github
https://tinyurl.com/y9qa6slj
https://github.com/rogerjdeangelis/utl_generating_a_non-normal_distribution_with_specified_skewness_and_kurtosis

see
https://tinyurl.com/y7duvngv
https://www.rdocumentation.org/packages/SimMultiCorrData/versions/0.1.0/topics/nonnormvar1

Generate 10,000 observarions form a probability distribution with these cumulants(moments)

  MEAN       SD     SKEW KURTOSIS

     2        2        2        6

INPUT
=====

  MEAN       SD     SKEW KURTOSIS

     2        2        2        6

PROCESS  (WPS proc R working code)
===================================

   * this generates standard cululants(moments);

   stcums <- calc_theory(Dist = "Exponential", params = 0.5) # rate = 1/mean;

   * this creates a polynomial and generates 10,000 realizations od a random variable;

   H_exp <- nonnormvar1("Polynomial", means = 2, vars = 2, skews = stcums[3],
                       skurts = stcums[4], fifths = stcums[5],
                       sixths = stcums[6], n = 10000, seed = 1234);

OUTPUT
======


  Up to 40 obs from wantwps total obs=10,000

    Obs      WANT

      1    0.75398
      2    1.91082
      3    3.39320
    ...
   9998    0.71993
   9999    1.26072
  10000    1.12118

* It has the correct Skewness and Kurtosis

The UNIVARIATE Procedure

Variable:  WANT

                            Moments

N                       10000    Sum Weights              10000
Mean               1.99990541    Sum Observations    19999.0541
Std Deviation      1.41590728    Variance            2.00479344

Skewness           2.03412151    Kurtosis            6.18436338

Uncorrected SS     60042.1462    Corrected SS        20045.9296
Coeff Variation    70.7987125    Std Error Mean      0.01415907


*                _              _       _
 _ __ ___   __ _| | _____    __| | __ _| |_ __ _
| '_ ` _ \ / _` | |/ / _ \  / _` |/ _` | __/ _` |
| | | | | | (_| |   <  __/ | (_| | (_| | || (_| |
|_| |_| |_|\__,_|_|\_\___|  \__,_|\__,_|\__\__,_|

;

 stcums <- calc_theory(Dist = "Exponential", params = 0.5) # rate = 1/mean;

 *          _       _   _
 ___  ___ | |_   _| |_(_) ___  _ __
/ __|/ _ \| | | | | __| |/ _ \| '_ \
\__ \ (_) | | |_| | |_| | (_) | | | |
|___/\___/|_|\__,_|\__|_|\___/|_| |_|

;

%utl_submit_wps64('
libname sd1 "d:/sd1";
options set=R_HOME "C:/Program Files/R/R-3.3.2";
libname wrk "%sysfunc(pathname(work))";
libname hlp "C:\Program Files\SASHome\SASFoundation\9.4\core\sashelp";
proc r;
submit;
source("C:/Program Files/R/R-3.3.2/etc/Rprofile.site", echo=T);
library(SimMultiCorrData);
stcums <- calc_theory(Dist = "Exponential", params = 0.5) # rate = 1/mean;
stcums;
H_exp <- nonnormvar1("Polynomial", means = 2, vars = 2, skews = stcums[3],
                    skurts = stcums[4], fifths = stcums[5],
                    sixths = stcums[6], n = 10000, seed = 1234);
want<-H_exp$continuous_variable$V1;
endsubmit;
import r=want data=wrk.wantwps;
run;quit;
');

proc univariate data=wantwps;
var want;
run;quit;