NCSint

Returns the end points of the interval which constitutes the CS proximity region for a point in the
interval <code>int</code>\(=(a,b)=\)<code>(rv=1,rv=2)</code>.
CS proximity region is constructed with respect to the interval <code>int</code>
with expansion parameter \(t&gt;0\) and centrality parameter \(c \in (0,1)\).
Vertex regions are based on the (parameterized) center, \(M_c\),
which is \(M_c=a+c(b-a)\) for the interval, <code>int</code>\(=(a,b)\).
The CS proximity region is constructed whether <code>x</code> is inside or outside the interval <code>int</code>.
See also (ceyhan:revstat-2016;textualpcds).

Contains the functions for construction and visualization of various families
of the proximity catch digraphs (PCDs), see (Ceyhan (2005) ISBN:978-3-639-19063-2),
for computing the graph invariants for testing the patterns of segregation and association against complete spatial randomness (CSR)
or uniformity in one, two and three dimensional cases.
The package also has tools for generating points from these spatial patterns.
The graph invariants used in testing spatial point data are the domination number (Ceyhan (2011)
<doi:10.1080/03610921003597211>) and arc density (Ceyhan et al. (2006) <doi:10.1016/j.csda.2005.03.002>;
Ceyhan et al. (2007) <doi:10.1002/cjs.5550350106>). The PCD families considered are Arc-Slice PCDs,
Proportional-Edge PCDs, and Central Similarity PCDs.

Elvan Ceyhan

pcds

Proximity Catch Digraphs and Their Applications

NCSint function

<dl><dt>x</dt>
<dd>A 1D point for which CS proximity region is constructed.</dd>
<dt>int</dt>
<dd>A <code>vector</code> of two real numbers representing an interval.</dd>
<dt>t</dt>
<dd>A positive real number which serves as the expansion parameter in CS proximity region.</dd>
<dt>c</dt>
<dd>A positive real number in \((0,1)\) parameterizing the center inside <code>int</code>\(=(a,b)\)
with the default <code>c=.5</code>.
For the interval, <code>int</code>\(=(a,b)\), the parameterized center is \(M_c=a+c(b-a)\).</dd></dl>

Arguments

Author

The end points of the Central Similarity (CS) Proximity Region for a point - one interval case — NCSint

<dl>

<dt>x</dt>
<dd>A 1D point for which CS proximity region is constructed.</dd>


<dt>int</dt>
<dd>A <code>vector</code> of two real numbers representing an interval.</dd>


<dt>t</dt>
<dd>A positive real number which serves as the expansion parameter in CS proximity region.</dd>


<dt>c</dt>
<dd>A positive real number in \((0,1)\) parameterizing the center inside <code>int</code>\(=(a,b)\)
with the default <code>c=.5</code>.
For the interval, <code>int</code>\(=(a,b)\), the parameterized center is \(M_c=a+c(b-a)\).</dd>

</dl>

NCSint: The end points of the Central Similarity (CS) Proximity Region for a point - one interval case

Description

Usage

Value

Arguments

Author

References

See Also

Examples