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