I was wondering if there is a function/subroutine to compute percentiles of an array in the Fortran standard library. So far I have been able only to find a function to compute the median in the stats module
Thanks!
There is selection – Fortran-lang/stdlib, from which percentiles could be computed:
selectis used to find the k-th smallest entry of an array. The input array is also modified in-place, and on return will be partially sorted such thatall(array(1:k) <= array(k)))andall(array(k) <= array((k+1):size(array)))is true. The user can optionally specifyleftandrightindices to constrain the search for the k-th smallest value. This can be useful if you have previously calledselectto find a smaller or larger rank (that will have led to partial sorting ofarray, thus implying some constraints on the location).arg_selectis used to find the index of the k-th smallest entry of an array. In this case the input array is not modified, but the user must provide an input index array with the same size asarray, having indices that are a permutation of1:size(array), which is modified instead. On return the index array is modified such thatall(array(index(1:k)) <= array(index(k)))andall(array(k) <= array(k+1:size(array))). The user can optionally specifyleftandrightindices to constrain the search for the k-th smallest value. This can be useful if you have previously calledarg_selectto find a smaller or larger rank (that will have led to partial sorting ofindex, thus implying some constraints on the location).
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You might be looking with the wrong terminology. You might try looking for “cumulative distribution function” or “probability distribution function” or other similar terms. Cumulative distribution function - Wikipedia
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If you are interested in finding sample quantiles, getQuan() is the function you are looking for. The current implementation contains five different approximation methods to the sample quantile (see the interface docs).
If you are interested in the empirical cumulative distribution function of a sample, then setECDF is the functionality you are looking for.
If you are looking for specific cumulative distribution functions, then there are the following distribution functionalities in the ParaMonte library:
| Module | Functionality |
|---|---|
| pm_distBand | This module contains procedures and generic interfaces for computing the Band photon distribution widely used in modeling the spectra of a class of celestial objects knowns Gamma-Ray Bursts. |
| pm_distBern | This module contains classes and procedures for generating Bernoulli-distributed random numbers. |
| pm_distBeta | This module contains classes and procedures for computing various statistical quantities related to the Beta distribution. |
| pm_distCosRaised | This module contains classes and procedures for computing various statistical quantities related to the Raised Cosine distribution. |
| pm_distCov | This module contains classes and procedures for generating random matrices distributed on the space of positive definite matrices, such that their determinants is uniformly or power-law distributed. |
| pm_distEggBox | This module contains classes and procedures for computing various statistical quantities related to the mathematical EggBox density function. |
| pm_distExp | This module contains classes and procedures for computing various statistical quantities related to the Exponential distribution. |
| pm_distExpGamma | This module contains classes and procedures for computing various statistical quantities related to the ExpGamma distribution. |
| pm_distGamma | This module contains classes and procedures for computing various statistical quantities related to the Gamma distribution. |
| pm_distGenExpGamma | This module contains classes and procedures for computing various statistical quantities related to the GenExpGamma distribution. |
| pm_distGenGamma | This module contains classes and procedures for computing various statistical quantities related to the GenGamma distribution. |
| pm_distGeom | This module contains classes and procedures for computing various statistical quantities related to the Geometric distribution. |
| pm_distGeomCyclic | This module contains classes and procedures for computing various statistical quantities related to the Cyclic Geometric distribution. |
| pm_distKolm | This module contains classes and procedures for computing various statistical quantities related to the Kolmogorov distribution. |
| pm_distLogNorm | This module contains classes and procedures for computing various statistical quantities related to the Lognormal distribution. |
| pm_distLogUnif | This module contains classes and procedures for computing various statistical quantities related to the LogUniform (or Reciprocal) distribution. |
| pm_distMultiNorm | This module contains classes and procedures for computing various statistical quantities related to the MultiVariate Normal (MVN) distribution. |
| pm_distNegExp | This module contains classes and procedures for computing various statistical quantities related to the Negative Exponential distribution. |
| pm_distNorm | This module contains classes and procedures for computing various statistical quantities related to the univariate Normal distribution. |
| pm_distNormShell | This module contains procedures and generic interfaces for computing the Multivariate Normal Shell density function or mixtures of such densities with varying parameters. |
| pm_distPareto | This module contains classes and procedures for computing various statistical quantities related to the (Truncated) Pareto distribution. |
| pm_distPois | This module contains classes and procedures for computing various statistical quantities related to the Poisson distribution. |
| pm_distPower | This module contains classes and procedures for computing various statistical quantities related to the (Truncated) Power distribution. |
| pm_distPoweto | This module contains classes and procedures for computing various statistical quantities related to the (Truncated) Power/Pareto distribution (hence the name Poweto). |
| pm_distUnif | This module contains classes and procedures for computing various statistical quantities related to the univariate Uniform distribution. |
| pm_distUnifEll | This module contains classes and procedures for computing various statistical quantities related to the MultiVariate Uniform Ellipsoid (MVUE) distribution. |
| pm_distUnifPar | This module contains classes and procedures for setting up and computing the properties of the MultiVariate Uniform Parallelepiped (MVUP) Distribution. |
| pm_distUnifSphere | This module contains classes and procedures for computing various statistical quantities related to the Uniform Spherical distribution. |
To start using your target functionality, I suggest you download a clone of the library and run the examples supplied with the target functionality to see how the library build and linking works. For example, to build and run examples for getQuan(), you could try:
./install.sh --exam getQuan
in Linux or macOS, or,
install.bat --exam getQuan
in Windows, or using CMake on any platform via,
mkdir bld && cd bld && cmake -Dexam="getQuan"
The library functionalities are quite extensive. If you are only interested in a specific functionality, I suggest adding the additional flag --mod pm_sampleQuan to the install scripts command above or -Dmod="pm_sampleQuan" to the CMake build command above.
See the full instructions here. All functionalities are generic and work for all real kinds supported by processors. I hope this helps!
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