Kdot(spatstat)
Kdot()所属R语言包：spatstat
Multitype K Function (i-to-any)
多类型K功能（任何）
译者：生物统计家园网 机器人LoveR
描述----------Description----------
For a multitype point pattern, estimate the multitype K function which counts the expected number of other points of the process within a given distance of a point of type i.
对于多类型的点模式，估计多类型K函数计算给定距离内的点的类型i预期数量的其他点的过程。
用法----------Usage----------
Kdot(X, i, 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 Ki.(r) will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor). See under Details.
观测点的模式，从估计的多类型K函数Ki.(r)将被计算。它必须是多类型的点模式（一个标记点图案的标记是一个因素）。请参阅“详细信息”下。
参数：i
The type (mark value) of the points in X from which distances are measured. A character string (or something that will be converted to a character string). Defaults to the first level of marks(X).
X距离的测量点的类型（标记值）。一个字符串（或东西都将被转换为一个字符串）。默认的第一级marks(X)。
参数：r
numeric vector. The values of the argument r at which the distribution function Ki.(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的分布函数Ki.(r)应该进行评估。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----------
This function Kdot and its companions Kcross and Kmulti are generalisations of the function Kest to multitype point patterns.
此功能Kdot和它的同伴Kcross和Kmulti的功能Kest多类型，点模式的概括。
A multitype point pattern is a spatial pattern of points classified into a finite number of possible “colours” or “types”. In the spatstat package, a multitype pattern is represented as a single point pattern object in which the points carry marks, and the mark value attached to each point determines the type of that point.
一个多类型的模式是一个空间格局分为有限数量的可能的“颜色”或“类型”的点。在spatstat包，多类型图案表示作为一个单一的点图案在该点进行标记的对象，并连接到每个点的标记值确定该点的类型。
The argument X must be a point pattern (object of class "ppp") or any data that are acceptable to as.ppp. It must be a marked point pattern, and the mark vector X$marks must be a factor.
参数X必须是点模式（类的对象"ppp"）或任何数据到as.ppp是可以接受的。它必须是一个显着的点图案，并标记矢量X$marks必须是一个因素。
The argument i will be interpreted as a level of the factor X$marks. If i is missing, it defaults to the first level of the marks factor, i = levels(X$marks)[1].
参数i将被解释为一个水平的因素X$marks。 i如果缺少，默认为第一级的标记因素，i = levels(X$marks)[1]。
The “type i to any type” multitype K function of a stationary multitype point process X is defined so that lambda Ki.(r) equals the expected number of additional random points within a distance r of a typical point of type i in the process X. Here lambda is the intensity of the process, i.e. the expected number of points of X per unit area. The function Ki. is determined by the second order moment properties of X.
“型i任何类型的”多类型K一个固定的多类型的功能点过程X的定义使lambda Ki.(r)等于预期的一些额外的随机点在距离r：一个典型的点类型i在这个过程中X。这是lambda过程的强度，即点X每单位面积的预期。是由二阶矩属性的Ki.的功能X。
An estimate of Ki.(r) is a useful summary statistic in exploratory data analysis of a multitype point pattern. If the subprocess of type i points were independent of the subprocess of points of all types not equal to i, then Ki.(r) would equal pi * r^2. Deviations between the empirical Ki. curve and the theoretical curve pi * r^2 may suggest dependence between types.
Ki.(r)的估计是一个多类型模式的探索性数据分析的一个有用的摘要统计。如果子类型i点是独立的子进程的的所有类型，i就等于Ki.(r)不等于pi * r^2点。的经验Ki.曲线和理论曲线pi * r^2之间的偏差可能会建议类型之间的依赖关系。
This algorithm estimates the distribution function Ki.(r) from the point pattern X. It 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$window) may have arbitrary shape. Biases due to edge effects are treated in the same manner as in Kest, using the border correction.
该算法估计分布函数Ki.(r)点模式X。它假定X可以被视为一个实现了一个固定的（的空间均匀）随机空间点在飞机上，观察到一个有限的窗口。窗口（中指定XX$window的）可以有任意形状的。边缘效应产生的偏差的处理中相同的方式，作为在Kest，使用边界校正。
The argument r is the vector of values for the distance r at which Ki.(r) should be evaluated. The values of r must be increasing nonnegative numbers and the maximum r value must exceed the radius of the largest disc contained in the window.
参数r是向量的值的距离r，Ki.(r)应该进行评估。 r的值，必须增加非负数和最大r值必须超过包含在窗口中的最大的光盘的半径。
The pair correlation function can also be applied to the result of Kdot; see pcf.
对相关功能也可以应用到的结果Kdot看pcf。
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 Ki.(r) has been estimated
的参数的值的r在哪些函数Ki.(r)已估计
参数：theo
the theoretical value of Ki.(r) for a marked Poisson process, namely pi * r^2
理论值的Ki.(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 Ki.(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Ki.(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 argument i is interpreted as a level of the factor X$marks. It is converted to a character string if it is not already a character string. The value i=1 does not refer to the first level of the factor.
解释的参数i作为的因素X$marks的水平。如果它不是已经是一个字符串，它被转换为一个字符串。值i=1不是指第一级的因素。
The reduced sample estimator of Ki. is pointwise approximately unbiased, but need not be a valid distribution function; it may not be a nondecreasing function of r. Its range is always within [0,1].
减少样本估计Ki.逐点约是公正的，但不必是一个有效的分布函数，它可能不会是一个非减函数的r。它的范围是总是在[0,1]。
（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.
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.
参见----------See Also----------
Kdot, Kest, Kmulti, pcf
Kdot，Kest，Kmulti，pcf
实例----------Examples----------
# Lansing woods data: 6 types of trees[蓝星树林数据：6种树木]
data(lansing)
## Not run: [＃不运行：]
Kh. <- Kdot(lansing, "hickory")
## End(Not run)[＃（不执行）]
# diagnostic plot for independence between hickories and other trees[山核桃和其他树木之间的独立性诊断图]
plot(Kh.)
## Not run: [＃不运行：]
# synthetic example with two marks "a" and "b"[合成例与2马克的“a”和“b”]
pp <- runifpoispp(50)
pp <- pp %mark% factor(sample(c("a","b"), npoints(pp), replace=TRUE))
K <- Kdot(pp, "a")
## End(Not run)[＃（不执行）]
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 13:39:24
