ChiSquaredNoncentral: Noncentral Chi-Squared Distribution Class
In distr6: The Complete R6 Probability Distributions Interface
ChiSquaredNoncentral R Documentation
Noncentral Chi-Squared Distribution Class
Description
Mathematical and statistical functions for the Noncentral Chi-Squared distribution, which
is commonly used to model the sum of independent squared Normal distributions and for confidence intervals.
Details
The Noncentral Chi-Squared distribution parameterised with degrees of freedom, ν, and location, λ, is defined by the pdf,
f(x) = exp(-λ/2) ∑_{r=0}^∞ ((λ/2)^r/r!) (x^{(ν+2r)/2-1}exp(-x/2))/(2^{(ν+2r)/2}Γ((ν+2r)/2))
for ν ≥ 0, λ ≥ 0.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on the Positive Reals.
Default Parameterisation
ChiSqNC(df = 1, location = 0)
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> ChiSquaredNoncentral
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
packagesPackages required to be installed in order to construct the distribution.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
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Inherited methods
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Method new()
Creates a new instance of this R6 class.
Usage
ChiSquaredNoncentral$new(df = NULL, location = NULL, decorators = NULL)
Arguments
df(integer(1))
Degrees of freedom of the distribution defined on the positive Reals.
location(numeric(1))
Location parameter, defined on the non-negative Reals.
decorators(character())
Decorators to add to the distribution during construction.
Method mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = ∑ p_X(x)*x
with an integration analogue for continuous distributions.
Usage
ChiSquaredNoncentral$mean(...)
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.
Usage
ChiSquaredNoncentral$variance(...)
Arguments
...Unused.
Method skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[((x - μ)/σ)^3]
where E_X is the expectation of distribution X, μ is the mean of the
distribution and σ is the standard deviation of the distribution.
Usage
ChiSquaredNoncentral$skewness(...)
Arguments
...Unused.
Method kurtosis()
The kurtosis of a distribution is defined by the fourth standardised moment,
k_X = E_X[((x - μ)/σ)^4]
where E_X is the expectation of distribution X, μ is the mean of the
distribution and σ is the standard deviation of the distribution.
Excess Kurtosis is Kurtosis - 3.
Usage
ChiSquaredNoncentral$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
If TRUE (default) excess kurtosis returned.
...Unused.
Method mgf()
The moment generating function is defined by
mgf_X(t) = E_X[exp(xt)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
ChiSquaredNoncentral$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at.
...Unused.
Method 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.
Usage
ChiSquaredNoncentral$cf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at.
...Unused.
Method clone()
The objects of this class are cloneable with this method.
Usage
ChiSquaredNoncentral$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Author(s)
Jordan Deenichin
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,
ChiSquared,
Dirichlet,
Erlang,
Exponential,
FDistributionNoncentral,
FDistribution,
Frechet,
Gamma,
Gompertz,
Gumbel,
InverseGamma,
Laplace,
Logistic,
Loglogistic,
Lognormal,
MultivariateNormal,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull
Other univariate distributions:
Arcsine,
Bernoulli,
BetaNoncentral,
Beta,
Binomial,
Categorical,
Cauchy,
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,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
distr6 documentation built on March 28, 2022, 1:05 a.m.
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| ChiSquaredNoncentral | R Documentation |
Noncentral Chi-Squared Distribution Class
Description
Mathematical and statistical functions for the Noncentral Chi-Squared distribution, which is commonly used to model the sum of independent squared Normal distributions and for confidence intervals.
Details
The Noncentral Chi-Squared distribution parameterised with degrees of freedom, ν, and location, λ, is defined by the pdf,
f(x) = exp(-λ/2) ∑_{r=0}^∞ ((λ/2)^r/r!) (x^{(ν+2r)/2-1}exp(-x/2))/(2^{(ν+2r)/2}Γ((ν+2r)/2))
for ν ≥ 0, λ ≥ 0.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on the Positive Reals.
Default Parameterisation
ChiSqNC(df = 1, location = 0)
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> ChiSquaredNoncentral
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
packagesPackages required to be installed in order to construct the distribution.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
Inherited methods
Method new()
Creates a new instance of this R6 class.
Usage
ChiSquaredNoncentral$new(df = NULL, location = NULL, decorators = NULL)
Arguments
df(integer(1))
Degrees of freedom of the distribution defined on the positive Reals.location(numeric(1))
Location parameter, defined on the non-negative Reals.decorators(character())
Decorators to add to the distribution during construction.
Method mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = ∑ p_X(x)*x
with an integration analogue for continuous distributions.
Usage
ChiSquaredNoncentral$mean(...)
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.
Usage
ChiSquaredNoncentral$variance(...)
Arguments
...Unused.
Method skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[((x - μ)/σ)^3]
where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution.
Usage
ChiSquaredNoncentral$skewness(...)
Arguments
...Unused.
Method kurtosis()
The kurtosis of a distribution is defined by the fourth standardised moment,
k_X = E_X[((x - μ)/σ)^4]
where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution. Excess Kurtosis is Kurtosis - 3.
Usage
ChiSquaredNoncentral$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
IfTRUE(default) excess kurtosis returned....Unused.
Method mgf()
The moment generating function is defined by
mgf_X(t) = E_X[exp(xt)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
ChiSquaredNoncentral$mgf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at....Unused.
Method 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.
Usage
ChiSquaredNoncentral$cf(t, ...)
Arguments
t(integer(1))
t integer to evaluate function at....Unused.
Method clone()
The objects of this class are cloneable with this method.
Usage
ChiSquaredNoncentral$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Author(s)
Jordan Deenichin
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,
ChiSquared,
Dirichlet,
Erlang,
Exponential,
FDistributionNoncentral,
FDistribution,
Frechet,
Gamma,
Gompertz,
Gumbel,
InverseGamma,
Laplace,
Logistic,
Loglogistic,
Lognormal,
MultivariateNormal,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull
Other univariate distributions:
Arcsine,
Bernoulli,
BetaNoncentral,
Beta,
Binomial,
Categorical,
Cauchy,
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,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
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