joint {cylcop}

Density, Distribution, Quantiles and Random Number Generation for joint distributions

Description

The bivariate joint distributions are described in terms of two marginal distributions and a copula

Usage

rjoint(n, copula, marginal_1, marginal_2)

djoint(x, copula, marginal_1, marginal_2)

pjoint(q, copula, marginal_1, marginal_2)

Arguments

n

integer value, the number of random samples to be generated with rjoint().

copula

R object of class 'cyl_copula'. or 'Copula' (package 'copula', only 2-dimensional).

marginal_1

named list (for parametric estimates) or a 'density' object (for linear kernel density estimates) or a 'density.circular' object (for circular kernel density estimates). The output of functions fit_angle() and fit_steplength() can be used here directly.

marginal_2

This input is similar to marginal_1.

x

matrix (or vector) of numeric values giving the points (in 2 dimensions) where the density function is evaluated.

q

matrix (or vector) of numeric values giving the points (in 2 dimensions) where the distribution function is evaluated.

Details

If entered "by hand", the named lists describing the parametric distributions (marginal_1 and marginal_2) must contain 2 entries:

1. name: a character string denoting the name of the distribution. For a circular distribution, it can be "vonmises", "vonmisesmix", or "wrappedcauchy". For a linear distribution, it must be a string denoting the name of a linear distribution in the environment, i.e. the name of its distribution function without the "p", e.g. "norm" for normal distribution

2. coef: For a circular distribution coef is a (named) list of parameters of the circular marginal distribution as taken by the functions qvonmises(), qvonmisesmix(), or qwrappedcauchy(). For a linear distribution, coef is a named list containing the parameters of the distribution given in "name".

Value

• djoint() gives a vector of length length(x) containing the density at x.

• pjoint() gives a vector of length length(q) containing the distribution function at the corresponding values of q.

• rjoint() generates a vector of length n containing the random samples.

Examples

cop <- copula::normalCopula(0.6)
marginal_1 <- list(name="exp",coef=list(rate=2))
marginal_2 <- list(name="lnorm", coef=list(0,0.1))

sample <- rjoint(10,cop,marginal_1,marginal_2)
pjoint(sample,cop,marginal_1,marginal_2)
djoint(sample,cop,marginal_1,marginal_2)

cop <- cyl_quadsec()
marginal_1 <- list(name="wrappedcauchy", coef=list(location=0,scale=0.3))
marginal_2 <- list(name="weibull",coef=list(shape=3))

sample <- rjoint(10,cop,marginal_1,marginal_2)
marginal_1 <- fit_angle(theta=sample[,1], parametric=FALSE)
marginal_2 <- fit_steplength(x=sample[,2],parametric="lnorm")
pjoint(c(0.3*pi,4),cop,marginal_1,marginal_2)
djoint(c(0,2),cop,marginal_1,marginal_2)