pcf.fasp(spatstat)
pcf.fasp()所属R语言包：spatstat
Pair Correlation Function obtained from array of K functions
对相关函数从一系列的K功能
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Estimates the (bivariate) pair correlation functions of a point pattern, given an array of (bivariate) K functions.
估计（二元）对相关功能的点模式，给定一个数组（二元）K功能。
用法----------Usage----------
## S3 method for class 'fasp'
pcf(X, ..., method="c")
参数----------Arguments----------
参数：X
An array of multitype K functions (object of class "fasp").
数组的多类型K函数（类的对象"fasp"“）。
参数：...
Arguments controlling the smoothing spline function smooth.spline.
参数控制的平滑样条函数smooth.spline。
参数：method
Letter "a", "b", "c" or "d" indicating the method for deriving the pair correlation function from the K function.
字母"a"，"b"，"c"或"d"表明K功能获得对相关功能的方法。
Details
详细信息----------Details----------
The pair correlation function of a stationary point process is
是一个固定的点过程中对相关函数
where K'(r) is the derivative of K(r), the reduced second moment function (aka “Ripley's K function”) of the point process. See Kest for information about K(r). For a stationary Poisson process, the pair correlation function is identically equal to 1. Values g(r) < 1 suggest inhibition between points; values greater than 1 suggest clustering.
K'(r) K(r)衍生，减少二阶矩（又名“里普利K函数”）的点处理功能。见Kest：信息K(r)的。对于一个固定的泊松过程，对相关函数是相同的等于1。值g(r) < 1建议点与点之间的抑制;值大于1，表明聚类。
We also apply the same definition to other variants of the classical K function, such as the multitype K functions (see Kcross, Kdot) and the inhomogeneous K function (see Kinhom). For all these variants, the benchmark value of K(r) = pi * r^2 corresponds to g(r) = 1.
我们也适用相同的定义，其他变种古典K函数，如多类型K函数（参见Kcross，Kdot）和不均匀K 函数（见Kinhom）。对于所有这些变种，K(r) = pi * r^2对应的基准值到g(r) = 1。
This routine computes an estimate of g(r) from an array of estimates of K(r) or its variants, using smoothing splines to approximate the derivatives. It is a method for the generic function pcf.
这个例程计算的估计g(r)的数组的估计K(r)或它的变种，使用平滑样条近似的衍生工具。这是一个方法的通用函数pcf。
The argument X should be a function array (object of class "fasp", see fasp.object) containing several estimates of K functions. This should have been obtained from alltypes with the argument fun="K".
参数X应该是一个函数数组（对象类"fasp"，fasp.object）包含几个估计K功能。这应该已经获得alltypes的说法fun="K"。
The smoothing spline operations are performed by smooth.spline and predict.smooth.spline from the modreg library. Four numerical methods are available:
样条函数操作都是由smooth.spline和predict.smooth.splinemodreg库。四个数值方法可供选择：
"a" apply smoothing to K(r), estimate its derivative, and plug in to the formula above;
“”适用于平滑度K(r)，估计它的衍生物，插在上面的公式;
"b" apply smoothing to Y(r) = K(r)/(2 * pi * r) constraining Y(0) = 0, estimate the derivative of Y, and solve;
“B”适用于平滑Y(r) = K(r)/(2 * pi * r)制约Y(0) = 0，估计Y衍生，和解决;
"c" apply smoothing to Y(r) = K(r)/(pi * r^2) constraining Z(0)=1, estimate its derivative, and solve.
“C”申请平滑Y(r) = K(r)/(pi * r^2)制约Z(0)=1，估计及其衍生物，和解决的问题。
"d" apply smoothing to V(r) = sqrt(K(r)), estimate its derivative, and solve.
“d”的申请平滑V(r) = sqrt(K(r))，估计及其衍生物，并解决。
Method "c" seems to be the best at suppressing variability for small values of r. However it effectively constrains g(0) = 1. If the point pattern seems to have inhibition at small distances, you may wish to experiment with method "b" which effectively constrains g(0)=0. Method "a" seems comparatively unreliable.
方法"c"似乎是最好的抑制变异小值r。然而，它有效地限制了g(0) = 1。如果点模式似乎有抑制作用小的距离，你不妨试验，与方法"b"这有效地限制了g(0)=0。方法"a"似乎比较不可靠的。
Useful arguments to control the splines include the smoothing tradeoff parameter spar and the degrees of freedom df. See smooth.spline for details.
有用的参数，来控制花键包括平滑权衡参数spar和度的自由df。见smooth.spline的详细信息。
值----------Value----------
A function array (object of class "fasp", see fasp.object) representing an array of pair correlation functions. This can be thought of as a matrix Y each of whose entries Y[i,j] is a function value table (class "fv") representing the pair correlation function between points of type i and points of type j.
一个函数数组（对象类"fasp"，看到fasp.object）表示数组对相关功能。这可以被看作是一个矩阵YY[i,j]是一个函数值表（类"fv"）代表之间的类型i点对相关函数，其作品和点类型j。
（作者）----------Author(s)----------
Adrian Baddeley
<a href="mailto:Adrian.Baddeley@csiro.au">Adrian.Baddeley@csiro.au</a>
<a href="http://www.maths.uwa.edu.au/~adrian/">http://www.maths.uwa.edu.au/~adrian/</a>
and Rolf Turner
<a href="mailto:r.turner@auckland.ac.nz">r.turner@auckland.ac.nz</a>
参考文献----------References----------
Stochastic geometry and its applications. 2nd edition. Springer Verlag.
Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.
参见----------See Also----------
Kest, Kinhom, Kcross, Kdot, Kmulti, alltypes, smooth.spline, predict.smooth.spline
Kest，Kinhom，Kcross，Kdot，Kmulti，alltypes，smooth.spline，predict.smooth.spline
实例----------Examples----------
# multitype point pattern[多类型的点模式]
data(betacells)
KK <- alltypes(betacells, "K")
p <- pcf.fasp(KK, spar=0.5, method="b")
plot(p)
# short range inhibition between all types[抑制所有类型之间的短距离]
# strong inhibition between "on" and "off"[较强的抑制作用之间的“开”和“关”]
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
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发表于 2012-9-30 13:53:42
