ParaMonte Fortran 2.0.0
Parallel Monte Carlo and Machine Learning Library
See the latest version documentation.
pm_sampleQuan Module Reference

This module contains procedures and data types for computing sample quantile.

Data Types

interface  getQuan
 Generate and return the approximate sample quantile for the given method at the specified probabilities. More...


character(*, SK), parameter MODULE_NAME = "@pm_sampleQuan"

Detailed Description

This module contains procedures and data types for computing sample quantile.

Quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way.
There is one fewer quantile than the number of groups created.
Common quantiles have special names, such as quartiles (four groups), deciles (ten groups), and percentiles (100 groups).
The groups created are termed halves, thirds, quarters, etc., though sometimes the terms for the quantile are used for the groups created, rather than for the cut points.

Q-quantiles are values that partition a finite set of values into \(q\) subsets of (nearly) equal sizes.
There are \(q − 1\) partitions of the \(q\)-quantiles, one for each integer \(k\) satisfying \(0 < k < q\).
In some cases the value of a quantile may not be uniquely determined, as can be the case for the median ( \(2\)-quantile) of a uniform probability distribution on a set of even size.
Quantiles can also be applied to continuous distributions, providing a way to generalize rank statistics to continuous variables.
When the cumulative distribution function of a random variable is known, the \(q\)-quantiles are the application of the quantile function (the inverse function of the cumulative distribution function) to the values \(\{1/q, 2/q, …, (q − 1)/q\}\).

See also

Final Remarks

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For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
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Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Amir Shahmoradi, Tuesday March 7, 2017, 3:50 AM, Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin

Variable Documentation


character(*, SK), parameter pm_sampleQuan::MODULE_NAME = "@pm_sampleQuan"

Definition at line 74 of file pm_sampleQuan.F90.