Let's say I have a column x with uniform distributed values. To these values, I applied a cdf-function.
Now I want to calculate the Gaussian Copula, but I can't find the function in python. I read already, that Gaussian Copula is something like the "inverse of the cdf function".
The reason why I'm doing it comes from this paragraph:
A visual depiction of applying the Gaussian Copula process to normalize an observation by applying 𝑛 = Phi^-1(𝐹(𝑥)). Calculating 𝐹(𝑥) yields a value 𝑢 ∈ [0, 1] representing the proportion of shaded area at the left. Then Phi^−1(𝑢) yields a value 𝑛 by matching the shaded area in a Gaussian distribution.
I need your help, does everyone has an idea how to calculate that?
I have 2 ideas so far:
1) gauss = 1/(sqrt(2*pi)*s)*e**(-0.5*(float(x-m)/s)**2) --> so transform all the values with this to a new value
2) norm.ppf(array,loc,scale) --> So give the ppf function the mean and the std and the array and it will calculate me the inverse of the CDF... But I doubt #2
The thing is
Is not what I want. The idea why I'm doing it, is transforming a not normal/gaussian distribution to a normal distribution.
Any other ideas or tipps?
Thank you very much :)
I found 2 links which are quite usefull: 1. How to transform an arcsine distribution to a normal distribution? 2. Transformation Chi-squared to Normal distribution
In this posts its said that you have to
All the details are in the answer already - you take your random variable, and transform it by its own cdf ..... yielding a uniform result.
Thats true for me. If I take a random distirbution and apply the norm.cdf(data, mean,std) function, I get a uniform distributed cdf
import pandas as pd
data = [1.5]*7 + [2.5]*2 + [3.5]*8 + [4.5]*3 + [5.5]*1 + [6.5]*8
But How can I do the
You then transform again, applying the quantile function (inverse cdf) of the desired distribution (in this case by the standard normal quantile function /inverse of the normal cdf, producing a variable with a standard normal distribution).
Because when I use f.e. the norm.ppf function, the values are not reasonable
EDIT: This link could be useful too enter link description here
SO FOR NOW THERE ARE 3 DIFFERENT IDEAS, AND NONE GIVE ME THE RESULTS I NEED:
- inverse transform method
- Box-Mueller Method
- ppf of cdf
- gauss = 1/(sqrt(2*pi)*s)*e**(-0.5*(float(x-m)/s)**2)