Generate time series with poisson distribution

poisson_timeseries_generator.py

import math
import random
from datetime import datetime, timedelta

def poisson_timeseries_generator(tau, start_time, end_time):
    """
    Generates a time series with a poisson distribution

    tau: interval lenght i.e. mean of the expected time between events
    start_time: starting date of the time series.  %Y-%m-%d %H:%M:%S format
    end_time: end date of the time series.  %Y-%m-%d %H:%M:%S format

    """
    time_series = []
    time_series.append(datetime.strptime(start_time, '%Y-%m-%d %H:%M:%S'))
    while time_series[-1] < datetime.strptime(end_time, '%Y-%m-%d %H:%M:%S'):
            time_series.append(time_series[-1] + timedelta(minutes = round(next_event(1/tau))))
    return time_series


def next_event(rate_parameter):
    """
    Draw the interval between events
    """
    return -math.log(1.0 - random.random()) / rate_parameter


if __name__ == "__main__":
    import pandas as pd
    tau_value = 5
    time_series = poisson_timeseries_generator(tau = tau_value, start_time = "2021-01-01  00:00:00", end_time = "2021-01-01  23:59:59")
    df = pd.DataFrame({'original': pd.Series(time_series), 'shifted': pd.Series(time_series).shift()})
    df['differences'] = (df.original - df.shifted) / pd.Timedelta(minutes = 1)
    print(f'Time between events: {df.differences.mean()} \nTau {tau_value}')
    print(f'Expected events {(24*60)/tau_value}')
    print(f'Simulated events: {df.shape[0]}')