Plotting probability density function with frequency counts

Question

I want to convert fitted distribution to frequency.

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
%matplotlib notebook

# sample data generation
np.random.seed(42)
data = sorted(stats.lognorm.rvs(s=0.5, loc=1, scale=1000, size=1000))

# fit lognormal distribution
shape, loc, scale = stats.lognorm.fit(data, loc=0)
pdf_lognorm = stats.lognorm.pdf(data, shape, loc, scale)

fig, ax = plt.subplots(figsize=(8, 4))

ax.hist(data, bins='auto', density=True)
ax.plot(data, pdf_lognorm)
ax.set_ylabel('probability')
ax.set_title('Linear Scale')

The above code snippet will generate the following plot:

As you can see, the y-axis is in terms of probability. But I want it to be in terms of frequencies.

fig, ax = plt.subplots(figsize=(8, 4))
ax.hist(data, bins='auto')
ax.set_ylabel('probability')
ax.set_title('Linear Scale')

By unsetting density=True, the histogram is displayed in terms of frequencies. But I do not know how to fit the distribution in the same way as it is in histograms - observe how I couldn't draw the orange fitted line in this histogram.

How can I do this? I think I should multiply the fitted distribution with the area under the curve of the histogram, but I don't know how to.

Answer 1

I had the same issue and found I needed to multiply the fitted distribution by the area of the new histogram as you mentioned. Assuming all the bins have the same width, the area of the histogram will be = the bin width (of one bin) * the number of samples (len(data))

Answer 2

Scientifically speaking, it is indeed expected that, since you decide to also plot the density, the y-axis will be in probability, and not in counts...

Nevertheless, you can have both using dual axes and twinx:

fig, ax = plt.subplots(figsize=(8, 4))
ax2 = ax.twinx()

ax.hist(data, bins='auto', density=True)
ax2.hist(data, bins='auto')
ax.plot(data, pdf_lognorm)
ax2.set_ylabel('frequency')
ax.set_ylabel('probability')
ax.set_title('Linear Scale')][1]][1]

where I have also used the more appropriate term 'frequency' for the counts.

Experimenting a little you may even bring the density curve in the front, or interchange the axes:

fig, ax = plt.subplots(figsize=(8, 4))
ax2 = ax.twinx()

ax2.hist(data, bins='auto', density=True)
ax.hist(data, bins='auto')
ax2.plot(data, pdf_lognorm)
ax2.set_ylabel('probability')
ax.set_ylabel('frequency')
ax.set_title('Linear Scale')