How to return the number of trials (n) in a binomial distribution for a given probability using library function scipy.stats.binom.pmf?

Question

Is it possible to get scipy.stats.binom.pmf(x, n, p) to return the number of trials ( n ) with the probabaility, number of successes ( x ), and probability of successes ( p ) known?

Example Problem:

How many throws does Alex need to do in order to be 90% sure of hitting the target at least 10 times?

where:

• Probability = 0.90
• p = 0.50
• x = 10

Answer 1

You can do something like this. What you want to compute is what scipy.stats calls the survival function ( sf ) which is 1-cdf . Since you are interested in greater than or equal to 10 success--that is the sum of the probabilities of 10 or more successes, that is precisely 1-cdf . The sf function can take a numpy array for the arguments, so we pass in an array for n (varying the number of trials). We then look for the number of trials that gave us a value greater than the defined confidence .

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


# Defining model parameters
p = 0.5
k = 10
confidence = 0.9
n = np.arange(k, 5*k)

# Generating survival function distribution and computing the number of required trials
binomSurvivalDist = scipy.stats.binom.sf(k, n, p)
nrequired = n[binomSurvivalDist >= confidence][0]

# Plotting the results to Verify that this works
fig, ax = plt.subplots(1, 1, figsize=(12, 10))
x = np.arange(0, nrequired+1, 1)
ax.plot(x, scipy.stats.binom.sf(x, nrequired, p), lw=2)
ax.set_xlabel("Number of Successes", fontsize=16)
ax.set_ylabel("Probability of Getting At Least this Many Success", fontsize=16)
ax.set_title("Distribution for %i Trials" % nrequired, fontsize=18)

print(nrequired)
plt.show()

The plot is not necessary for the computation, but allows us to verify that the procedure does give us the correct answer.