当有两个未知数时 R 中的 uniroot

uniroot in R when there are two unknowns

考虑两个参数 xa 的函数 f。首先,我将 fx 进行积分,它成为 a 的函数 g。其次,我想找到 a 的结果函数 g 的根。我可以在 R 中使用 unirootintegrate 来做到这一点吗?如果是这样,如何?如果没有,有没有办法做到这一点?谢谢。

b <- 2

truncfn <- function(x) pmin(b, pmax(x, -b))

# thetashape and thetascale are constants
# x and a are arguments
f <- function(x, thetashape, thetascale, a){
  term1 <- -1/thetascale
  term2 <- (1-thetashape)/thetascale
  term3 <- x/(thetascale-thetashape*x)
  term1 + term2*term3 - a
}

# First, integrate f with respect to x
g <- integrate(truncfn(f), lower=0, upper=Inf)

# Second, find root of g
uniroot(g, ...)

你可以定义一个函数(我叫它truncfn2),在f的调用结果上调用truncfn,然后g整合truncfn2。最后 uniroot 搜索 g 的根:

b <- 2
truncfn <- function(x) pmin(b, pmax(x, -b))

# thetashape and thetascale are constants
# x and a are arguments
f <- function(x, thetashape, thetascale, a){
  term1 <- -1/thetascale
  term2 <- (1-thetashape)/thetascale
  term3 <- x/(thetascale-thetashape*x)
  term1 + term2*term3 - a
}
truncfn2 <- function(x, thetashape, thetascale, a) truncfn(f(x, thetashape, thetascale, a))

g <- function(a) integrate(truncfn2, thetascale=1, thetashape=0.6, a=a, lower=0, upper=10)$value
uniroot(g, lower=-10, upper=10)
# $root
# [1] -1.867932
# 
# $f.root
# [1] 1.134733e-07
# 
# $iter
# [1] 7
# 
# $init.it
# [1] NA
# 
# $estim.prec
# [1] 6.103516e-05