从零构建统计随机变量生成器之泊松分布

http://www.columbia.edu/~ks20/4404-Sigman/4404-Notes-ITM.pdf

https://www.win.tue.nl/~marko/2WB05/lecture8.pdf

泊松分布

import random
from math import exp


def poisson(lambdda: float) -> int:
    total = 1.0
    i = 0
    threshold = exp(-1 * lambdda)
    while total >= threshold:
        u = random.random()
        total *= u
        i += 1
    return i - 1

https://github.com/MyEncyclopedia/stats_simulation/blob/main/distrib_sim/discrete_poisson_inv.py

from numpy.random import exponential

def poisson(lambdda: float) -> int:
    total = 0.0
    i = 0
    while total <= lambdda:
        y = exponential(1)
        total += y
        i += 1
    return i - 1

https://github.com/MyEncyclopedia/stats_simulation/blob/main/distrib_sim/discrete_poisson_from_exp.py

泊松分布

$ E_{1}, E_{2}, E_{3}, (1) $

\[ \mathbb{P}(K \geqslant k)=\mathbb{P}\left(E_{1}+\cdots+E_{k} \leqslant \lambda\right) \]

from numpy.random import exponential

def poisson(lambdda: float) -> int:
    total = 0.0
    i = 0
    while total <= lambdda:
        y = exponential(1)
        total += y
        i += 1
    return i - 1

Github 代码地址：

https://github.com/MyEncyclopedia/stats_simulation/blob/main/distrib_sim/discrete_poisson_from_exp.py