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<table width="100%" summary="page for cmod.std"><tr><td>cmod.std</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>Standard covariance models for geostatistical data.</h2>

<h3>Description</h3>

<p>Creates a standard covariance model (<code>cmodStd</code>)
object for geostatistical data. This function will be
deprecated in the future. Please update your code to use
the <code>cmod_std</code> function, which also
allows the user to specify geometric anisotropy.
</p>


<h3>Usage</h3>

<pre>
cmod.std(model, psill, r, evar = 0, fvar = 0, par3 = 0.5)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>model</code></td>
<td>
<p>A covariance model (e.g.,
<code>"exponential"</code>). See Details for the complete
list of choices.</p>
</td></tr>
<tr valign="top"><td><code>psill</code></td>
<td>
<p>The partial sill of the model.  Must be a
positive number.</p>
</td></tr>
<tr valign="top"><td><code>r</code></td>
<td>
<p>The range parameter <code>r</code>.  Must be a
positive number.</p>
</td></tr>
<tr valign="top"><td><code>evar</code></td>
<td>
<p>The variance of the errors.  Must be
non-negative number.  The default is 0.</p>
</td></tr>
<tr valign="top"><td><code>fvar</code></td>
<td>
<p>The finescale variance (microscale error).
Must be a non-negative number.  The default is 0.</p>
</td></tr>
<tr valign="top"><td><code>par3</code></td>
<td>
<p>The value of the third parameter for 3
parameter models.  Must be a positive number.  The
default is 0.5.</p>
</td></tr>
</table>


<h3>Details</h3>

<p>The general form of the specified covariance function is
<code>psill</code> * <i>&rho;</i>(<code>d</code>; <code>r</code>) +
(<code>evar</code> + <code>fvar</code>)*(<code>d==0</code>), where
<i>&rho;</i> is the covariance function of the parametric
models.
</p>
<p>For the <code>exponential</code> model, <i>&rho;</i>(<code>d</code>;
<code>r</code>) is exp(-<code>d</code>/<code>r</code>).
</p>
<p>For the <code>gaussian</code> model, <i>&rho;</i>(<code>d</code>;
<code>r</code>) is exp(-<code>d^2</code>/<code>r^2</code>).
</p>
<p>For the <code>matern</code> model, <i>&rho;</i>(<code>d</code>;
<code>r</code>) is
2^(1-<code>par3</code>)/<code>gamma</code>(<code>par3</code>)*<code>sd</code>^<code>par3</code>*<code>besselK(sd,
nu = par3)</code>, where <code>sd = d/r</code>.
</p>
<p>For the <code>amatern</code> (alternative Matern) model,
<i>&rho;</i>(<code>d</code>; <code>r</code>) is
<code>2^(1-par3)/gamma(par3)*sd^par3*besselK(sd, nu =
par3)</code>, where <code>sd = 2 * sqrt(par3) * d/r</code>.
</p>
<p>For the <code>spherical</code> model, <i>&rho;</i>(<code>d</code>;
<code>r</code>) is <code>1 - 1.5*sd + 0.5*(sd)^3</code> if <code>d &lt;
r</code>, and 0 otherwise, with <code>sd = d/r</code>.
</p>
<p>For the <code>wendland1</code> model, <i>&rho;</i>(<code>d</code>;
<code>r</code>) is <code>(1 - sd)^4 * (4*sd + 1)</code> if <code>d &lt;
r</code>, and 0 otherwise, with <code>sd = d/r</code>.
</p>
<p>For the <code>wendland2</code> model, <i>&rho;</i>(<code>d</code>;
<code>r</code>) is <code>(1 - sd)^6 * (35*sd^2 + 18*sd + 3))/3</code>
if <code>d &lt; r</code>, and 0 otherwise, with <code>sd = d/r</code>.
</p>
<p>For the <code>wu1</code> model, <i>&rho;</i>(<code>d</code>; <code>r</code>)
is <code>(1 - sd)^3 * (1 + 3*sd + sd^2)</code> if <code>d &lt; r</code>,
and 0 otherwise, with <code>sd = d/r</code>.
</p>
<p>For the <code>wu2</code> model, <i>&rho;</i>(<code>d</code>; <code>r</code>)
is <code>(1 - sd)^4*(4 + 16*sd + 12*sd^2 + 3*sd^3))/4</code> if
<code>d &lt; r</code>, and 0 otherwise, with <code>sd = d/r</code>.
</p>
<p>For the <code>wu3</code> model, <i>&rho;</i>(<code>d</code>; <code>r</code>)
is <code>(1 - sd)^6 * (1 + 6*sd + 41/3*sd^2 + 12*sd^3 +
5*sd^4 + 5/6*sd^5)</code> if <code>d &lt; r</code>, and 0 otherwise,
with <code>sd = d/r</code>.
</p>


<h3>Value</h3>

<p>Returns a <code>cmodStd</code> object.
</p>


<h3>Author(s)</h3>

<p>Joshua French
</p>


<h3>References</h3>

<p>Waller, L. A., &amp; Gotway, C. A. (2004).
Applied Spatial Statistics for Public Health Data. John
Wiley &amp; Sons.
</p>


<h3>Examples</h3>

<pre>
cmod.std(model = "exponential", psill = 1, r = 1)
</pre>


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