displot for a specific histogram (not normal)

Question

I am trying to overlay a truncated normal distribution with specific a and b parameters over a histogram of samples generated from the very same distribution.

How do I fit with a pdf of truncnorm(a,b)?

import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as stats
import matplotlib.mlab as mlab

from IPython.display import Math, Latex
# for displaying images
from IPython.core.display import Image
# import seaborn
import seaborn as sns
# settings for seaborn plotting style
sns.set()
# settings for seaborn plot sizes
sns.set(rc={'figure.figsize':(5,5)})

tempdist=[]

samples=100

for k in range(1,samples):
    #Probability
    #Storage temp as truncated normal
    #temperature as normal mean 55 with 5F variation
    storagetempfarenht = 57 #55
    storagetempkelvin = (storagetempfarenht + 459.67) * (5.0/9.0)
    highesttemp=storagetempfarenht + 5
    lowesttemp= storagetempfarenht -5
    sigma = ((highesttemp + 459.67) * (5.0/9.0)) - storagetempkelvin
    mu, sigma = storagetempkelvin, sigma
    lower, upper = mu-2*sigma , mu+2*sigma
    a=(lower - mu) / sigma
    b=(upper - mu) / sigma
    temp =stats.truncnorm.rvs(a, b, loc=mu, scale=sigma, size=1)
    mean, var, skew, kurt = stats.truncnorm.stats(a, b, moments='mvsk')

    tempdist.append(temp)

#Theses are the randomly generated values
tempdist=np.array(tempdist)

x = range(250,350)

ax = sns.distplot(tempdist,
                  bins=500,
                  kde=True,
                  color='r',
                  fit=stats.truncnorm,
                  hist_kws={"linewidth": 15,'alpha':1})
ax.set(xlabel='Trunc Normal Distribution', ylabel='Frequency')

Answer 1

The fit parameter of sns.distplot doesn't work well for the truncnorm , at least not with limited data. truncnorm.fit needs some guesses, and distplot doesn't know how to provide them.

This post explains how you could manually fit a truncnorm . The code below just draws the truncnorm.pdf with the initial parameters. To get fitted parameters, you can use the code from the linked post.

Some remarks:

• A lot of numpy (and scipy) functions operate on complete arrays and can generate complete arrays in one go. Eg stats.truncnorm.rvs(..., size=N) generates an array with N samples.
• Setting bins=500 in distplot would create 500 histogram bins, which is not really helpful when there are only 100 samples.
• kde=True plots a pdf of an estimated distribution; default this is a sum of gaussian kernels; the more bins, the more the kde follows the detail of the data (instead of its general form)
• Setting "linewidth": 15 in hist_kws creates lines around the histogram bars of 15 pixels wide. This is much wider than the bars themselves, leading to a weird-looking plot. Better set the linewidth to 1 or so.
• In Python, for k in range(1,samples) runs sample-1 times. This is related to Python starting array indices with 0 and not with 1.

import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as stats
import matplotlib.mlab as mlab
import seaborn as sns
sns.set()
sns.set(rc={'figure.figsize': (5, 5)})

samples = 100

storagetempfarenht = 57  # 55
storagetempkelvin = (storagetempfarenht + 459.67) * (5.0 / 9.0)
highesttemp = storagetempfarenht + 5
lowesttemp = storagetempfarenht - 5
sigma = ((highesttemp + 459.67) * (5.0 / 9.0)) - storagetempkelvin
mu, sigma = storagetempkelvin, sigma
lower, upper = mu - 2 * sigma, mu + 2 * sigma
a = (lower - mu) / sigma
b = (upper - mu) / sigma
temp = stats.truncnorm.rvs(a, b, loc=mu, scale=sigma, size=1)
# mean, var, skew, kurt = stats.truncnorm.stats(a, b, moments='mvsk')

# Theses are the randomly generated values
tempdist = stats.truncnorm.rvs(a, b, loc=mu, scale=sigma, size=samples)

ax = sns.distplot(tempdist,
                  # bins=10,  # 10 bins is the default
                  kde=True,
                  color='r',
                  # fit=stats.truncnorm, # doesn't work for truncnorm
                  hist_kws={"linewidth": 1, 'alpha': 1, 'label': 'Histogram'},
                  kde_kws={"linewidth": 2, 'alpha': 1, 'color': 'dodgerblue', 'label': 'Estimated kde'})
ax.set(xlabel='Trunc Normal Distribution', ylabel='Frequency')
x_left, x_right = ax.get_xlim()
x = np.linspace(x_left, x_right, 500)
y = stats.truncnorm.pdf(x, a, b, loc=mu, scale=sigma)
ax.plot(x, y, color='limegreen', label='Given truncnormal')
# for xi in (lower, upper):   # optionally draw vertical lines at upper and lower
#    ax.axvline(xi, linestyle=':', color='limegreen')
plt.legend()
plt.tight_layout()
plt.show()