poisson

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

def poisson(l, n):
    if not(l>0 or n>0 or isinstance(n, int)):
        d = 0
    else:
        d = ((l**n)*np.exp(-l))/scipy.special.factorial(n)
    return d
def distr(l, n):
    a = np.arange(n+1)
    return poisson(l,a)

def moment(distr, k):
    if not isinstance(k, int):
        return 0
    else:
        n = np.arange(len(distr))
        c = distr*n**k
        return c.sum()
def av(distr):
    return moment(distr,1,)

def disp(distr):
    n = np.arange(len(distr))
    return (distr*(n-av(distr))**2).sum()

def function_to_test(l, n, d):
    dist = distr(l, n)
    aver = av(dist)
    disper = disp(dist)
    if abs(aver-l) < l*d and abs(disper-l) < l*d:
        return True
    else:
        return False
if __name__ == '__main__':
    assert function_to_test(5, 100, 0.01) == True
    assert function_to_test(6, 100, 0.01) == True
    assert function_to_test(8, 110, 0.01) == True
    plt.plot(distr(6,100))
    plt.show()