Source code for simplestatistics.statistics.quantile

"""
Implements quantile() function, and the helper get_q_value() function (not exposed).
"""

def get_q_value(data, p):
"""
Helper function to be used for quantile().
Given data and a p value, returns the value from data below which you would
find (p*100)% of the values.
"""
q = len(data) * p

for index, _ in enumerate(data):
if (index + 1) >= q:
return(data[index])

[docs]def quantile(data, p=[0, .25, .5, .75, 1]): # pylint: disable=dangerous-default-value
"""
Quantiles_ are "are cutpoints dividing the range of a probability distribution
into contiguous intervals with equal probabilities, or dividing the observations
in a sample in the same way".
This function assumes the data provided is a statistical population, not sample.

Consider the first example below:

>>> quantile([3, 6, 7, 8, 8, 9, 10, 13, 15, 16, 20], .25)
7

Given the probability 0.25, 7 is the value below which you can find 25%
of the values after the data is sorted.

.. _Quantiles: https://en.wikipedia.org/wiki/Quantile

Args:
data: The sample. A list of numerical objects.
p: Can be a numerical object (int or float) indicating one quantile, or a list of
numerical objects indicating several quantiles.
p is [0, 0.25, 0.5, 0.75, 1] by default.

Returns:
A numerical object if provided p was a single value, or a list of quantiles
if provided p was a list.
The list will be returned in the order of quantiles provided.

Examples:

>>> quantile([3, 6, 7, 8, 8, 9, 10, 13, 15, 16, 20], .25)
7
>>> quantile([3, 6, 7, 8, 8, 9, 10, 13, 15, 16, 20], .5)
9
>>> quantile([3, 6, 7, 8, 8, 9, 10, 13, 15, 16, 20], .75)
15
>>> quantile([3, 6, 7, 8, 8, 9, 10, 13, 15, 16, 20], 1)
20
>>> quantile([3, 6, 7, 8, 8, 9, 10, 13, 15, 16, 20])
[3, 7, 9, 15, 20]
>>> quantile([3, 6, 7, 8, 8, 9, 10, 13, 15, 16, 20], [.75, .25])
[15, 7]

>>> quantile(4, .5)
Traceback (most recent call last):
...
TypeError: quantile expects a list of numerical objects.
"""
# this function needs a list
if type(data) is not list:
raise TypeError("quantile expects a list of numerical objects.")

data.sort()

if type(p) in [int, float]:
return(get_q_value(data, p))
elif type(p) is list:
quantiles = []
for prob in p:
quantiles.append(get_q_value(data, prob))

return(quantiles)