是否可以求解非线性方程 R？

Question

I want to build a function that takes E[x] and Var[X] and give me the mean and standard error of a univariate lognormal variable.

E[x] = exp(mu + theta) 
Var[x] =  exp(2*mu + theta)*(exp(theta) - 1)

The function would take E[x] and Var[x] as input and as output would give me theta and mu

Answer 1

There are several packages that provide ways and means to solve a system of nonlinear equations. One of these is nleqslv .

You nee to provide a function that function that returns the differences between the actual value of the equations and the desired value.

Load package nleqslv and define the following function

library(nleqslv)

f <- function(x,Ex,Varx) {
    y<- numeric(length(x))    
    mu <- x[1]
    theta <- x[2]
    y[1] <- exp(mu+theta) - Ex
    y[2] <- exp(2*mu+theta)*(exp(theta)-1) - Varx

    y
}

The vector x in the function contains the values of mu and theta . An example with Ex=2 and Varx=3 and some random starting values

xstart <- c(1,1)
nleqslv(xstart,f,Ex=2,Varx=3)

gives the following

$x
[1] -0.6931472  1.3862944

$fvec
[1] -8.095125e-11 -8.111645e-11

$termcd
[1] 1

$message
[1] "Function criterion near zero"

$scalex
[1] 1 1

$nfcnt
[1] 31

$njcnt
[1] 2

$iter
[1] 22

See the manual of nleqslv for the meaning of the different elements of the return value of nleqslv .

If you want to investigate the effect of the different solving methods try this

testnslv(xstart,f,Ex=2,Varx=3)