Is there a way to fit a normal curve to points? - matplotlib

Question

As a small project I've made a program the throws nd dice an nt number of times. At each throw it sums the results from the dice and adds it to a list. At the end the data is rappresented with matplot.
import random
from collections import Counter
import matplotlib.pyplot as plt
nd = int(input("Insert number of dice: "))
nt = int(input("Insert number of throws: "))
print(nd, " dice thrown ", nt, " times")
print("Generating sums, please hold....")
c = 0
i = 0
sum = 0
sums = []
while nt >= i :
while nd >= c:
g = random.randint(1, 6)
sum = sum + g
c += 1
sums.append(sum)
i = i+1
c=0
sum = 0
print("Throw ", i, " of ", nt)
sums.sort()
max = max(sums)
min = min(sums)
print("||Maximum result: ", max, " ||Minimum result: ", min)
print("Now ordering results")
f = Counter(sums)
y = list(f.values())
x = list(f.keys())
print("Rappresenting results")
plt.plot(x, y)
plt.xlabel("Risultati")
plt.ylabel("Frequenza")
plt.title("Distribuzione delle somme")
plt.grid(True)
plt.tight_layout()
plt.show()
The resultant graph looks something like this:
I would like to know how to fit a gaussian curve to the points in order to make the graph clearer

Answer 1

The mean and the standard deviation of the sums are the parameters needed for the Gaussian normal. The pdf of a distribution has an area of 1. To scale it to the same size as the histogram, it needs to be multiplied with the number of input values (len(sums)).
Converting the code to work with numpy arrays, makes everything much faster:
import numpy as np
from collections import Counter
import matplotlib.pyplot as plt
from scipy.stats import norm
nd = 10000 # int(input("Insert number of dice: "))
nt = 10000 # int(input("Insert number of throws: "))
print(nd, "dice thrown", nt, "times")
print("Generating sums, please hold....")
sums = np.zeros(nt, dtype=np.int)
for i in range(nt):
sums[i] = np.sum(np.random.randint(1, 7, nd))
sums.sort()
xmax = sums.max()
xmin = sums.min()
print("||Maximum result: ", xmax, " ||Minimum result: ", xmin)
print("Now ordering results")
f = Counter(sums)
y = list(f.values())
x = list(f.keys())
print("Plotting results")
plt.plot(x, y)
mean = sums.mean()
std = sums.std()
xs = np.arange(xmin, xmax + 1)
plt.plot(xs, norm.pdf(xs, mean, std) * len(sums), color='red', alpha=0.7, lw=3)
plt.margins(x=0)
plt.xlim(xmin, xmax)
plt.ylim(ymin=0)
plt.tight_layout()
plt.show()
PS: Here is some code to add to the code of the question, using numpy only for calculating the mean and the standard deviation. (Note that as you use sum as a variable name, you get an error when you try to use Python's sum() function. Therefore, it is highly recommended to avoid naming variables such as sum and max.)
def f(x):
return norm.pdf(x, mean, std) * len(sums)
mean = np.mean(sums)
std = np.std(sums)
xs = range(xmin, xmax+1)
ys = [f(x) for x in xs]
plt.plot(xs, ys, color='red', lw=3)