dnct: Non Central Student t - Density

In alessandrocolombi/ACutils: Collection of utilities

Non Central Student t - Density

Description

\loadmathjax

This function evaluates the density of a Non Central Student t in a given point. Such a distribution is defined as follow: \mjsdeqnX~\sim~nct(n_0,\mu_0,\gamma_0) if \mjtdeqn$$\begineqnarray*f(X|n_0,\mu_0,\gamma_0) = \frac\Gamma(\fracn_0+12)\Gamma(\fracn_02)\frac1\sqrt\pi\gamma_0n_0\left(1+\frac1n_0(\fracx-\mu_0\gamma_0)^2\right)^-\fracn_0+12 eqnarray*$$\begineqnarray*f(X|n_0,\mu_0,\gamma_0) = \frac\Gamma(\fracn_0+12)\Gamma(\fracn_02)\frac1\sqrt\pi\gamma_0n_0\left(1+\frac1n_0(\fracx-\mu_0\gamma_0)^2\right)^-\fracn_0+12 \endeqnarray*\begineqnarray* f(X|n_0,\mu_0,\gamma_0) = \frac\Gamma(\fracn_0+12)\Gamma(\fracn_02)\frac1\sqrt\pi\gamma_0n_0\left(1+\frac1n_0(\fracx-\mu_0\gamma_0)^2\right)^-\fracn_0+12 \endeqnarray* where \mjseqnn_0 are the degree of freedom, \mjseqn\mu_0 is the location parameter and \mjseqn\gamma_0 is the scale parameter. The usual t density can be recovered by placing \mjseqn\mu_0=0 and \mjseqn\gamma_0 = 1.

Usage

dnct(x, n0, mu0, gamma0)

Arguments

x	the point where to evaluate the density.
n0	the degree of fredoom.
mu0	the location parameter.
gamma0	the scale parameter.

Value

scalar representing the evaluation of the density at x

alessandrocolombi/ACutils documentation built on March 3, 2023, 4:06 a.m.