gamma2

dgamma2

pgamma2

qgamma2

rgamma2

Density, distribution function, quantile function and random generation for
the gamma distribution reparametrised in terms of mean and standard deviation.

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

gamma2 function

<dl><dt>x, q</dt>
<dd>vector of quantiles</dd>
<dt>mean</dt>
<dd>mean parameter, must be positive scalar.</dd>
<dt>sd</dt>
<dd>standard deviation parameter, must be positive scalar.</dd>
<dt>log, log.p</dt>
<dd>logical; if <code>TRUE</code>, probabilities/ densities \(p\) are returned as \(\log(p)\).</dd>
<dt>lower.tail</dt>
<dd>logical; if <code>TRUE</code>, probabilities are \(P[X &lt;= x]\), otherwise, \(P[X &gt; x]\).</dd>
<dt>p</dt>
<dd>vector of probabilities</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></dl>

Arguments

Reparametrised gamma distribution — gamma2

<dl>

<dt>x, q</dt>
<dd>vector of quantiles</dd>


<dt>mean</dt>
<dd>mean parameter, must be positive scalar.</dd>


<dt>sd</dt>
<dd>standard deviation parameter, must be positive scalar.</dd>


<dt>log, log.p</dt>
<dd>logical; if <code>TRUE</code>, probabilities/ densities \(p\) are returned as \(\log(p)\).</dd>


<dt>lower.tail</dt>
<dd>logical; if <code>TRUE</code>, probabilities are \(P[X &lt;= x]\), otherwise, \(P[X &gt; x]\).</dd>


<dt>p</dt>
<dd>vector of probabilities</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>

</dl>

gamma2: Reparametrised gamma distribution

Description

Usage

Value

Arguments

Details

Examples