Inverse Transform method for discrete dataset

Hi all

I have a dataset that looks like this:

The red line I obtained by fitting a distribution via:

pd = fitdist(Z_vec,'kernel')

Now I would actually like to transform this data to a Gaussian Standard Normal (0,1).

I tried to follow Inverse Transform method, only the cdf function of Matlab can't create this for a kernel fitted distribution. It failed to do it just like this:

d = cdf(pd , data_vector); 

Or are there any other statistical methods to transform a non-Gaussian dataset like this directly?

Answer 1

[Willemijn Wolf]

Found solution

quantiles = linspace(0,1,datasize); 
[f,x, flo, fup] = ecdf(datavector); %experimental cdf
finv = interp1(f,x,quantile,'next');%Inverse experimental cdf 
pdnorm = makedist('Normal'); transf = icdf(pdnorm,f); %create equivalent cdf values for N(0,1) distribution
plot(x,f); hold on; plot(finv,quantile, 'ro');