Calculate the 3rd standard deviation for an array

Question

Say, I have an array:

import numpy as np

x = np.array([0, 1, 2, 5, 6, 7, 8, 8, 8, 10, 29, 32, 45])

How can I calculate the 3rd standard deviation for it, so I could get the value of +3sigma as shown on the picture below?

enter image description here

Typically, I use std = np.std(x), but to be honest, I don’t know if it returns the 1sigma value or maybe 2sigma, or whatever. I’ll very grateful for you help. Thank you in advance.

Asked By: bluevoxel

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Source

Answer 1

NumPy’s std yields the standard deviation, which is usually denoted with “sigma”. To get the 2-sigma or 3-sigma ranges, you can simply multiply sigma with 2 or 3:

print [x.mean() - 3 * x.std(), x.mean() + 3 * x.std()]

Output:

[-27.545797458510656, 52.315028227741429]

For more detailed information, you might refer to the documentation, which states:

The standard deviation is the square root of the average of the
squared deviations from the mean, i.e., std = sqrt(mean(abs(x –
x.mean())**2)).

http://docs.scipy.org/doc/numpy/reference/generated/numpy.std.html

Answered By: Falko

Answer 2

For anyone who stumbles on this, use something like this – which gives you a rounded column of which standard deviation based on some other column’s values:

# get percentile and which standard deviation for daily decline pct change
def which_std_dev(row,df,col):
    std_1 = round(df[col].mean() + 1 * df[col].std(),0)
    std_2 = round(df[col].mean() + 2 * df[col].std(),0)
    std_3 = round(df[col].mean() + 3 * df[col].std(),0)
    std_4 = round(df[col].mean() + 4 * df[col].std(),0)
    std_5 = round(df[col].mean() + 5 * df[col].std(),0)
    std_6 = round(df[col].mean() + 6 * df[col].std(),0)
    std_7 = round(df[col].mean() + 7 * df[col].std(),0)
    std_8 = round(df[col].mean() + 8 * df[col].std(),0)
    std_9 = round(df[col].mean() + 9 * df[col].std(),0)
    std_10 = round(df[col].mean() + 10 * df[col].std(),0)

    if row[col] <= std_1:
        return 1
    elif row[col] > std_1 and row[col] < std_2:
        return 2
    elif row[col] >= std_2 and row[col] < std_3:
        return 3
    elif row[col] >= std_3 and row[col] < std_4:
        return 4
    elif row[col] >= std_4 and row[col] < std_5:
        return 5
    elif row[col] >= std_6 and row[col] < std_6:
        return 6
    elif row[col] >= std_7 and row[col] < std_7:
        return 7
    elif row[col] >= std_8 and row[col] < std_8:
        return 8
    elif row[col] >= std_9 and row[col] < std_9:
        return 9
    else:
        return 10

df_day['percentile'] = round(df_day['daily_decline_pct_change'].rank(pct=True),3)
df_day['which_std_dev'] = df_day.apply(lambda row: which_std_dev(row,df_day,'daily_decline_pct_change'), axis = 1)

Answered By: max

Calculate the 3rd standard deviation for an array

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