Create a Weibull distribution in Excel
In my last video I discussed how to create a chi squared distribution, and that post can be read here:- https://tracyrenee61.medium.com/create-a-chi-squared-distribution-in-excel-b2b113d99c37
In this post I intend to discuss how to create a Weibull distribution in Excel.
The Weibull distribution is named after Swedish mathematician Waloddi Weibull, who described it in detail in 1939, although it was first identified by Rene Maurice Frechet and first applied by Rosen & Ramler in 1933 to describe a particle size distribution.
The Weibull distribution is a continuous probability distribution that can fit an extensive range of distribution shapes. Like the normal distribution, the Weibull distribution is unimodal and describes the probabilities associated with continuous data. Unlike the normal distribution, the Weibull distribution can also model skewed data, even left and right skewed data.
The Weibull distribution can fit a variety of shapes, approximating the normal and other distributions. This distribution can be used in a broad range of settings, such as quality control, capability analysis, medical studies, and engineering. It is also frequently used in reliability analysis and warranty analysis to assess time to failure for systems and parts.
There are two versions of the Weibull distribution. One version is the three parameter version that has three parameters of shape, scale, and threshold. When the threshold parameter is set to 0 it is known as the two parameter version.
The formula for the Weibull distribution is:-
In order to create the Weibull distribution, it is first necessary to define the alpha (scale) and beta (shape) variables. In this example I have defined the alpha variable as 3 and the beta variable as 2.
Once the alpha and beta have been defined, it is necessary to enter the input values. For the purposes of this exercise, I have entered random numbers up to 4 from cells A3 to A103 using the following formula:-
=RAND()*4
It is now necessary to enter the formula that creates the Weibull PDF distribution. I have entered the following formula in cell B3 and have copied it down to cell B103:-
=WEIBULL.DIST(A3, $E$3, $F$3, FALSE)
The below graph has been made by the weibull PDF:-
It is now necessary to enter the formula that creates the Weibull CDF distribution. I have entered the following formula in cell D3 and have copied it down to cell D103:-
=WEIBULL.DIST(A3, $E$3, $F$3, TRUE)
The below graph has been made by the weibull CDF:-
The analyst can experiment with the shape and scale of the Weibull distribution to see how the graph changes as the variables change.
I have created a video to accompany this blog post, and it can be viewed here:- https://youtu.be/3xdchDIyJJ4
If you would like to know about other statistical distributions then please refer to my blog post that reviews 25 popular distributions in Python:- https://medium.com/@tracyrenee61/a-review-of-the-25-most-popular-distributions-in-statistics-using-python-eabae1ddfb45
