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.

## Value

Returns an R6 object inheriting from class SDistribution.

## Details

The Noncentral Student's T distribution parameterised with degrees of freedom, $$\nu$$ and location, $$\lambda$$, is defined by the pdf, $$f(x) = (\nu^{\nu/2}exp(-(\nu\lambda^2)/(2(x^2+\nu)))/(\sqrt{\pi} \Gamma(\nu/2) 2^{(\nu-1)/2} (x^2+\nu)^{(\nu+1)/2}))\int_{0}^{\infty} y^\nu exp(-1/2(y-x\lambda/\sqrt{x^2+\nu})^2)$$ for $$\nu > 0$$, $$\lambda \epsilon R$$.

## Distribution support

The distribution is supported on the Reals.

## Default Parameterisation

TNS(df = 1, location = 0)

N/A

N/A

## 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, Arrdist, 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

Jordan Deenichin

## 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.

alias

Alias of the distribution.

packages

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

## 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.