Poisson replicated

poisson.py

from scipy.stats import poisson

from dataclasses import dataclass
from math import factorial, exp

@dataclass
class Poisson:
    mu : float
    
    def __postinit__(self):
        assert self.mu > 0
        
    def probability(self, k):
        return (self.mu ** k) / factorial (k) * exp(-1 * self.mu)
    
assert abs(Poisson(5).probability(4) - poisson(5).pmf(4)) < 0.0001

"""
https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.poisson.html#scipy.stats.poisson

http://www.stats.ox.ac.uk/~filippi/Teaching/psychology_humanscience_2015/lecture5.pdf

https://stats.stackexchange.com/questions/504701/why-is-poisson-distribution-centered-left-of-mean

https://u.math.biu.ac.il/~amirgi/CTMCnotes.pdf

"""