0-1 transformation

gistfile1.txt

from scipy.stats import beta, norm
import numpy as np

data = np.array([0.0, 0.0, 0.1, 0.1, 0.2, 0.4, 0.5, 0.7, 0.8, 0.8, 0.9, 1.0, 1.0, 1.0])
eps = 0.000001

data[data==0.0] += eps
data[data==1.0] -= eps

a, b, loc, scale = beta.fit(data, floc=0, fscale=1)

def to_beta(data, a, b, loc, scale):
    return beta.cdf(data, a=a, b=b, loc=loc, scale=scale)

def to_inv_norm(data):
    return norm.ppf(data, loc=0, scale=1)

def to_norm(data):
    return norm.cdf(data, loc=0, scale=1)

def to_inv_beta(data, a, b, loc, scale):
    return beta.ppf(data, a=a, b=b, loc=loc, scale=scale)

transformed = to_inv_norm(to_beta(data, a, b, loc, scale))
reverted = to_inv_beta(to_norm(transformed), a, b, loc, scale)
print(transformed, reverted.round(5), data.round(5))

# also see: https://machinelearningmastery.com/empirical-distribution-function-in-python/