Built-in Mathematica Symbol

NoncentralStudentTDistribution

,

]
represents a noncentral Student t distribution with

degrees of freedom and noncentrality parameter

.

NoncentralStudentTDistribution allows to be any positive real number and to be any real number.

The mean and variance of a noncentral Student t distribution depend on the Gamma function:

The probability density function of the noncentral Student t distribution depends on both the Hypergeometric1F1 and Gamma functions:

The mean and variance of a noncentral Student t distribution depend on the Gamma function:

The probability density function of the noncentral Student t distribution depends on both the Hypergeometric1F1 and Gamma functions:

Generate a set of pseudorandom numbers that have the noncentral Student t distribution:

Properties based on higher-order moments:

The 0.75 quantile of a noncentral Student t distribution:

Plot the cumulative distribution function of the random variable:

The probability density function integrates to unity:

, 0] is equivalent to StudentTDistribution[

]:

is not a positive real number:

is not a real number:

The characteristic function of a noncentral Student t distribution has no closed-form representation:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful: