QUANTILE Function

Computes quantiles in a distribution.

Usage

q = QUANTILE(data, fvalues, f=f)

Input Parameters

data—A vector of any Real data-type.

fvalues—A vector of values in the range (0,1], for which the quantiles are computed.

Returned Value

q—A 1D vector of doubles of same length as fvalues, where q(i) is the quantile of the distribution (possibly interpolated) associated with fvalues(i).

Keywords

f—(Output) A 1D vector of doubles (of the same length as data) of f-values, where f(i) is the f-value of data(i).

Discussion

The ith quantile is defined in terms of X(k), the kth order statistic: if 0 < ith < 1 and 1 <= k <= n, quantile is X(ceil(n*Ith)) if n*Ith is not integral, otherwise (X(n*Ith)+ X(n*Ith + 1))/2.

From The Elements of Graphing Data, Cleveland, 1994, pg 136: "An f quantile of a distribution is a number, q, such that approximately a fraction f of the values of the distribution is less than or equal to q. f is the f-value of q. The median is the 0.5 quantile, the lower quartile is the 0.25 quantile, and the upper quartile is the 0.75 quantile".

Example

data = [5, 1, 9, 3, 14, 9, 7]

fvalues = [0.01, 0.25, 0.6, 0.75, 0.928472, 0.99]

q = QUANTILE(data, fvalues, f=f)

PM,  '     Observation     Data          f-value'

obs = LINDGEN(N_ELEMENTS(data))

FOR i=0L, N_ELEMENTS(data)-1 DO $

PRINT, obs(i), '     ', data(i), '    ',f(i)

PM, ''

; PV-WAVE prints:

;    0            5           0.35714286

;    1            1          0.071428571

;    2            9           0.78571429

;    3            3           0.21428571

;    4           14           0.92857143

;    5            9           0.64285714

;    6            7           0.50000000

PM, '   Input f-values       Associated quantiles '

FOR i=0L, N_ELEMENTS(fvalues)-1 DO $

   PRINT, fvalues(i), '    ', q(i)

; PV-WAVE prints:

;      0.0100000            1.0000000

;      0.250000            3.5000000

;      0.600000            8.4000003

;      0.750000            9.0000000

;      0.928472            13.996519

;      0.990000            14.000000