NPEint

A 1D point for which PE proximity region is constructed.

A positive real number which serves as the expansion parameter in PE proximity region;
must be \(\ge 1\).

A positive real number in \((0,1)\) parameterizing the center inside <code>int</code>\(=(a,b)\).
For the interval, <code>int</code>\(=(a,b)\), the parameterized center is \(M_c=a+c(b-a)\), and default=<code>0.5</code>

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

Returns the end points of the interval which constitutes the PE proximity region for a point in the
interval <code>int</code>\(=(a,b)=\)<code>(rv=1,rv=2)</code>. PE proximity region is constructed with respect to the interval <code>int</code>
with expansion parameter \(r \ge 1\) 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 PE proximity region is constructed whether <code>x</code> is inside or outside the interval <code>int</code>.
See also (ceyhan:metrika-2012;textualpcds).

Contains the functions for generating patterns of segregation, association, complete spatial randomness (CSR))
and Uniform data in one, two and three dimensional cases, for testing these patterns based on two invariants of
various families of the proximity catch digraphs (PCDs) (see (Ceyhan (2005) ISBN:978-3-639-19063-2).
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>) of for two-dimensional data for visualization of PCDs for one,
two and three dimensional data. The PCD families considered are Arc-Slice PCDs,
Proportional-Edge PCDs and Central Similarity PCDs.

Elvan Ceyhan

pcds

Proximity Catch Digraphs and Their Applications

NPEint function

<dl><dt>x</dt>
<dd>A 1D point for which PE proximity region is constructed.</dd>
<dt>r</dt>
<dd>A positive real number which serves as the expansion parameter in PE proximity region;
must be \(\ge 1\).</dd>
<dt>c</dt>
<dd>A positive real number in \((0,1)\) parameterizing the center inside <code>int</code>\(=(a,b)\).
For the interval, <code>int</code>\(=(a,b)\), the parameterized center is \(M_c=a+c(b-a)\), and default=<code>0.5</code></dd>
<dt>int</dt>
<dd>A <code>vector</code> of two real numbers representing an interval.</dd></dl>

Arguments

Author

The end points of the Proportional Edge (PE) Proximity Region for a point - one interval case — NPEint

<dl>

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


<dt>r</dt>
<dd>A positive real number which serves as the expansion parameter in PE proximity region;
must be \(\ge 1\).</dd>


<dt>c</dt>
<dd>A positive real number in \((0,1)\) parameterizing the center inside <code>int</code>\(=(a,b)\).
For the interval, <code>int</code>\(=(a,b)\), the parameterized center is \(M_c=a+c(b-a)\), and default=<code>0.5</code></dd>


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

</dl>

NPEint: The end points of the Proportional Edge (PE) Proximity Region for a point - one interval case

Description

Usage

Value

Arguments

Author

References

See Also

Examples