rvmmix {BAMBI} | R Documentation |

## The univariate von Mises mixtures

### Description

The univariate von Mises mixtures

### Usage

```
rvmmix(n, kappa, mu, pmix)
dvmmix(x, kappa, mu, pmix, log = FALSE)
```

### Arguments

`n` |
number of observations. Ignored if at least one of the other parameters have length k > 1, in which case, all the parameters are recycled to length k to produce k random variates. |

`kappa` |
vector of component concentration (inverse-variance) parameters, |

`mu` |
vector of component means. |

`pmix` |
vector of mixing proportions. |

`x` |
vector of angles (in radians) where the densities are to be evaluated. |

`log` |
logical. Should the log density be returned instead? |

### Details

`pmix`

, `mu`

and `kappa`

must be of the same length, with `j`

-th element corresponding to the `j`

-th component of the mixture distribution.

The univariate von Mises mixture distribution with component size `K = length(pmix)`

has density

`g(x) = p[1] * f(x; \kappa[1], \mu[1]) + ... + p[K] * f(x; \kappa[K], \mu[K])`

where `p[j], \kappa[j], \mu[j]`

respectively denote the mixing proportion, concentration parameter and the mean parameter for the `j`

-th component
and `f(. ; \kappa, \mu)`

denotes the density function of the (univariate) von Mises distribution with mean parameter `\mu`

and concentration parameter `\kappa`

.

### Value

`dvmmix`

computes the density and `rvmmix`

generates random deviates from the mixture density.

### Examples

```
kappa <- 1:3
mu <- 0:2
pmix <- c(0.3, 0.3, 0.4)
x <- 1:10
n <- 10
# mixture densities calculated at each point in x
dvmmix(x, kappa, mu, pmix)
# number of observations generated from the mixture distribution is n
rvmmix(n, kappa, mu, pmix)
```

*BAMBI*version 2.3.5 Index]