Scilab's probability distribution functions can compute any of the parameters of a distribution as a function of the others. For example, the built-in cdfnor can compute the cumulative probability P and reliability Q, or the value of the ordinate X, or the Mean, or the standard deviation Std, depending on how the function is called, as follows:

[P,Q]=cdfnor("PQ",X,Mean,Std)

X=cdfnor("X",Mean,Std,P,Q)

Mean=cdfnor("Mean",Std,P,Q,X)

Std=cdfnor("Std",P,Q,X,Mean)

Note that if P is given, Q=P-1 must be given also, even though it is trivial.

In addition to the built-in distributions, one can install the ``distfun'' function toolbox to make more distributions available. The toolboxes are distributed through ATOMS at https://atoms.scilab.org/. We illustrate the process with ``distfun''.

To install the "distfun" toolbox, or any other, in Windows \> open the Scilab Console \> type atomsInstall("distfun"). To quit \> type "exit". It will download and install the toolbox automatically. As of 7/7/2016, it installs the following:

SCI\contrib\disfun\1.0\

SCI\contrib\helptbx\0.4\

SCI\contrib\apifun\0.4.1\

SCI\contrib\specfun\0.4.1\

That is, it installs the ``distfun'' functions listed in https://atoms.scilab.org/toolboxes/distfun/1.0/ Specifically, for each distribution x, the following five functions are provided

distfun_xcdf : x CDF

distfun_xinv : x Inverse CDF (quantile)

distfun_xpdf : x PDF

distfun_xrnd : x random numbers

distfun_xstat : x mean and variance

The toolbox installation also adds those functions to the help system, so from the Scilab console one can request help to learn what parameters are needed and in what order as follows

help distfun_xyyy

where yyy is the name of the function, namely cdf, inv, pdf, rnd, or stat.

Specifically for the non-central T-distribution, the following functions are provided:

distfun_nctcdf : cdf

distfun_nctinv : icdf

distfun_nctpdf : pdf

distfun_nctrnd : random numbers

distfun_nctstat : mean and variance