CODEWITHSUNDEEP
python-3.xrandomstatisticsnumpy-ndarraynormal-distribution
BC Smith
BC Smith

Reputation: 767

How can I generate data which will show inverted bell curve for normal distribution

I have generated random data which follows normal distribution using the below code:

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns

rng = np.random.default_rng()
number_of_rows = 10000
mu = 0
sigma = 1
data = rng.normal(loc=mu, scale=sigma, size=number_of_rows)

dist_plot_data = sns.distplot(data, hist=False)
plt.show()

The above code generates the below distribution plot as expected:

enter image description here

If I want to create a distribution plot that is exactly an inverse curve like below then how can I generate the random normal distribution data?

enter image description here

I want the data for which the distribution plot will show the inverse curve. How can I generate this normal distribution data?

Upvotes: 4

Views: 2280

Answers (1)

Sam Mason
Sam Mason

Reputation: 16194

not sure how useful this is, but it's easy to do with rejection sampling. Borrowing the API from Peter O's previous solution but working with blocks for performance gives me:

import numpy as np

def invNormal(low, high, mu=0, sd=1, *, size=1, block_size=1024):
    remain = size
    result = []
    
    mul = -0.5 * sd**-2

    while remain:
        # draw next block of uniform variates within interval
        x = np.random.uniform(low, high, size=min((remain+5)*2, block_size))
        
        # reject proportional to normal density
        x = x[np.exp(mul*(x-mu)**2) < np.random.rand(*x.shape)]
        
        # make sure we don't add too much
        if remain < len(x):
            x = x[:remain]

        result.append(x)
        remain -= len(x)

    return np.concatenate(result)

can be used as sns.histplot(invNormal(-4, 4, size=100_000), bins=51), giving me:

histogram

note that probability densities have to integrate to 1, so the "wider" you make it the smaller the densities will be (i.e. you can't have a density of 0.4 on the y-axis if the range on the x-axis is [-4, +4]). also, it feels less useful to generate a KDE because it'll struggle with the discontinuity at the edges

Upvotes: 2

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