minor statistics definitions

src/modules/statistics.py

@@ -1,6 +1,13 @@
+## This module represents the third chapter of the book 
+##  "Essential Math for Data Science" - Thomas Nield
+##  Chapter 3 - Statistics 
+
 from math import sqrt, pi, e, exp
 from scipy.stats import norm
 
+import random
+import plotly.express as px
+
 def mean(list):
 	return sum(list) / len(list)
 
@@ -73,6 +80,27 @@ def z_score(value, data_mean, std_deviation):
 def coeficient_of_variation(std_deviation, mean):
 	return (std_deviation / mean)
 
+def test_central_limit_theorem(sample_size, sample_count):
+	x_values = [(sum([random.uniform(0.0,1.0) for i in range(sample_size)]) / sample_size) for _ in range(sample_count)]
+	y_values = [1 for _ in range(sample_count)]
+	px.histogram(x=x_values, y=y_values, nbins=20).show()
+
+def generic_critical_z_value(probability):
+	norm_dist = norm(loc=0.0, scale=1.0)
+	left_tail_area = (1.0 - p) / 2.0
+	upper_area = 1.0 - ((1.0 - p) / 2.0)
+	return norm_dist.ppf(left_tail_area), norm_dist.ppf(upper_area)
+
+def margin_of_error(sample_size, standard_deviation, z_value):
+	return z_value * (standard_deviation / sqrt(sample_size)) # +-, we return the one provided by the z_value (tail or upper)
+
+# How confident we are at a population metric given a sample (the interval we are "probability" sure the value will be)
+def confidence_interval(probability, sample_size, standard_deviation, z_value, mean):
+	critical_z = generic_critical_z_value(probability)
+	margin_error = margin_error(sample_size, standard_deviation, z_value)
+	return mean + margin_error, mean - margin_error
+
+
 def test_statistics_module():
 	print("=== Statistics module ===")
 	list = [ 1, 2, 3, 4, 5, 6]
@@ -100,3 +128,7 @@ def test_statistics_module():
 	print("The House A is much more expensive because its z-score is higher.")
 	print("The neighborhood of B has a coeficient of variation: {0}, and the one of A: {1}".format(coeficient_of_variation(3000, 140000), coeficient_of_variation(10000, 800000)))
 	print("This means that the neighborhood of A has more spread in its prices")
+
+	## Central limit theorem
+	test_central_limit_theorem(sample_size=1, sample_count=1000)
+	test_central_limit_theorem(sample_size=31, sample_count=1000)