`scipy.stats._mstats_basic:mquantiles`

source: /scipy/stats/_mstats_basic.py :3191

Signature

   def     mquantiles (    a    ,    prob    =  (0.25, 0.5, 0.75)   ,    alphap    =  0.4   ,    betap    =  0.4   ,    axis    =  None   ,    limit    =  ()     )

Summary

Computes empirical quantiles for a data array.

Extended Summary

Samples quantile are defined by Q(p) = (1-gamma)*x[j] + gamma*x[j+1], where x[j] is the j-th order statistic, and gamma is a function of j = floor(n*p + m), m = alphap + p*(1 - alphap - betap) and g = n*p + m - j.

Reinterpreting the above equations to compare to R lead to the equation: p(k) = (k - alphap)/(n + 1 - alphap - betap)

Typical values of (alphap,betap) are:

(0,1)p(k) = k/nlinear interpolation of cdf (R type 4)
(.5,.5)p(k) = (k - 1/2.)/npiecewise linear function (R type 5)
(0,0)p(k) = k/(n+1) : (R type 6)
(1,1)p(k) = (k-1)/(n-1): p(k) = mode[F(x[k])]. (R type 7, R default)
(1/3,1/3): p(k) = (k-1/3)/(n+1/3): Then p(k) ~ median[F(x[k])]. The resulting quantile estimates are approximately median-unbiased regardless of the distribution of x. (R type 8)
(3/8,3/8): p(k) = (k-3/8)/(n+1/4): Blom. The resulting quantile estimates are approximately unbiased if x is normally distributed (R type 9)
(.4,.4)approximately quantile unbiased (Cunnane)
(.35,.35): APL, used with PWM

Parameters

a : array_like: Input data, as a sequence or array of dimension at most 2.
prob : array_like, optional: List of quantiles to compute.
alphap : float, optional: Plotting positions parameter, default is 0.4.
betap : float, optional: Plotting positions parameter, default is 0.4.
axis : int, optional: Axis along which to perform the trimming. If None (default), the input array is first flattened.
limit : tuple, optional: Tuple of (lower, upper) values. Values of a outside this open interval are ignored.

Returns

mquantiles : MaskedArray: An array containing the calculated quantiles.

Notes

This formulation is very similar to R except the calculation of m from alphap and betap, where in R m is defined with each type.

Examples

import numpy as np
from scipy.stats.mstats import mquantiles
a = np.array([6., 47., 49., 15., 42., 41., 7., 39., 43., 40., 36.])

✓

mquantiles(a)

✗

Using a 2D array, specifying axis and limit.

data = np.array([[   6.,    7.,    1.],
                 [  47.,   15.,    2.],
                 [  49.,   36.,    3.],
                 [  15.,   39.,    4.],
                 [  42.,   40., -999.],
                 [  41.,   41., -999.],
                 [   7., -999., -999.],
                 [  39., -999., -999.],
                 [  43., -999., -999.],
                 [  40., -999., -999.],
                 [  36., -999., -999.]])
print(mquantiles(data, axis=0, limit=(0, 50)))

✓

data[:, 2] = -999.
print(mquantiles(data, axis=0, limit=(0, 50)))

✓

Aliases

scipy.stats._mstats_basic.mquantiles