scipy.stats.mstats.mquantiles#
- scipy.stats.mstats.mquantiles(a, prob=[0.25, 0.5, 0.75], alphap=0.4, betap=0.4, axis=None, limit=())[source]#
Computes empirical quantiles for a data array.
Samples quantile are defined by
Q(p) = (1-gamma)*x[j] + gamma*x[j+1]
, wherex[j]
is the j-th order statistic, and gamma is a function ofj = floor(n*p + m)
,m = alphap + p*(1 - alphap - betap)
andg = 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/n
: linear interpolation of cdf (R type 4)(.5,.5) :
p(k) = (k - 1/2.)/n
: piecewise 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
- aarray_like
Input data, as a sequence or array of dimension at most 2.
- probarray_like, optional
List of quantiles to compute.
- alphapfloat, optional
Plotting positions parameter, default is 0.4.
- betapfloat, optional
Plotting positions parameter, default is 0.4.
- axisint, optional
Axis along which to perform the trimming. If None (default), the input array is first flattened.
- limittuple, optional
Tuple of (lower, upper) values. Values of a outside this open interval are ignored.
- Returns
- mquantilesMaskedArray
An array containing the calculated quantiles.
Notes
This formulation is very similar to R except the calculation of
m
fromalphap
andbetap
, where in Rm
is defined with each type.References
- 1
R statistical software: https://www.r-project.org/
- 2
R
quantile
function: http://stat.ethz.ch/R-manual/R-devel/library/stats/html/quantile.html
Examples
>>> from scipy.stats.mstats import mquantiles >>> a = np.array([6., 47., 49., 15., 42., 41., 7., 39., 43., 40., 36.]) >>> mquantiles(a) array([ 19.2, 40. , 42.8])
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))) [[19.2 14.6 1.45] [40. 37.5 2.5 ] [42.8 40.05 3.55]]
>>> data[:, 2] = -999. >>> print(mquantiles(data, axis=0, limit=(0, 50))) [[19.200000000000003 14.6 --] [40.0 37.5 --] [42.800000000000004 40.05 --]]