R: Marginal Distributions

margins {copulaedas}

R Documentation

Marginal Distributions

Description

Functions that implement marginal distributions.

Usage

fnorm(x, lower, upper)

ftruncnorm(x, lower, upper)

fkernel(x, lower, upper)
pkernel(q, X, h)
qkernel(p, X, h)

ftrunckernel(x, lower, upper)
ptrunckernel(q, a, b, X, h)
qtrunckernel(p, a, b, X, h)

Arguments

`x`, `q`	Vector of quantiles.
`lower`, `a`	Lower bound of the variable.
`upper`, `b`	Upper bound of the variable.
`p`	Vector of probabilities
`X`	Observations of the variable.
`h`	Bandwidth of the kernel.

Details

The functions fnorm, pnorm, and qnorm implement the normal marginal distributions for EDAs with the margin parameter set to "norm". The fnorm function fits the parameters, it returns a list object with the mean (mean component) and the standard deviation (sd component). These components determine the values of the corresponding arguments of the pnorm and qnorm functions.

The functions ftruncnorm, ptruncnorm, and qtruncnorm implement the normal marginal distributions for EDAs with the margin parameter set to "truncnorm". The ftruncnorm function fits the parameters, it returns a list object with the lower and upper bounds (a and b components, respectively), the mean (mean component) and the standard deviation (sd component). These components determine the values of the corresponding arguments of the ptruncnorm and qtruncnorm functions.

The functions fkernel, pkernel, and qkernel implement the kernel-smoothed empirical marginal distributions for EDAs with the margin parameter set to "kernel". The fkernel function fits the marginal distribution, it returns a list object with the observations of the variable (X component) and the bandwidth of a Gaussian kernel density estimator (h component). The bandwidth is calculated using Silverman's rule of thumb (see bw.nrd0). The components of the list object returned by fkernel are used as aditional arguments in the pkernel and qkernel functions. The pkernel function calculates the empirical cumulative distribution function. The expression of the empirical cumulative distribution function includes the modification used in the copula context to avoid problems in the boundary of the [0,1] interval. The qkernel function uses the Gaussian kernel density estimator fitted by fkernel to evaluate the inverse of the cumulative distribution function, following the procedure suggested in (Azzalini 1981).

The functions ftrunckernel, ptrunckernel, and qtrunckernel implement the truncated kernel-smoothed empirical marginal distributions for EDAs with the margin parameter set to "trunckernel". The distribution is computed from the corresponding kernel-smoothed empirical marginal distributions without truncation by following the procedure illustrated in (Nadarajah and Kotz 2006).

References

Azzalini, A (1981) A Note on the Estimation of a Distribution Function and Quantiles by a Kernel Method, Biometrika, 68, 326-328.

Gonzalez-Fernandez Y, Soto M (2014). copulaedas: An R Package for Estimation of Distribution Algorithms Based on Copulas. Journal of Statistical Software, 58(9), 1-34. http://www.jstatsoft.org/v58/i09/.