Mathematical and statistical functions for the 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.
Returns an R6 object inheriting from class SDistribution.
The Student's T distribution parameterised with degrees of freedom, \(\nu\), is defined by the pdf, $$f(x) = \Gamma((\nu+1)/2)/(\sqrt(\nu\pi)\Gamma(\nu/2)) * (1+(x^2)/\nu)^(-(\nu+1)/2)$$ for \(\nu > 0\).
The distribution is supported on the Reals.
T(df = 1)
N/A
N/A
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,
StudentTNoncentral,
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,
StudentTNoncentral,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
distr6::Distribution -> distr6::SDistribution -> StudentT
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
aliasAlias of the distribution.
packagesPackages required to be installed in order to construct the distribution.
Inherited methods
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$workingSupport()
new()Creates a new instance of this R6 class.
StudentT$new(df = NULL, decorators = NULL)mean()The arithmetic mean of a (discrete) probability distribution X is the expectation $$E_X(X) = \sum p_X(x)*x$$ with an integration analogue for continuous distributions.
mode()The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).
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.
skewness()The skewness of a distribution is defined by the third standardised moment, $$sk_X = E_X[\frac{x - \mu}{\sigma}^3]$$ where \(E_X\) is the expectation of distribution X, \(\mu\) is the mean of the distribution and \(\sigma\) is the standard deviation of the distribution.
kurtosis()The kurtosis of a distribution is defined by the fourth standardised moment, $$k_X = E_X[\frac{x - \mu}{\sigma}^4]$$ where \(E_X\) is the expectation of distribution X, \(\mu\) is the mean of the distribution and \(\sigma\) is the standard deviation of the distribution. Excess Kurtosis is Kurtosis - 3.
entropy()The entropy of a (discrete) distribution is defined by $$- \sum (f_X)log(f_X)$$ where \(f_X\) is the pdf of distribution X, with an integration analogue for continuous distributions.
mgf()The moment generating function is defined by $$mgf_X(t) = E_X[exp(xt)]$$ where X is the distribution and \(E_X\) is the expectation of the distribution X.
cf()The characteristic function is defined by $$cf_X(t) = E_X[exp(xti)]$$ where X is the distribution and \(E_X\) is the expectation of the distribution X.
pgf()The probability generating function is defined by $$pgf_X(z) = E_X[exp(z^x)]$$ where X is the distribution and \(E_X\) is the expectation of the distribution X.