In a binomial issue, how to compute the p param required for known P(X=x) and N trial

Question

Issue

I have users who connect from source device to a target one, randomly. Each at his own frequency.

If a user has done a connexion in the last N days before his next one occurs, the system will remember him. Some user connect fewer than one in N days.

The question, how to compute the connexion frequency a user should have to be remembered by the system, at a certain confidence.

Answer 1

Python code

from scipy.stats import binom
import numpy as np

def compute_p_param(n_trial, confidence):
    for p in np.arange(0, 1, 0.05):
        connexion = binom(n_trial, p)
        if p == 0:
            continue
        # Looking for p(at least 2 connexions in N days)
        proba = 1 - connexion.cdf(1)
        if proba >= confidence:
            print("p param:", p, "n:", n_trial, "confidence", confidence)
            break

if __name__ == '__main__':
    compute_p_param(n_trial=30, 0.80 )