How to calculate skewness & kurtosis ?

Hi,

I would like to calculate the third and fourth moment with returns data (matrix 1x132)

Do you know the function that can I use for that?

Thanks!

[SUBHASMITA DASH]

Hi,

You can refer to the following links:

https://in.mathworks.com/help/stats/kurtosis.html

https://in.mathworks.com/help/stats/skewness.html

Answer 1

[Star Strider]

If you have the Statistics Toolbox, you can calculate the skewness and kurtosis directly with their respective functions.

If you don’t have the Toolbox, it would be relatively easy to code those functions:

skewns = @(x) (sum((x-mean(x)).^3)./length(x)) ./ (var(x,1).^1.5);
kurtss = @(x) (sum((x-mean(x)).^4)./length(x)) ./ (var(x,1).^2);

These work for numeric vectors.

P.S. — Are your data double arrays or cells? If cells, you’ll likely have to use cellfun or cell2mat to work with any of these functions.

[Nidhi Singh]

@(x) showing me function handle .. But didn't show any values

[Star Strider]

@Nidhi Singh —

Perhaps evaluating the functions with an argument vector would work?

skewns = @(x) (sum((x-mean(x)).^3)./length(x)) ./ (var(x,1).^1.5);
kurtss = @(x) (sum((x-mean(x)).^4)./length(x)) ./ (var(x,1).^2);

x = randn(1, 5000);
sk = skewns(x)

sk = 0.0412

kt = kurtss(x)

kt = 3.0302

.

Answer 2

[Image Analyst]

I have code where I do it from the histogram. You could easily adapt it to handle data not from a histogram. See the function at the bottom of the attached file. Let me know if you can't figure it out.