# Source code for simplestatistics.statistics.normal

# I need sane division that returns a float not int
from __future__ import division

from .decimalize import decimalize
import math

def norm_single_calculation(x, mean, standard_deviation):
# break the normal distribution probability density function
# into two components

# component 1
#   1 / (sqrt(2 * sd^2 * pi))

# component 2
#   e ^ (- (x - mean) ^ 2 / 2 sd^2)

# x = decimalize(x)
# mean = decimalize(mean)
# standard_deviation = decimalize(standard_deviation)

# before we do a lot of math, let's check if sd is 0
if standard_deviation == 0:
return(0)

# component 1
comp1 = 1 / (math.sqrt(2 * pow(standard_deviation, 2) * math.pi))

# component 2
comp2 = pow(math.e, (-1 * (pow(x - mean, 2)) / (2 * pow(standard_deviation, 2))))

# return the product of the two components
return(comp1 * comp2)

[docs]def normal(x, mean, standard_deviation):
"""
The Normal Distribution_ is, quoting from the Wikipedia page:

A very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.

The normal distribution is useful because of the central limit theorem. In its most general form, under some conditions (which include finite variance), it states that averages of random variables independently drawn from independent distributions converge in distribution to the normal, that is, become normally distributed when the number of random variables is sufficiently large. Physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have distributions that are nearly normal. Moreover, many results and methods (such as propagation of uncertainty and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed.

.. _Normal Distribution: https://en.wikipedia.org/wiki/Normal_distribution

Probability density function equation:
.. math::
f(x \\mid \\mu, \\sigma^2) = \\frac{1}{\\sqrt{2 \\sigma^2 \\pi}} e^{-\\frac{(x - \\mu)^2}{2\\sigma^2}}

Args:
x: Int or float or list of ints or floats representing values for which the normal distribution density is desired.
mean: Mean of the sample or population.
standard_deviation: Standard deviation of the sample or population.

Returns:
Float or (or list of floats if provided x was a list)
representing the normal distribution density function for x
or each value in x.

Examples:
>>> normal(4, 8, 2)
0.02699548325659403
>>> normal([1, 4], 8, 2)
[0.00043634134752288024, 0.02699548325659403]
>>> normal(4, 8, 0)
0
"""

if type(x) in [int, float]:
return(norm_single_calculation(x, mean, standard_deviation))
elif type(x) in [list, tuple]:
norm_distribution_list = [norm_single_calculation(value, mean, standard_deviation) for value in x]

return(norm_distribution_list)