Add some stats methods

distribution.py

@@ -0,0 +1,254 @@
+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)

law_total_probability.py

@@ -0,0 +1,37 @@
+from utils import *
+
+def i(A, B):
+	"""
+	:param A: First probability
+	:param B: Second probability
+	:return: The intersection of A and B
+	"""
+	return A * B
+
+
+def u(A, B):
+	"""
+	:param A: The first probability
+	:param B: The second probability
+	:return: The union of A and B
+	"""
+	return A + B - i(A, B)
+
+
+def g(A, B):
+	"""
+	:param A: The first probability
+	:param B: The second probability
+	:return: The conditional probability of A given B
+	"""
+	return g(A, B) / B
+
+
+def n(A):
+	"""
+	:param A: The probability
+	:return: The negation of A
+	"""
+	return 1 - A
+
+man(man)

utils.py

@@ -0,0 +1,6 @@
+def man(func):
+	"""
+	Prints the manual for the function.
+	:param func: function
+	"""
+	print(func.__doc__)