Generating discrete random variables

Monte Carlo Simulations in Python

Izzy Weber

Curriculum Manager, DataCamp

Required imports

import scipy.stats as st

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

Discrete uniform distribution

Theoretical probability mass function (PMF):

Sampling from the discrete uniform distribution

low = 3 
high = 21
samples = st.randint.rvs(low, high, size=1000)
samples_dict = {"nums":samples}
sns.histplot(x="nums", data=samples_dict, bins=6, binwidth=0.3)

graph of sample results from discrete uniform distribution

Geometric distribution

The probability distribution of the number of trials, $X$, needed to get one success, given the success probability, $p$.

Probability Mass Function, p = 0.5 Theoretical probability mass function for geometric distribution where p = 0.5

Geometric distribution

Probability Mass Function, p = 0.3 Theoretical probability mass function for geometric distribution where p = 0.3

Sampling from geometric distribution

p = 0.2
samples = st.geom.rvs(p, size=1000)
samples_dict = {"nums":samples}
sns.histplot(x="nums", data=samples_dict)

graph of sample results from geometric distribution

More discrete probability distributions

Poisson (scipy.stats.poisson)
- Expresses the probability of a given number of events occurring in a fixed interval of time or space
Binomial (scipy.stats.binom)
- Expresses probability of the number of successes in a sequence of $n$ independent experiments.
And more!

¹ https://docs.scipy.org/doc/scipy/reference/stats.html#discrete-distributions

Let's practice!

Monte Carlo Simulations in Python