Random variates and distribution parameters are conventionally distinguished (for example in Wikipedia and Wolfram MathWorld by placing a semi-colon after the random variate (whose value you 'choose'), to separate the variate from the parameter(s) that defines the shape of the distribution.
For example, the binomial distribution has two parameters: n (the number of trials) and p (the probability of success on one trial). It also has the random variate k: the number of successes observed. This means the probability density/mass function (pdf) is written as f(k; n, p).
Translating this into code the
constructor therefore has two parameters:
binomial_distribution(RealType n, RealType p);
While the function
pdf(binomial_distribution<RealType>(n, p), k);