numpy.quantile — NumPy v1.23 Manual (2024)

numpy.quantile(a, q, axis=None, out=None, overwrite_input=False, method='linear', keepdims=False, *, interpolation=None)[source]#

Compute the q-th quantile of the data along the specified axis.

New in version 1.15.0.

Parameters

aarray_like

Input array or object that can be converted to an array.

qarray_like of float

Quantile or sequence of quantiles to compute, which must be between0 and 1 inclusive.

axis{int, tuple of int, None}, optional

Axis or axes along which the quantiles are computed. The default isto compute the quantile(s) along a flattened version of the array.

outndarray, optional

Alternative output array in which to place the result. It must havethe same shape and buffer length as the expected output, but thetype (of the output) will be cast if necessary.

overwrite_inputbool, optional

If True, then allow the input array a to be modified byintermediate calculations, to save memory. In this case, thecontents of the input a after this function completes isundefined.

methodstr, optional

This parameter specifies the method to use for estimating thequantile. There are many different methods, some unique to NumPy.See the notes for explanation. The options sorted by their R typeas summarized in the H&F paper [1] are:

‘inverted_cdf’
‘averaged_inverted_cdf’
‘closest_observation’
‘interpolated_inverted_cdf’
‘hazen’
‘weibull’
‘linear’ (default)
‘median_unbiased’
‘normal_unbiased’

The first three methods are discontinuous. NumPy further defines thefollowing discontinuous variations of the default ‘linear’ (7.) option:

See also

mean
percentile: equivalent to quantile, but with q in the range [0, 100].
median: equivalent to quantile(..., 0.5)
nanquantile

Notes

Given a vector V of length N, the q-th quantile of V is thevalue q of the way from the minimum to the maximum in a sorted copy ofV. The values and distances of the two nearest neighbors as well as themethod parameter will determine the quantile if the normalizedranking does not match the location of q exactly. This function is thesame as the median if q=0.5, the same as the minimum if q=0.0 andthe same as the maximum if q=1.0.

The optional method parameter specifies the method to use when thedesired quantile lies between two data points i < j.If g is the fractional part of the index surrounded by i and j,and alpha and beta are correction constants modifying i and j:

\[i + g = (q - alpha) / ( n - alpha - beta + 1 )\]

The different methods then work as follows

inverted_cdf:

method 1 of H&F [1].This method gives discontinuous results:

if g > 0 ; then take j
if g = 0 ; then take i

averaged_inverted_cdf:

method 2 of H&F [1].This method gives discontinuous results:

if g > 0 ; then take j
if g = 0 ; then average between bounds

closest_observation:

method 3 of H&F [1].This method gives discontinuous results:

if g > 0 ; then take j
if g = 0 and index is odd ; then take j
if g = 0 and index is even ; then take i

interpolated_inverted_cdf:

method 4 of H&F [1].This method gives continuous results using:

alpha = 0
beta = 1

hazen:

method 5 of H&F [1].This method gives continuous results using:

alpha = 1/2
beta = 1/2

weibull:

method 6 of H&F [1].This method gives continuous results using:

alpha = 0
beta = 0

linear:

method 7 of H&F [1].This method gives continuous results using:

alpha = 1
beta = 1

median_unbiased:

method 8 of H&F [1].This method is probably the best method if the sampledistribution function is unknown (see reference).This method gives continuous results using:

alpha = 1/3
beta = 1/3

normal_unbiased:

method 9 of H&F [1].This method is probably the best method if the sampledistribution function is known to be normal.This method gives continuous results using:

alpha = 3/8
beta = 3/8

lower:

NumPy method kept for backwards compatibility.Takes i as the interpolation point.

higher:

NumPy method kept for backwards compatibility.Takes j as the interpolation point.

nearest:

NumPy method kept for backwards compatibility.Takes i or j, whichever is nearest.

midpoint:

NumPy method kept for backwards compatibility.Uses (i + j) / 2.

References

1(1,2,3,4,5,6,7,8,9,10): R. J. Hyndman and Y. Fan,“Sample quantiles in statistical packages,”The American Statistician, 50(4), pp. 361-365, 1996

Examples

>>> a = np.array([[10, 7, 4], [3, 2, 1]])>>> aarray([[10, 7, 4], [ 3, 2, 1]])>>> np.quantile(a, 0.5)3.5>>> np.quantile(a, 0.5, axis=0)array([6.5, 4.5, 2.5])>>> np.quantile(a, 0.5, axis=1)array([7., 2.])>>> np.quantile(a, 0.5, axis=1, keepdims=True)array([[7.], [2.]])>>> m = np.quantile(a, 0.5, axis=0)>>> out = np.zeros_like(m)>>> np.quantile(a, 0.5, axis=0, out=out)array([6.5, 4.5, 2.5])>>> marray([6.5, 4.5, 2.5])>>> b = a.copy()>>> np.quantile(b, 0.5, axis=1, overwrite_input=True)array([7., 2.])>>> assert not np.all(a == b)

See also numpy.percentile for a visualization of most methods.