from gauss import NormalDist

# Simple scaling and translation
temperature_february = NormalDist(5, 2.5)            # Celsius
print(temperature_february * (9/5) + 32)             # Fahrenheit


# Classic probability problems
# https://blog.prepscholar.com/sat-standard-deviation
# The mean score on a SAT exam is 1060 with a standard deviation of 195
# What percentage of students score between 1100 and 1200?
sat = NormalDist(1060, 195)
fraction = sat.cdf(1200) - sat.cdf(1100)
print(f'{fraction * 100 :.1f}% score between 1100 and 1200')


# Combination of normal distributions by summing variances
birth_weights = NormalDist.from_samples([2.5, 3.1, 2.1, 2.4, 2.7, 3.5])
drug_effects = NormalDist(0.4, 0.15)
print(birth_weights + drug_effects)


# Statistical calculation estimates using simulations
# Estimate the distribution of X * Y / Z
n = 100_000
X = NormalDist(350, 15).examples(n)
Y = NormalDist(47, 17).examples(n)
Z = NormalDist(62, 6).examples(n)
print(NormalDist.from_samples(x * y / z for x, y, z in zip(X, Y, Z)))


# Naive Bayesian Classifier
# https://en.wikipedia.org/wiki/Naive_Bayes_classifier#Sex_classification

height_male = NormalDist.from_samples([6, 5.92, 5.58, 5.92])
height_female = NormalDist.from_samples([5, 5.5, 5.42, 5.75])
weight_male = NormalDist.from_samples([180, 190, 170, 165])
weight_female = NormalDist.from_samples([100, 150, 130, 150])
foot_size_male = NormalDist.from_samples([12, 11, 12, 10])
foot_size_female = NormalDist.from_samples([6, 8, 7, 9])

prior_male = 0.5
prior_female = 0.5
posterior_male = prior_male * height_male.pdf(6) * weight_male.pdf(130) * foot_size_male.pdf(8)
posterior_female = prior_female * height_female.pdf(6) * weight_female.pdf(130) * foot_size_female.pdf(8)
print('Predict', 'male' if posterior_male > posterior_female else 'female')