Finding parameters values given the solution with two non-linear equations in R -

i have 2 equations describe moments (mean , variance) of truncated gaussian distribution. built following function compute them:

trunc_moments <- function(moments, a, b){    require(truncnorm)    mu <- moments[1]   sigma <- moments[2]    alpha <- (a - mu) / sigma; beta <- (b - mu) / sigma    mu_trunc <- mu + sigma*     ((dnorm(alpha, mu, sigma) - dnorm(beta, mu, sigma)) /        (pnorm(beta, mu, sigma) - pnorm(alpha, mu, sigma)))    sigma_trunc <- sigma^2 * (1 +         ((alpha*dnorm(alpha, mu, sigma) - beta*dnorm(beta, mu, sigma))         / (pnorm(beta, mu, sigma) - pnorm(alpha, mu, sigma))) -        ((dnorm(alpha, mu, sigma) - dnorm(beta, mu, sigma))          / (pnorm(beta, mu, sigma) - pnorm(alpha, mu, sigma)))^2)    return(c(mu_trunc, sigma_trunc))  } 

given mu , sigma, function returns mu_trunc , sigma_trunc.

trunc_moments(c(0.25, 0.02), a=0, b=1) 

now, reverse results: given function, mu_trunc , sigma_trunc, can obtain values of mu , sigma ?

i tried nleqslv r package not sure looking for.

library(nleqslv) nleqslv(c(0.25, 0.0004), trunc_moments, = 0, b = 1)$x 

you need write function takes output of trunc_moments , calculates required input trunc_moments. can so:

trunc_inverse <- function(minput,a,b) {      temp <- trunc_moments(minput,a,b)     y <- c(0.25,0.02) - temp     y } 

minput result of trunc_moments given input passed in argument moments function trunc_moments. return value of trunc_inverse after solving should original input. there problem.

if this:

nleqslv(c(0.25, 0.0004), trunc_inverse, a=0, b=1) 

a part of output is

$x [1] 0.2500000 0.1414214 

which not original input.

if insert these values in call of trunc_moments this

trunc_moments(c(0.25,0.1414214),a=0,b=1) 

the result is

[1] 0.25000000 0.02000001 

so original function give same output different combinations of moments input. implies function trunc_moments give same output different inputs.

you have work do.