| Portability | portable |
|---|---|
| Stability | experimental |
| Maintainer | bos@serpentine.com |
Statistics.Quantile
Description
Functions for approximating quantiles, i.e. points taken at regular intervals from the cumulative distribution function of a random variable.
The number of quantiles is described below by the variable q, so with q=4, a 4-quantile (also known as a quartile) has 4 intervals, and contains 5 points. The parameter k describes the desired point, where 0 ≤ k ≤ q.
Quantile estimation functions
Arguments
| :: Int | k, the desired quantile. |
| -> Int | q, the number of quantiles. |
| -> Sample | x, the sample data. |
| -> Double |
Estimate the kth q-quantile of a sample, using the weighted average method.
Parameters a and b to the continuousBy function.
Arguments
| :: ContParam | Parameters a and b. |
| -> Int | k, the desired quantile. |
| -> Int | q, the number of quantiles. |
| -> Sample | x, the sample data. |
| -> Double |
Estimate the kth q-quantile of a sample x, using the continuous sample method with the given parameters. This is the method used by most statistical software, such as R, Mathematica, SPSS, and S.
Parameters for the continuous sample method
California Department of Public Works definition, a=0, b=1. Gives a linear interpolation of the empirical CDF. This corresponds to method 4 in R and Mathematica.
Hazen's definition, a=0.5, b=0.5. This is claimed to be popular among hydrologists. This corresponds to method 5 in R and Mathematica.
Definition used by the S statistics application, with a=1,
b=1. The interpolation points divide the sample range into n-1
intervals. This corresponds to method 7 in R and Mathematica.
Definition used by the SPSS statistics application, with a=0, b=0 (also known as Weibull's definition). This corresponds to method 6 in R and Mathematica.
medianUnbiased :: ContParamSource
Median unbiased definition, a=1/3, b=1/3. The resulting quantile estimates are approximately median unbiased regardless of the distribution of x. This corresponds to method 8 in R and Mathematica.
normalUnbiased :: ContParamSource
Normal unbiased definition, a=3/8, b=3/8. An approximately unbiased estimate if the empirical distribution approximates the normal distribution. This corresponds to method 9 in R and Mathematica.
References
- Weisstein, E.W. Quantile. MathWorld. http://mathworld.wolfram.com/Quantile.html
- Hyndman, R.J.; Fan, Y. (1996) Sample quantiles in statistical packages. American Statistician 50(4):361–365. http://www.jstor.org/stable/2684934