我有一个两列的表,它包含一个已经计算出的2个变量的索引,简单的引用如下:
V1, V2
0.46,1.08
0.84,1.05
-0.68,0.93
-0.99,0.68
-0.87,0.30
-1.08,-0.09
-1.16,-0.34
-0.61,-0.43
-0.65,-0.48
0.73,-0.48
为了找出上述数据之间的相关性,我在R中使用了copula包。
我用来确定要使用哪个Copula系列的以下VineCopula代码:
library(VineCopula)
selectedCopula <- BiCopSelect(u,v,familyset=NA)
selectedCopula
根据copula R手册(Link),建议使用生存的Gumbel,即Gumbel Copula的旋转版本
但是,我选择了Frank copula,因为它提供了对称的依存关系结构,并且允许在数据中将正依存关系建模为负依存关系,
在运行以下自我解释的copula代码之后,还有一件事:
# Estimate V1 distribution parameters and visually compare simulated vs observed data
x_mean <- mean(mydata$V1)
#Normal Distribution
hist(mydata$V1, breaks = 20, col = "green", density = 30)
hist(rnorm( nrow(mydata), mean = x_mean, sd = sd(mydata$V1)),
breaks = 20,col = "blue", add = T, density = 30, angle = -45)
# Same for V2
y_mean <- mean(mydata$V2)
#Normal Distribution
hist(mydata$V2, breaks = 20, col = "green", density = 30)
hist(rnorm(nrow(mydata), mean = y_mean,sd = sd(mydata$V2)),
breaks = 20, col = "blue", add = T, density = 30, angle = -45)
# Measure association using Kendall's Tau
cor(mydata, method = "kendall")
#Fitting process with copula choice
# Estimate copula parameters
cop_model <- frankCopula(dim = 2)
m <- pobs(as.matrix(mydata))
fit <- fitCopula(cop_model, m, method = 'ml')
coef(fit)
# Check Kendall's tau value for the frank copula with = 3.236104
tau(frankCopula(param = 3.23))
#Building the bivariate distribution using frank copula
# Build the bivariate distribution
sdx =sd(mydata$V1)
sdy =sd(mydata$V2)
my_dist <- mvdc(frankCopula(param = 3.23, dim = 2), margins = c("norm","norm"),
paramMargins = list(list(mean = x_mean, sd=sdx),
list(mean = y_mean, sd=sdy)))
# Generate 439 random sample observations from the multivariate distribution
v <- rMvdc(439, my_dist)
# Compute the density
pdf_mvd <- dMvdc(v, my_dist)
# Compute the CDF
cdf_mvd <- pMvdc(v, my_dist)
# Sample 439 observations from the distribution
sim <- rMvdc(439,my_dist)
# Plot the data for a visual comparison
plot(mydata$V1, mydata$V2, main = 'Test dataset x and y', col = "blue")
points(sim[,1], sim[,2], col = 'red')
legend('bottomright', c('Observed', 'Simulated'), col = c('blue', 'red'), pch=21)
所绘制的数据集即使对于极值也显示出良好的拟合结果。
在这里,我想通过在同一条线图中将原始数据应用于坦率的copula来显示相关值, 我不知道如何提取坦率的copula结果? (只有一列,因此我可以绘制原始数据并进行视觉比较)
答案 0 :(得分:0)
我不确定我是否正确理解您的问题。但是,如果要获取(从Frank copula生成的)关联数据,它们将存储在sim
中。如果您要输入Kendall
头,则应将其存储在fitcopula
中。您不能将坦率的copula数据作为一列,因为它必须是矩阵。同样,pobs
函数将为您提供矩阵结果,因此您无需使用as.matrix
。如果您需要更多帮助,我们非常乐意为您提供帮助。