rndvar

Each object of this class is a RV, which can be instantiated and used to compute the expectation of functions or the PDF (via Monte Carlo simulation).

The RVs may combined to form others ('rndvar' uses a synchronization mechanism to ensure that the dependencies of RVs are correctly represented when the RVs are instantiated).

The probability distribution corresponding to a 'rndvar' object may be specified in one of the following ways:

(i) selecting from MATLAB's built-in distributions
e.g.
>> X = rndvar.builtInVar('Gamma',1,2);
>> mean(X) % note: same as X.expecationOf(@(x)x)
ans =
2.0003

for more info: help rndvar.builtInVar

(ii) explicit definition (providing the inverse CDF)
e.g.
>> Y = rndvar.defineVar(@(y)-log(1-y));
% note: exponential CDF is y = F(x) = 1 - exp(-x)
>> mean(Y)
ans =
1.004

for more info: help rndvar.defineVar

(iii) as functions of other RVs
(iii-a) using overloaded basic arithmetic and elementary operators
e.g.
>> X = rndvar.builtInVar('Gamma',1,2);
>> Y = rndvar.builtInVar('Gamma',1,4);
>> Z = X^2 + sin(Y) + 1;
>> mean(Z)
ans =
9.2311

>> U = X + 1; V = X + Y; mean(U*V)-mean(X^2)-mean(X*Y)-mean(Y)-mean(X)
ans =
0.0182
% reaches 0 for higher # MC points

overloaded operators:
plus (+), minus (-), uminus (unary -), uplus (unary +), mtimes (*), mrdivide (/), mldivide (\), mpower (^), lt (<), gt (>), le (<=), ge (>=), ne (!=), eq (==)

overloaded functions:
sin, sinh, asin, asinh, cos, cosh, acos, acosh, tan, tanh, atan, atanh, sec, sech, asec, asech, csc, csch, acsc, acsch, cot, coth, acot, acoth, exp, log, log10, log2, sqrt, abs, angle, complex (binary), conj, imag, real, isreal, fix, floor, ceil, round, mod (binary), rem (binary), sign, mean

(iii-b.) using rndvar.compositeVar (for more complicated relations)
e.g.
>> Z = rndvar.compositeVar(X,Y,@(x,y)max(x.^2,y.^3));

Each `rndvar' object is automatically assigned a unique identifier.
The RVs can be explicitly labeled using setLabel method.
e.g.
>> X = rndvar.builtInVar('Gamma',1,2); X.setLabel('Variable 1');
>> X.Label
ans =
Variable 1

Public methods: (use `help rndvar.method_name' to get help for `method_name')
instantiate, pdf, expecationOf, setLabel
e.g.
>> help rndvar.instantiate

A java.util.TreeMap data structure is used to internally keep track of SyncState of each `rndvar' object. (static method `rndvar.reset' clears the storage it uses).