percentile(a, q, axis=None, out=None, overwrite_input=False, method='linear', keepdims=False, *, interpolation=None)
Returns the q-th percentile(s) of the array elements.
Given a vector V
of length N
, the q-th percentile of V
is the value q/100
of the way from the minimum to the maximum in a sorted copy of V
. The values and distances of the two nearest neighbors as well as the :None:None:`method` parameter will determine the percentile if the normalized ranking does not match the location of q
exactly. This function is the same as the median if q=50
, the same as the minimum if q=0
and the same as the maximum if q=100
.
This optional :None:None:`method` parameter specifies the method to use when the desired quantile lies between two data points i < j
. If g
is the fractional part of the index surrounded by i
and alpha and beta are correction constants modifying i and j.
Below, 'q' is the quantile value, 'n' is the sample size and alpha and beta are constants. The following formula gives an interpolation "i + g" of where the quantile would be in the sorted sample. With 'i' being the floor and 'g' the fractional part of the result.
$$i + g = (q - alpha) / ( n - alpha - beta + 1 )$$The different methods then work as follows
inverted_cdf:
method 1 of H&F . 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 . This method give discontinuous results: * if g > 0 ; then take j * if g = 0 ; then average between bounds
closest_observation:
method 3 of H&F . This method give 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 . This method give continuous results using: * alpha = 0 * beta = 1
hazen:
method 5 of H&F . This method give continuous results using: * alpha = 1/2 * beta = 1/2
weibull:
method 6 of H&F . This method give continuous results using: * alpha = 0 * beta = 0
linear:
method 7 of H&F . This method give continuous results using: * alpha = 1 * beta = 1
median_unbiased:
method 8 of H&F . This method is probably the best method if the sample distribution function is unknown (see reference). This method give continuous results using: * alpha = 1/3 * beta = 1/3
normal_unbiased:
method 9 of H&F . This method is probably the best method if the sample distribution function is known to be normal. This method give 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
.
Input array or object that can be converted to an array.
Percentile or sequence of percentiles to compute, which must be between 0 and 100 inclusive.
Axis or axes along which the percentiles are computed. The default is to compute the percentile(s) along a flattened version of the array.
A tuple of axes is supported
Alternative output array in which to place the result. It must have the same shape and buffer length as the expected output, but the type (of the output) will be cast if necessary.
If True, then allow the input array a to be modified by intermediate calculations, to save memory. In this case, the contents of the input a after this function completes is undefined.
This parameter specifies the method to use for estimating the percentile. There are many different methods, some unique to NumPy. See the notes for explanation. The options sorted by their R type as summarized in the H&F paper are:
'inverted_cdf'
'averaged_inverted_cdf'
'closest_observation'
'interpolated_inverted_cdf'
'hazen'
'weibull'
'linear' (default)
'median_unbiased'
'normal_unbiased'
The first three methods are discontiuous. NumPy further defines the following discontinuous variations of the default 'linear' (7.) option:
'lower'
'higher',
'midpoint'
'nearest'
This argument was previously called "interpolation" and only offered the "linear" default and last four options.
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array a.
Deprecated name for the method keyword argument.
If q is a single percentile and :None:None:`axis=None`, then the result is a scalar. If multiple percentiles are given, first axis of the result corresponds to the percentiles. The other axes are the axes that remain after the reduction of a. If the input contains integers or floats smaller than float64
, the output data-type is float64
. Otherwise, the output data-type is the same as that of the input. If :None:None:`out` is specified, that array is returned instead.
Compute the q-th percentile of the data along the specified axis.
median
equivalent to percentile(..., 50)
quantile
equivalent to percentile, except q in the range [0, 1].
>>> a = np.array([[10, 7, 4], [3, 2, 1]])
... a array([[10, 7, 4], [ 3, 2, 1]])
>>> np.percentile(a, 50) 3.5
>>> np.percentile(a, 50, axis=0) array([6.5, 4.5, 2.5])
>>> np.percentile(a, 50, axis=1) array([7., 2.])
>>> np.percentile(a, 50, axis=1, keepdims=True) array([[7.], [2.]])
>>> m = np.percentile(a, 50, axis=0)
... out = np.zeros_like(m)
... np.percentile(a, 50, axis=0, out=out) array([6.5, 4.5, 2.5])
>>> m array([6.5, 4.5, 2.5])
>>> b = a.copy()
... np.percentile(b, 50, axis=1, overwrite_input=True) array([7., 2.])
>>> assert not np.all(a == b)
The different methods can be visualized graphically:
.. plot::
import matplotlib.pyplot as plt
See :a = np.arange(4) p = np.linspace(0, 100, 6001) ax = plt.gca() lines = [ ('linear', '-', 'C0'), ('inverted_cdf', ':', 'C1'), # Almost the same as
inverted_cdf: ('averaged_inverted_cdf', '-.', 'C1'), ('closest_observation', ':', 'C2'), ('interpolated_inverted_cdf', '--', 'C1'), ('hazen', '--', 'C3'), ('weibull', '-.', 'C4'), ('median_unbiased', '--', 'C5'), ('normal_unbiased', '-.', 'C6'), ] for method, style, color in lines: ax.plot( p, np.percentile(a, p, method=method), label=method, linestyle=style, color=color) ax.set( title='Percentiles for different methods and data: ' + str(a), xlabel='Percentile', ylabel='Estimated percentile value', yticks=a) ax.legend() plt.show()
The following pages refer to to this document either explicitly or contain code examples using this.
numpy.quantile
scipy.stats._stats_py.scoreatpercentile
pandas.core.frame.DataFrame.quantile
pandas.core.series.Series.quantile
numpy.nanpercentile
pandas.core.groupby.groupby.GroupBy.quantile
numpy.nanmedian
dask.array.percentile.percentile
numpy.median
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