Kmulti(spatstat)
Kmulti()所属R语言包：spatstat
Marked K-Function
标记K-功能
译者：生物统计家园网 机器人LoveR
描述----------Description----------
For a marked point pattern, estimate the multitype K function which counts the expected number of points of subset J within a given distance from a typical point in subset I.
一个显着的点模式，估计多类型K函数计算的预期数目的子集J在一个典型的点在子集I中一个给定的距离。
用法----------Usage----------
Kmulti(X, I, J, r=NULL, breaks=NULL, correction, ..., ratio=FALSE)
参数----------Arguments----------
参数：X
The observed point pattern, from which an estimate of the multitype K function KIJ(r) will be computed. It must be a marked point pattern. See under Details.
观测点的模式，从估计的多类型K函数KIJ(r)将被计算。它必须是一个显着的点模式。请参阅“详细信息”下。
参数：I
Subset index specifying the points of X from which distances are measured. See Details.
指定X距离的测量点的子集指数。查看详细信息。
参数：J
Subset index specifying the points in X to which distances are measured. See Details.
指定点的子集指数在X距离的测量。查看详细信息。
参数：r
numeric vector. The values of the argument r at which the multitype K function KIJ(r) should be evaluated. There is a sensible default. First-time users are strongly advised not to specify this argument. See below for important conditions on r.
数字矢量。的参数的值r多类型K函数KIJ(r)应进行评估。有一个合理的默认。我们强烈建议用户第一次不指定此参数。请参阅下面的重要条件r。
参数：breaks
An alternative to the argument r. Not normally invoked by the user. See the Details section.
替代到的参数r。通常不是由用户调用。查看详细信息“一节。
参数：correction
A character vector containing any selection of the options "border", "bord.modif", "isotropic", "Ripley", "translate", "none" or "best". It specifies the edge correction(s) to be applied.
字符向量含有任何选择的选项"border"，"bord.modif"，"isotropic"，"Ripley"，"translate"，"none"或"best" 。指定，边缘校正（S）。
参数：...
Ignored.
忽略。
参数：ratio
Logical. If TRUE, the numerator and denominator of each edge-corrected estimate will also be saved, for use in analysing replicated point patterns.
逻辑。如果TRUE，分子和分母的每个边缘校正的估计也将被保存，用于在分析复制的点图案。
Details
详细信息----------Details----------
The function Kmulti generalises Kest (for unmarked point patterns) and Kdot and Kcross (for multitype point patterns) to arbitrary marked point patterns.
的功能Kmulti Kest（未标记的点模式）和Kdot和Kcross下的多点模式任意标记点模式可以推广。
Suppose X[I], X[J] are subsets, possibly overlapping, of a marked point process. The multitype K function is defined so that lambda[J] KIJ(r) equals the expected number of additional random points of X[J] within a distance r of a typical point of X[I]. Here lambda[J] is the intensity of X[J] i.e. the expected number of points of X[J] per unit area. The function KIJ is determined by the second order moment properties of X.
假设X[I]，X[J]子集，可能有重叠，出现了明显的点过程。多类型K函数被定义，使得lambda[J] KIJ(r)等于预期数目的额外的随机点X[J]的距离内rX[I]一个典型的点。这是lambda[J]是X[J]即预期数量的点X[J]每单位面积的强度。是由二阶矩属性的KIJ的功能X。
The argument X must be a point pattern (object of class "ppp") or any data that are acceptable to as.ppp.
参数X必须是点模式（类的对象"ppp"）或任何数据到as.ppp是可以接受的。
The arguments I and J specify two subsets of the point pattern. They may be any type of subset indices, for example, logical vectors of length equal to npoints(X), or integer vectors with entries in the range 1 to npoints(X), or negative integer vectors.
的参数I和J指定两个点模式的子集。它们可以是任何类型的子集的索引，例如，逻辑向量长度等于npoints(X)，或整数向量的条目中的取值范围为1到npoints(X)，或负整数向量。
Alternatively, I and J may be functions that will be applied to the point pattern X to obtain index vectors. If I is a function, then evaluating I(X) should yield a valid subset index. This option is useful when generating simulation envelopes using envelope.
另外，I和J可能是点模式X获得索引向量将被应用到的功能。如果I是一个函数，然后计算I(X)应该产生一个有效的子集指数。此选项是有用的时生成模拟信封使用envelope。
The argument r is the vector of values for the distance r at which KIJ(r) should be evaluated. It is also used to determine the breakpoints (in the sense of hist) for the computation of histograms of distances.
参数r是向量的值的距离r，KIJ(r)应该进行评估。它也可以用来确定断点（在感hist）的直方图的距离的计算。
First-time users would be strongly advised not to specify r. However, if it is specified, r must satisfy r[1] = 0, and max(r) must be larger than the radius of the largest disc contained in the window.
用户第一次将强烈建议不指定r的。然而，如果它被指定，r必须满足r[1] = 0，和max(r)必须大于包含在窗口中的最大的光盘的半径。
This algorithm assumes that X can be treated as a realisation of a stationary (spatially homogeneous) random spatial point process in the plane, observed through a bounded window. The window (which is specified in X as X$window) may have arbitrary shape.
此算法假定X可以被视为一个实现了一个固定的（的空间均匀）随机空间点在飞机上，观察到有界的窗口。窗口（中指定XX$window的）可以有任意形状的。
Biases due to edge effects are treated in the same manner as in Kest. The edge corrections implemented here are
边缘效应产生的偏差的处理中相同的方式，当在Kest。这里实现的边缘修正
border the border method or “reduced sample” estimator (see Ripley, 1988). This is the least efficient (statistically) and the fastest to compute. It can be computed for a window of arbitrary shape.
毗邻边界的方法或“减少样本”估计（见里普利，1988年）。这是最有效的（统计），以最快的速度计算。它可以计算一个窗口的任意形状。
isotropic/Ripley Ripley's isotropic correction (see Ripley, 1988; Ohser, 1983). This is currently implemented only for rectangular windows.
各向同性/ Ripley旅游Ripley的各向同性修正（见里普利，1988; Ohser，1983年）。这是目前实施的矩形窗。
translate Translation correction (Ohser, 1983). Implemented for all window geometries.
翻译的翻译的校正（Ohser，1983）。实现所有窗口的几何形状。
The pair correlation function pcf can also be applied to the result of Kmulti.
对相关函数pcf也可以应用于结果Kmulti。
值----------Value----------
An object of class "fv" (see fv.object).
类的一个对象"fv"（见fv.object）。
Essentially a data frame containing numeric columns
本质上是一个数据框包含数字的列
参数：r
the values of the argument r at which the function KIJ(r) has been estimated
的参数的值的r在哪些函数KIJ(r)已估计
参数：theo
the theoretical value of KIJ(r) for a marked Poisson process, namely pi * r^2
理论值的KIJ(r)显着的泊松过程，即pi * r^2，
together with a column or columns named "border", "bord.modif", "iso" and/or "trans", according to the selected edge corrections. These columns contain estimates of the function KIJ(r) obtained by the edge corrections named.
连同一列或多列名为"border"，"bord.modif"，"iso"和/或"trans"，根据选定的边修正。这些列包含的功能KIJ(r)命名的边缘修正的估计。
If ratio=TRUE then the return value also has two attributes called "numerator" and "denominator" which are "fv" objects containing the numerators and denominators of each estimate of K(r).
如果ratio=TRUE，则返回值也有两个属性，称为"numerator"和"denominator""fv"含有的分子和分母的每一个估计的K(r)的对象。
警告----------Warnings----------
The function KIJ is not necessarily differentiable.
函数KIJ不一定是微。
The border correction (reduced sample) estimator of KIJ used here is pointwise approximately unbiased, but need not be a nondecreasing function of r, while the true KIJ must be nondecreasing.
边界校正（减少样本）估计KIJ这里使用的是逐点近似无偏的，但不必是一个非降函数的r，而真正的KIJ必须单调不减。
（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----------
John Wiley and Sons, 1991.
Academic Press, 1983.
Displaced amacrine cells in the retina of a rabbit : analysis of a bivariate spatial point pattern. J. Neurosci. Meth. 18, 115–125.
A bivariate spatial point pattern of ants' nests. Applied Statistics 32, 293–303
Methods for analysing spatial processes of several types of points. J. Royal Statist. Soc. Ser. B 44, 406–413.
Cambridge University Press, 1988.
Stochastic geometry and its applications. 2nd edition. Springer Verlag, 1995.
Indices of dependence between types in multivariate point patterns. Scandinavian Journal of Statistics 26, 511–532.
参见----------See Also----------
Kcross, Kdot, Kest, pcf
Kcross，Kdot，Kest，pcf
实例----------Examples----------
# Longleaf Pine data: marks represent diameter[长叶松数据：标记代表直径]
K <- Kmulti(longleaf, longleaf$marks <= 15, longleaf$marks >= 25)
plot(K)
# functions determining subsets[功能确定的子集]
f1 <- function(X) { marks(X) <= 15 }
f2 <- function(X) { marks(X) >= 15 }
K <- Kmulti(longleaf, f1, f2)
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。
注2：由于是机器人自动翻译，难免有不准确之处，使用时仔细对照中、英文内容进行反复理解，可以帮助R语言的学习。
注3：如遇到不准确之处，请在本贴的后面进行回帖，我们会逐渐进行修订。
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发表于 2012-9-30 13:40:18
