The normalization results are not same-CodePudding

I am performing normalization on the random data. I calculated the mean and standard deviation of the data and normalizing by the formula Norm = (data - mean) / std, but I am not getting the result same as numpy normalization function gives and also I am not getting the bell shape curve.

import numpy as np
from scipy.stats import norm

a = np.arange(-4, 4)

mean = sum(a/len(a))
std = (np.sqrt(sum((a-mean)**2)/(len(a)-1)))

y1 = norm.pdf(a, mean, std)
y2 = (a - mean) / std

print(y1)
print(y2)

output

y2 = [0.05868028 0.09674742 0.1350219  0.15950953 0.15950953 0.1350219
 0.09674742 0.05868028]

y1 = [-1.42886902 -1.02062073 -0.61237244 -0.20412415  0.20412415  0.61237244
  1.02062073  1.42886902]

What is the problem?

CodePudding user response：

From the

Then, the y2 you calculate is the result of standardization or z-score. In order to calculate z-score with scipy, you should you scipy.stats.zscore() instead of scipy.stats.norm.pdf().

import numpy as np
from scipy.stats import zscore

a = np.arange(-4, 4)

y1 = (a - a.mean()) / a.std()
y2 = zscore(a)

y1 and y2 will be the same.

CodePudding user response：

Put yet another way, adding this to your code will produce a value equal to norm.pdf:

pdf = np.exp(-y2*y2/2)/((2*np.pi)**0.5) / std