cpp/numeric/random/student t distribution

Produces random floating-point values $x$, distributed according to probability density function:



where $n$ is known as the number of degrees of freedom. This distribution is used when estimating the mean of an unknown normally distributed value given $n+1$ independent measurements, each with additive errors of unknown standard deviation, as in physical measurements. Or, alternatively, when estimating the unknown mean of a normal distribution with unknown standard deviation, given $n+1$ samples.

satisfies all requirements of.