Density, distribution function and random generation for the von Mises distribution.

A variety of latent Markov models, including hidden Markov models, hidden semi-Markov models,
state-space models and continuous-time variants can be formulated and estimated within the same framework via directly maximising the likelihood function using the so-called forward algorithm.
Applied researchers often need custom models that standard software does not easily support.
Writing tailored 'R' code offers flexibility but suffers from slow estimation speeds.
We address these issues by providing easy-to-use functions (written in 'C++' for speed) for common tasks like the forward algorithm.
These functions can be combined into custom models in a Lego-type approach, offering up to 10-20 times faster estimation via standard numerical optimisers.
To aid in building fully custom likelihood functions, several vignettes are included that show how to simulate data from and estimate all the above model classes.

Jan-Ole Koslik

LaMa

Fast Numerical Maximum Likelihood Estimation for Latent Markov
Models

vm function

<dl><dt>x, q</dt>
<dd>vector of angles measured in radians at which to evaluate the density function.</dd>
<dt>mu</dt>
<dd>mean direction of the distribution measured in radians.</dd>
<dt>kappa</dt>
<dd>non-negative numeric value for the concentration parameter of the distribution.</dd>
<dt>log</dt>
<dd>logical; if <code>TRUE</code>, densities are returned on the log scale.</dd>
<dt>from</dt>
<dd>value from which the integration for CDF starts. If <code>NULL</code>, is set to <code>mu - pi</code>.</dd>
<dt>tol</dt>
<dd>the precision in evaluating the distribution function</dd>
<dt>n</dt>
<dd>number of observations. If <code>length(n) &gt; 1</code>, the length is taken to be the number required.</dd>
<dt>wrap</dt>
<dd>logical; if <code>TRUE</code>, generated angles are wrapped to the interval [-pi, pi].</dd></dl>

Arguments

von Mises distribution — vm

<dl>

<dt>x, q</dt>
<dd>vector of angles measured in radians at which to evaluate the density function.</dd>


<dt>mu</dt>
<dd>mean direction of the distribution measured in radians.</dd>


<dt>kappa</dt>
<dd>non-negative numeric value for the concentration parameter of the distribution.</dd>


<dt>log</dt>
<dd>logical; if <code>TRUE</code>, densities are returned on the log scale.</dd>


<dt>from</dt>
<dd>value from which the integration for CDF starts. If <code>NULL</code>, is set to <code>mu - pi</code>.</dd>


<dt>tol</dt>
<dd>the precision in evaluating the distribution function</dd>


<dt>n</dt>
<dd>number of observations. If <code>length(n) &gt; 1</code>, the length is taken to be the number required.</dd>


<dt>wrap</dt>
<dd>logical; if <code>TRUE</code>, generated angles are wrapped to the interval [-pi, pi].</dd>

</dl>

vm: von Mises distribution

Description

Usage

Value

Arguments

Details

Examples