feat: beta distribution

src/modules/probability.py

@@ -1,8 +1,8 @@
 ## This module represents the second chapter of the book 
 ##  "Essential Math for Data Science" - Thomas Nield
-##  Chaper 2 - Probability 
+##  Chapter 2 - Probability 
 
-from scipy.stats import binom
+from scipy.stats import binom, beta
 from math import factorial
 
 # 2.0 odds means than an events has twice the probabilities to happen than not
@@ -12,31 +12,58 @@ def p_odds_to_probability(o):
 def p_probability_to_odds(p):
 	return (p / (1 - p))
 
-## Binomial distribution
+class BinomialDistribution:
-def p_binomial_distribution_example():
+	@staticmethod
-	n = 10
+	def example():
-	p = 0.9
+		n = 10
+		p = 0.9
 
-	for k in range(n + 1):
+		for k in range(n + 1):
-		probability = binom.pmf(k, n, p)
+			probability = binom.pmf(k, n, p)
-		print("{0} >> {1}".format(k, probability))
+			print("{0} >> {1}".format(k, probability))
 
-def binomial_coeficient(pool, count):
+	@staticmethod
-	return factorial(pool) / (factorial(count) * factorial(pool - count))
+	def binomial_coeficient(pool, count):
+		return factorial(pool) / (factorial(count) * factorial(pool - count))
+
+	@staticmethod
+	def from_scratch(p, n):
+		# For each number calc the probability of that exact number of outcomes (no order)
+		for k in range(n + 1):
+			# 1. Simple combinatory with the binomial coeficient (combinations of k elements out of a pool of n without repetition without order)
+			combinatory = BinomialDistribution.binomial_coeficient(n, k)	
+			# 2. Probability of success, the probability of making it k times
+			probability_of_success = p ** k
+			# 3. Probability of failure, inverse of the success
+			probability_of_failure = (1 - p) ** (n - k)
+			k_binomital_distribution_probability = combinatory * probability_of_success * probability_of_failure
+			print("[{0}]: {1}".format(k, k_binomital_distribution_probability))
+
+# Study probability of probabilities
+# > Given X success rate, get the likelihood of that success rate
+# > Returns a continuous function, so the final probability of X or better must be calculated using integrals (the area under the curve)
+class BetaDistribution:
+	@staticmethod
+	def calc(probability, success_count, failure_count):	
+		# Only calcs the rpbability to the left
+		return beta.cdf(probability, success_count, failure_count)
+
+	@staticmethod
+	def calc_right(probability, success_count, failure_count):
+		return 1.0 - BetaDistribution.calc(probability, success_count, failure_count)
+	
+	@staticmethod
+	def calc_region(init_probability, end_probability, success_count, failure_count):
+		return BetaDistribution.calc(end_probability, success_count, failure_count) - BetaDistribution.calc(init_probability, success_count, failure_count)
+
+class Exercises:
 
-def p_binomial_distribution_scratch(p, n):
-	# For each number calc the probability of that exact number of outcomes (no order)
-	for k in range(n + 1):
-		# 1. Simple combinatory with the binomial coeficient (combinations of k elements out of a pool of n without repetition without order)
-		combinatory = binomial_coeficient(n, k)	
-		# 2. Probability of success, the probability of making it k times
-		probability_of_success = p ** k # p * p, k times
-		# 3. Probability of failure, inverse of the success
-		probability_of_failure = (1 - p) ** (n - k) # inverse of probability the rest of the times
-		k_binomital_distribution_probability = combinatory * probability_of_success * probability_of_failure
-		print("[{0}]: {1}".format(k, k_binomital_distribution_probability))
 
 
 def test_probability_module():
-	p_binomial_distribution_example()
+	print(">> Binomial distribution")
-	p_binomial_distribution_scratch(0.9, 10)
+	BinomialDistribution.example()
+	BinomialDistribution.from_scratch(0.9, 10)
+	print(">> Beta distribution")
+	print(BetaDistribution.calc(0.9,8,2))
+	print(BetaDistribution.calc_region(0.8, 0.9, 8, 2))