WEIBULL.DIST Function in Excel?
In this example, we will compute the WEIBULL.DIST function is used to get the cumulative distribution form of the Weibull Distribution.
Solution
Step 1 − Consider the sample dataset where x equals 1320, Alpha is set to 14.71, Beta is set to 1243.44, and cumulative values are set to TRUE. You may enter the formula =WEIBULL.DIST(C2,C3,C4,C5) in the C6 cell and press the Enter tab.
Therefore, the WEIBULL.DIST function returns the 0.910032206.
Step 2 − Furthermore, to compute the probability density form of the WEIBULL distribution that can be achieved by setting the FALSE value in the Cumulative argument, you may write the expression =WEIBULL.DIST(C2,C3,C4,FALSE) in the C8 cell and hit the Enter tab.
Therefore, the resulting value is 0.002414555.
Example 2
If x, alpha, or beta argument contains a value other than numeric, WEIBULL.DIST returns the #VALUE! Error.
Solution
You may enter the formula =WEIBULL.DIST("Style",0.3,0.4,TRUE) in the B3 cell. Here, the x contains the text value, which is strictly prohibited.
Hence, the WEIBULL.DIST function retrieves the #VALUE! error.
Example 3
If the x argument contains the negative value, the WEIBULL.DIST function retrieves the #NUM! error.
Solution
You may write the formula =WEIBULL.DIST(-3.2,0.3,0.4,TRUE) in the B5 cell and hit the Enter tab. Here, the x contains negative value.
Hence, the WEIBULL.DIST function returns the #NUM! error as it cannot work perfectly if the x is negative.
Download Practice Sheet
You can download and use the sample data sheet to practice the WEIBULL.DIST function.