Kcross(spatstat)
Kcross()所属R语言包：spatstat
Multitype K Function (Cross-type)
多类型K功能（十字型）
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 points of type j 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函数计算的预期点的数量型j给定距离内的点的类型i。
用法----------Usage----------
Kcross(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 cross type K function Kij(r) will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor). See under Details.
所观察到的点图案，从其中一个估计的交叉型K函数Kij(r)将被计算。它必须是一个多类型的点模式（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：j
The type (mark value) of the points in X to which distances are measured. A character string (or something that will be converted to a character string). Defaults to the second level of marks(X).
距离的测量点X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）。默认的第二个层次的marks(X)。
参数：r
numeric vector. The values of the argument r at which the distribution 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的分布函数Kij(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 Kcross and its companions Kdot and Kmulti are generalisations of the function Kest to multitype point patterns.
此功能Kcross和它的同伴Kdot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 arguments i and j will be interpreted as levels of the factor X$marks. If i and j are missing, they default to the first and second level of the marks factor, respectively.
的参数i和j将被解释为水平的因素X$marks。如果i和j缺少，它们默认为第一级和第二级的标记因素，分别。
The “cross-type” (type i to type j) K function of a stationary multitype point process X is defined so that lambda[j] Kij(r) equals the expected number of additional random points of type j within a distance r of a typical point of type i in the process X. Here lambda[j] is the intensity of the type j points, i.e. the expected number of points of type j per unit area. The function Kij is determined by the second order moment properties of X.
“十字型”（类型i输入j）K一个固定的多类型的功能点过程X的定义，使lambda[j] Kij(r)等于预计一些额外的随机点的类型j的距离内r类型i在这个过程中X一个典型的点。这是lambda[j]是强度的类型j点，即点类型j每单位面积的预期数目。是由二阶矩属性的Kij的功能X。
An estimate of Kij(r) is a useful summary statistic in exploratory data analysis of a multitype point pattern. If the process of type i points were independent of the process of type j points, then Kij(r) would equal pi * r^2. Deviations between the empirical Kij curve and the theoretical curve pi * r^2 may suggest dependence between the points of types i and j.
Kij(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。如果该过程的类型i点独立类型j点的过程中，那么Kij(r)将等于pi * r^2。的经验Kij曲线和理论曲线pi * r^2之间的偏差可能会建议点之间的类型i和j的依赖。
This algorithm estimates the distribution function Kij(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$window) may have arbitrary shape. Biases due to edge effects are treated in the same manner as in Kest, using the border correction.
该算法估计分布函数Kij(r)点模式X。它假定X可以被视为一个实现了一个固定的（的空间均匀）随机空间点在飞机上，观察到一个有限的窗口。窗口（中指定XX$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 Kij(r) should be evaluated. The values of r must be increasing nonnegative numbers and the maximum r value must not exceed the radius of the largest disc contained in the window.
参数r是向量的值的距离r，Kij(r)应该进行评估。 r的值，必须增加非负数和最大r值必须不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 Kcross; see pcf.
对相关功能也可以应用到的结果Kcross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 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 arguments i and j are always interpreted as levels of the factor X$marks. They are converted to character strings if they are not already character strings. The value i=1 does not refer to the first level of the factor.
的参数i和j总是被解释为水平的因素X$marks。它们被转换为字符串，如果他们不已经字符串。值i=1不是指第一级的因素。
（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----------
data(betacells)
# cat retina data[猫的视网膜数据]
K01 <- Kcross(betacells, "off", "on")
plot(K01)
## Not run: [＃不运行：]
K10 <- Kcross(betacells, "on", "off")
# synthetic example: point pattern with marks 0 and 1[合成例如：点标记0和1模式]
pp <- runifpoispp(50)
pp <- pp %mark% factor(sample(0:1, npoints(pp), replace=TRUE))
K <- Kcross(pp, "0", "1")
K <- Kcross(pp, 0, 1) # equivalent[当量]
## 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。
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发表于 2012-9-30 13:39:11
