# StudentTNoncentral: Noncentral Student's T Distribution Class In distr6: The Complete R6 Probability Distributions Interface

 StudentTNoncentral R Documentation

## Noncentral Student's T Distribution Class

### Description

Mathematical and statistical functions for the Noncentral Student's T distribution, which is commonly used to estimate the mean of populations with unknown variance from a small sample size, as well as in t-testing for difference of means and regression analysis.

### Details

The Noncentral Student's T distribution parameterised with degrees of freedom, ν and location, λ, is defined by the pdf,

f(x) = (ν^{ν/2}exp(-(νλ^2)/(2(x^2+ν)))/(√{π} Γ(ν/2) 2^{(ν-1)/2} (x^2+ν)^{(ν+1)/2}))\int_{0}^{∞} y^ν exp(-1/2(y-xλ/√{x^2+ν})^2)

for ν > 0, λ ε R.

### Value

Returns an R6 object inheriting from class SDistribution.

### Distribution support

The distribution is supported on the Reals.

### Default Parameterisation

TNS(df = 1, location = 0)

N/A

N/A

### Super classes

distr6::Distribution -> distr6::SDistribution -> StudentTNoncentral

### Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

packages

Packages required to be installed in order to construct the distribution.

### Methods

#### Public methods

Inherited methods

#### Method new()

Creates a new instance of this R6 class.

##### Arguments
...

Unused.

#### Method variance()

The variance of a distribution is defined by the formula

var_X = E[X^2] - E[X]^2

where E_X is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

##### Arguments
deep

Whether to make a deep clone.

Jordan Deenichin

### References

McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.

Other continuous distributions: Arcsine, BetaNoncentral, Beta, Cauchy, ChiSquaredNoncentral, ChiSquared, Dirichlet, Erlang, Exponential, FDistributionNoncentral, FDistribution, Frechet, Gamma, Gompertz, Gumbel, InverseGamma, Laplace, Logistic, Loglogistic, Lognormal, MultivariateNormal, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentT, Triangular, Uniform, Wald, Weibull
Other univariate distributions: Arcsine, Bernoulli, BetaNoncentral, Beta, Binomial, Categorical, Cauchy, ChiSquaredNoncentral, ChiSquared, Degenerate, DiscreteUniform, Empirical, Erlang, Exponential, FDistributionNoncentral, FDistribution, Frechet, Gamma, Geometric, Gompertz, Gumbel, Hypergeometric, InverseGamma, Laplace, Logarithmic, Logistic, Loglogistic, Lognormal, Matdist, NegativeBinomial, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentT, Triangular, Uniform, Wald, Weibull, WeightedDiscrete