distr6 (version 1.6.9)

StudentTNoncentral: 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.

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)

Omitted Methods

N/A

Also known as

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

• StudentTNoncentral$new()

• StudentTNoncentral$mean()

• StudentTNoncentral$variance()

• StudentTNoncentral$clone()

• distr6::Distribution$cdf()

• distr6::Distribution$confidence()

• distr6::Distribution$correlation()

• distr6::Distribution$getParameterValue()

• distr6::Distribution$iqr()

• distr6::Distribution$liesInSupport()

• distr6::Distribution$liesInType()

• distr6::Distribution$median()

• distr6::Distribution$parameters()

• distr6::Distribution$pdf()

• distr6::Distribution$prec()

• distr6::Distribution$print()

• distr6::Distribution$quantile()

• distr6::Distribution$rand()

• distr6::Distribution$setParameterValue()

• distr6::Distribution$stdev()

• distr6::Distribution$strprint()

• distr6::Distribution$summary()

• distr6::Distribution$workingSupport()

Method new()

Creates a new instance of this R6 class.

Usage

StudentTNoncentral$new(df = NULL, location = NULL, decorators = NULL)

Arguments

df

(integer(1)) Degrees of freedom of the distribution defined on the positive Reals.

location

(numeric(1)) Location parameter, defined on the Reals.

decorators

(character()) Decorators to add to the distribution during construction.

Method mean()

The arithmetic mean of a (discrete) probability distribution X is the expectation $$E_X(X)=\sum p_X(x)\ast x$$ with an integration analogue for continuous distributions.

Usage

StudentTNoncentral$mean(...)

Arguments

...

Unused.

Method variance()

The variance of a distribution is defined by the formula $$va{r}_X=E[X^2]-E[X{]}^2$$ where $E_X$ is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

Usage

StudentTNoncentral$variance(...)

Arguments

...

Unused.

Method clone()

The objects of this class are cloneable with this method.

Usage

StudentTNoncentral$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Details

The Noncentral Student's T distribution parameterised with degrees of freedom, $\nu$ and location, $\lambda$, is defined by the pdf, $$f(x)=({\nu }^{\nu /2}exp(-(\nu {\lambda }^2)/(2(x^2+\nu )))/(\sqrt{\pi }\mathrm{\Gamma }(\nu /2)2^{(\nu -1)/2}(x^2+\nu {)}^{(\nu +1)/2})){\int }_0^{\mathrm{\infty }}{y}^{\nu }exp(-1/2(y-x\lambda /\sqrt{x^2+\nu }{)}^2)$$ for $\nu >0$, $\lambda ϵR$.

References

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

See Also

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