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<table width="100%" summary="page for eta.s.exact"><tr><td>eta.s.exact</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>Strong asymmetry measure <i>eta(X)</i>.</h2>

<h3>Description</h3>

<p>Returns the strong asymmetry measure <i>eta(X)</i> of <a href="https://link.springer.com/article/10.1007/s13171-013-0034-z">Patil, Bagkavos and Wood (2014)</a>.
</p>


<h3>Usage</h3>

<pre>
  eta.s.exact(xin, dist, GridLength, p1, p2)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>xin</code></td>
<td>
<p>A vector of data points - the available sample.</p>
</td></tr>
<tr valign="top"><td><code>dist</code></td>
<td>
<p>Character string, specifies selected distribution function.</p>
</td></tr>
<tr valign="top"><td><code>GridLength</code></td>
<td>
<p>A non-negative number, which will be rounded up if fractional.Desired length of the sequence. </p>
</td></tr>
<tr valign="top"><td><code>p1</code></td>
<td>
<p>A scalar. Parameter 1 (vector or object) of the selected distribution.</p>
</td></tr>
<tr valign="top"><td><code>p2</code></td>
<td>
<p>A scalar. Parameter 2 (vector or object) of the selected distribution.</p>
</td></tr>
</table>


<h3>Details</h3>

<p>Implements
</p>
<p style="text-align: center;"><i>&eta;(X)= -0.5 sign(&rho;_1)\max|&rho;_p + &rho;_p^*|</i></p>
<p> with <i>1/2 &le; p &le; 1</i>
This version uses exact p.d.f. and c.d.f. evaluation and not estimates of the unknown functionals.</p>


<h3>Value</h3>

<p>Returns a scalar, the value of the strong asymmetry measure <i>&eta;(X)</i>.</p>


<h3>Author(s)</h3>

<p>Dimitrios Bagkavos and Lucia Gamez Gallardo
</p>
<p>R implementation and documentation: Dimitrios Bagkavos &lt;dimitrios.bagkavos@gmail.com&gt; , Lucia Gamez Gallardo &lt;gamezgallardolucia@gmail.com&gt;
</p>


<h3>References</h3>


<ul>
<li>   <p><a href="https://link.springer.com/article/10.1007/s13171-013-0034-z">Patil P.N., Bagkavos D. and Wood A.T.A., (2014). A measure of asymmetry based on a new necessary and sufficient condition for symmetry, Sankhya A, 76, 123&ndash;145.</a>
</p>
</li>
<li>  <p><a href="https://link.springer.com/chapter/10.1007/978-3-319-41582-6_1">Bagkavos D., Patil P.N., Wood A.T.A. (2016), A Numerical Study of the Power Function of a New Symmetry Test. In: Cao R., GonzÃ¡lez Manteiga W., Romo J. (eds) Nonparametric Statistics. Springer Proceedings in Mathematics and Statistics, vol 175, Springer.
</a></p>
</li></ul>


<h3>See Also</h3>

<p><code>eta.w.hat.bc, eta.w.hat, eta.w.breve,eta.w.breve.bc, eta.w.tilde,eta.w.tilde.bc,eta.s
  </code></p>


<h3>Examples</h3>

<pre>

selected.dist &lt;- "norm" #select norm as the distribution
m.use &lt;- 2
sd.use&lt;- 2
grid &lt;- 50
s.use&lt;- rnorm(100)
eta.s.exact(s.use,selected.dist,grid,m.use,sd.use)  # calculate eta.s at xout

</pre>


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