StudentTNoncentral | R Documentation |
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.
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.
Returns an R6 object inheriting from class SDistribution.
The distribution is supported on the Reals.
TNS(df = 1, location = 0)
N/A
N/A
distr6::Distribution
-> distr6::SDistribution
-> StudentTNoncentral
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.
new()
Creates a new instance of this R6 class.
StudentTNoncentral$new(df = NULL, location = NULL, decorators = NULL)
df
(integer(1))
Degrees of freedom of the distribution defined on the positive Reals.
location
(numeric(1))
Location parameter, defined on the Reals.
decorators
(character())
Decorators to add to the distribution during construction.
mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = ∑ p_X(x)*x
with an integration analogue for continuous distributions.
StudentTNoncentral$mean(...)
...
Unused.
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.
StudentTNoncentral$variance(...)
...
Unused.
clone()
The objects of this class are cloneable with this method.
StudentTNoncentral$clone(deep = FALSE)
deep
Whether to make a deep clone.
Jordan Deenichin
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
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