255 lines
7.0 KiB
Python
255 lines
7.0 KiB
Python
import math
|
|
from utils import *
|
|
|
|
|
|
def bnd(x, n, p):
|
|
"""
|
|
Computes the binomial distribution.
|
|
:param x: Number of successes.
|
|
:param n: Number of trials.
|
|
:param p: Probability of success.
|
|
:return: Returns the probability of getting x successes in n trials.
|
|
"""
|
|
return math.comb(n, x) * p ** x * (1 - p) ** (n - x)
|
|
|
|
|
|
def bnd_mean(n, p):
|
|
"""
|
|
Computes the mean of the binomial distribution.
|
|
:param n: Number of trials.
|
|
:param p: Probability of success.
|
|
:return: Returns the mean of the binomial distribution.
|
|
"""
|
|
return n * p
|
|
|
|
|
|
def bnd_var(n, p):
|
|
"""
|
|
Computes the variance of the binomial distribution.
|
|
:param n: Number of trials.
|
|
:param p: Probability of success.
|
|
:return: Returns the variance of the binomial distribution.
|
|
"""
|
|
return n * p * (1 - p)
|
|
|
|
|
|
def bnd_std(n, p):
|
|
"""
|
|
Computes the standard deviation of the binomial distribution.
|
|
:param n: Number of trials.
|
|
:param p: Probability of success.
|
|
:return: Returns the standard deviation of the binomial distribution.
|
|
"""
|
|
return bnd_var(n, p) ** 0.5
|
|
|
|
|
|
def bnd_upto(x, n, p):
|
|
"""
|
|
Computes the cumulative probability of getting upto x successes in n trials.
|
|
:param x: Number of successes.
|
|
:param n: Number of trials.
|
|
:param p: Probability of success.
|
|
:return: Returns the cumulative probability of getting upto x successes in n trials.
|
|
"""
|
|
return sum(bnd(i, n, p) for i in range(x + 1))
|
|
|
|
|
|
def bnd_from(x, n, p):
|
|
"""
|
|
Computes the cumulative probability of getting from x successes in n trials.
|
|
:param x: Number of successes.
|
|
:param n: Number of trials.
|
|
:param p: Probability of success.
|
|
:return: Returns the cumulative probability of getting from x successes in n trials.
|
|
"""
|
|
return 1 - bnd_upto(x - 1, n, p)
|
|
|
|
|
|
def gd(x, p, q=None):
|
|
"""
|
|
Computes the geometric distribution.
|
|
:param x: Number of trials until the first success.
|
|
:param p: Probability of success.
|
|
:param q: Probability of failure.
|
|
:return: Returns the probability of getting the first success on the xth trial.
|
|
"""
|
|
if q is None:
|
|
q = 1 - p
|
|
return q ** (x - 1) * p
|
|
|
|
|
|
def gd_mean(p):
|
|
"""
|
|
Computes the mean of the geometric distribution.
|
|
:param p: Probability of success.
|
|
:return: Returns the mean of the geometric distribution.
|
|
"""
|
|
return 1 / p
|
|
|
|
|
|
def gd_var(p):
|
|
"""
|
|
Computes the variance of the geometric distribution.
|
|
:param p: Probability of success.
|
|
:return: Returns the variance of the geometric distribution.
|
|
"""
|
|
return (1 - p) / p ** 2
|
|
|
|
|
|
def gd_std(p):
|
|
"""
|
|
Computes the standard deviation of the geometric distribution.
|
|
:param p: Probability of success.
|
|
:return: Returns the standard deviation of the geometric distribution.
|
|
"""
|
|
return gd_var(p) ** 0.5
|
|
|
|
|
|
def gd_upto(x, p):
|
|
"""
|
|
Computes the cumulative probability of getting upto x trials until the first success.
|
|
:param x: Number of trials until the first success.
|
|
:param p: Probability of success.
|
|
:return: Returns the cumulative probability of getting upto x trials until the first success.
|
|
"""
|
|
return sum(gd(i, p) for i in range(1, x + 1))
|
|
|
|
|
|
def gd_from(x, p):
|
|
"""
|
|
Computes the cumulative probability of getting from x trials until the first success.
|
|
:param x: Number of trials until the first success.
|
|
:param p: Probability of success.
|
|
:return: Returns the cumulative probability of getting from x trials until the first success.
|
|
"""
|
|
return 1 - gd_upto(x - 1, p)
|
|
|
|
|
|
def hgd(x, N, n, k):
|
|
"""
|
|
Computes the hyper geometric distribution.
|
|
:param x: Number of successes in the sample.
|
|
:param N: Number of items in the population.
|
|
:param n: Number of draws.
|
|
:param k: Number of successes in the population.
|
|
:return: Returns the probability of getting x successes in n draws from a population of size N with k successes.
|
|
"""
|
|
return (math.comb(k, x) * math.comb(N - k, n - x)) / math.comb(N, n)
|
|
|
|
|
|
def hgd_mean(N, n, k):
|
|
"""
|
|
Computes the mean of the hyper geometric distribution.
|
|
:param N: Number of items in the population.
|
|
:param n: Number of draws.
|
|
:param k: Number of successes in the population.
|
|
:return: Returns the mean of the hyper geometric distribution.
|
|
"""
|
|
return n * (k / N)
|
|
|
|
|
|
def hgd_var(N, n, k):
|
|
"""
|
|
Computes the variance of the hyper geometric distribution.
|
|
:param N: Number of items in the population.
|
|
:param n: Number of draws.
|
|
:param k: Number of successes in the population.
|
|
:return: Returns the variance of the hyper geometric distribution.
|
|
"""
|
|
return (n * k * (N - k) * (N - n)) / (N ** 2 * (N - 1))
|
|
|
|
|
|
def hgd_std(N, n, k):
|
|
"""
|
|
Computes the standard deviation of the hyper geometric distribution.
|
|
:param N: Number of items in the population.
|
|
:param n: Number of draws.
|
|
:param k: Number of successes in the population.
|
|
:return: Returns the standard deviation of the hyper geometric distribution.
|
|
"""
|
|
return hgd_var(N, n, k) ** 0.5
|
|
|
|
|
|
def hgd_upto(x, N, n, k):
|
|
"""
|
|
Computes the cumulative probability of getting upto x successes in n draws from a population of size N with k successes.
|
|
:param x: Number of successes in the sample.
|
|
:param N: Number of items in the population.
|
|
:param n: Number of draws.
|
|
:param k: Number of successes in the population.
|
|
:return: Returns the cumulative probability of getting upto x successes in n draws from a population of size N with k successes.
|
|
"""
|
|
return sum(hgd(i, N, n, k) for i in range(x + 1))
|
|
|
|
|
|
def hgd_from(x, N, n, k):
|
|
"""
|
|
Computes the cumulative probability of getting from x successes in n draws from a population of size N with k successes.
|
|
:param x: Number of successes in the sample.
|
|
:param N: Number of items in the population.
|
|
:param n: Number of draws.
|
|
:param k: Number of successes in the population.
|
|
:return: Returns the cumulative probability of getting from x successes in n draws from a population of size N with k successes.
|
|
"""
|
|
return 1 - hgd_upto(x - 1, N, n, k)
|
|
|
|
|
|
def pd(x, l):
|
|
"""
|
|
Computes the poisson distribution.
|
|
:param x: Number of occurrences.
|
|
:param l: Average number of occurrences.
|
|
:return: Returns the probability of getting x occurrences.
|
|
"""
|
|
return (l ** x * math.e ** -l) / math.factorial(x)
|
|
|
|
|
|
def pd_mean(l):
|
|
"""
|
|
Computes the mean of the poisson distribution.
|
|
:param l: Average number of occurrences.
|
|
:return: Returns the mean of the poisson distribution.
|
|
"""
|
|
return l
|
|
|
|
|
|
def pd_var(l):
|
|
"""
|
|
Computes the variance of the poisson distribution.
|
|
:param l: Average number of occurrences.
|
|
:return: Returns the variance of the poisson distribution.
|
|
"""
|
|
return l
|
|
|
|
|
|
def pd_std(l):
|
|
"""
|
|
Computes the standard deviation of the poisson distribution.
|
|
:param l: Average number of occurrences.
|
|
:return: Returns the standard deviation of the poisson distribution.
|
|
"""
|
|
return l ** 0.5
|
|
|
|
|
|
def pd_upto(x, l):
|
|
"""
|
|
Computes the cumulative probability of getting upto x occurrences.
|
|
:param x: Number of occurrences.
|
|
:param l: Average number of occurrences.
|
|
:return: Returns the cumulative probability of getting upto x occurrences.
|
|
"""
|
|
return sum(pd(i, l) for i in range(x + 1))
|
|
|
|
|
|
def pd_from(x, l):
|
|
"""
|
|
Computes the cumulative probability of getting from x occurrences.
|
|
:param x: Number of occurrences.
|
|
:param l: Average number of occurrences.
|
|
:return: Returns the cumulative probability of getting from x occurrences.
|
|
"""
|
|
return 1 - pd_upto(x - 1, l)
|
|
|
|
|
|
man(man)
|