# Density, Distribution, Quantiles and Random Number Generation for joint distributions The bivariate joint distributions are described in terms of two marginal distributions and a copula ```r 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`: 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. ## Returns * `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. ## 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"`. ## Examples ```r 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) ```

joint function