rmaxlin(SpatialExtremes)
rmaxlin()所属R语言包:SpatialExtremes
Simulation from max-linear models
从最大线性模型的模拟
译者:生物统计家园网 机器人LoveR
描述----------Description----------
This function generates realisations from a max-linear
这个函数生成实现从最大线性
用法----------Usage----------
rmaxlin(n, coord, cov.mod = "gauss", dsgn.mat, grid = FALSE, p = 500,
...)
参数----------Arguments----------
参数:n
Integer. The number of observations.
整数。的若干意见。
参数:coord
A vector or matrix that gives the coordinates of each location. Each row corresponds to one location - if any. May be missing if dsgn.mat is specified.
的向量或基质,给出了每一个位置的坐标。每一行对应于一个位置 - 如果有的话。可能会丢失,如果dsgn.mat指定。
参数:cov.mod
A character string that specifies the max-linear model. Currently only the discretized Smith model is implemented, i.e., cov.mod = "gauss".
一个字符串,指定的最大线性模型。目前,只有离散Smith模型来实现,即cov.mod = "gauss"。
参数:dsgn.mat
The design matrix of the max-linear model — see Section Details. May be missing if coord and cov.mod are given.
设计矩阵的的最大线性模型 - 部分详细介绍。如果coord和cov.mod给出可能会丢失。
参数:grid
Logical. Does coord defines a grid?
逻辑。 coord定义了一个网格?
参数:p
An integer corresponding to the number of unit Frechet random variable used in the max-linear model — see Section Details.
一个整数,对应的单元导数随机变量的最大线性模型中 - 部分详细介绍。
参数:...
The parameters of the max-stable model — see Section Details.
最大稳定模型的参数 - 见第详情。
Details
详细信息----------Details----------
A max-linear process {Y(x)} is defined by
一个最大线性过程{Y(x)}被定义为
where p is a positive integer, f_j are non negative functions and Z_j are independent unit Frechet random variables. Most often, the max-linear process will be generated at locations x_1, …, x_k in R^d and an alternative but equivalent formulation is
p是一个正整数,f_j非负函数和Z_j是独立的单元导数的随机变量。大多数情况下,最大线性的过程将产生在位置x_1, …, x_k in R^d和其它相等的制定是
where Y = {Y(x_1), …, Y(x_k)}, Z = (Z_1, …, Z_p), * is the max-linear operator, see the first equation, and A is the design matrix of the max-linear model. The design matrix A is a k x p matrix with non negative entries and whose i-th row is {f_1(x_i), …, f_i(x_p)}.
Y = {Y(x_1), …, Y(x_k)},Z = (Z_1, …, Z_p),*是的最大线性算子,看到的第一个方程,并A是最大线性模型的设计矩阵。设计矩阵A是一个k x p矩阵与非负项,而其i是{f_1(x_i), …, f_i(x_p)}-th行。
Currently only the discretized Smith model is implemented for which f_j(x) = c(p) phi(x - u_j ; Sigma) where phi( . ; Sigma) is the zero mean (multivariate) normal density with covariance matrix Sigma, u_j is a sequence of deterministic points appropriately chosen and c(p) is a constant ensuring unit Frechet margins. Hence if this max-linear model is used, users must specify var for one dimensional processes, and cov11, cov12, cov22 for two dimensional processes.
目前,只有离散Smith模型实施的f_j(x) = c(p) phi(x - u_j ; Sigma),其中phi( . ; Sigma)是零均值(多元)正常密度的协方差矩阵Sigma,u_j是一个序列的确定性点适当地选择和c(p)是一个常数确保单位的Frechet空间。因此,如果使用这个最大线性模型,用户必须指定var一维的过程,并cov11,cov12,cov22二维的过程。
值----------Value----------
A matrix containing observations from the max-linear model. Each column represents one stations. If grid = TRUE, the function returns an array of dimension nrow(coord) x nrow(coord) x n.
最大线性模型的矩阵观测。每一列代表一个站。如果grid = TRUE,该函数返回一个数组的维NROW(经纬度)所述NROW(经纬度)X N。
(作者)----------Author(s)----------
Mathieu Ribatet
参考文献----------References----------
Random Fields. Advances in Applied Probability.
参见----------See Also----------
condrmaxlin, rmaxstab
condrmaxlin,rmaxstab
实例----------Examples----------
## A one dimensional simulation from a design matrix. This design matrix[#A三维仿真的设计矩阵。这样的设计矩阵]
## corresponds to a max-moving average process MMA(alpha)[#对应一个最大的移动平均过程MMA(α)]
n.site <- 250
x <- seq(-10, 10, length = n.site)
## Build the design matrix[#建立设计矩阵]
alpha <- 0.8
dsgn.mat <- matrix(0, n.site, n.site)
dsgn.mat[1,1] <- 1
for (i in 2:n.site){
dsgn.mat[i,1 i-1)] <- alpha * dsgn.mat[i-1,1 i-1)]
dsgn.mat[i,i] <- 1 - alpha
}
data <- rmaxlin(3, dsgn.mat = dsgn.mat)
matplot(x, t(log(data)), pch = 1, type = "l", lty = 1, ylab =
expression(log(Y(x))))
## One realisation from the discretized Smith model (2d sim)[第一个实现从离散Smith模型(2D SIM)]
x <- y <- seq(-10, 10, length = 100)
data <- rmaxlin(1, cbind(x, y), cov11 = 3, cov12 = 1, cov22 = 4, grid =
TRUE, p = 2000)
image(x, y, log(data), col = heat.colors(64))
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注:
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