[R] uniroot

[Petr Savicky]

On Fri, Feb 04, 2011 at 04:35:00AM -0800, dpender wrote:
> 
> Hi,
> 
> I am using the uniroot function in order to carry out a bivariate Monte
> Carlo simulation using the logistics model.
> 
> I have defined the function as:
> 
> BV.FV <- function(x,y,a,A)
> (((x^(-a^-1)+y^(-a^-1))^(a-1))*(y^(a-1/a))*(exp(-((1^(-a^-1)+y^(-a^-1))^a)+y^-1)))-A
> 
> and the procedure is as follows:
> 
> Randomly generate values of A~(0,1), y0 = -(lnA)^-1
> 
> Where: A=Pr{X<xi|Y=yi-1} and a is the dependency between X and y (0.703)
> 
> Use y0 to determine x where x = x(i) and y = y0(i-1) in the above equation.
> 
> Unfortunately when the randomly defined A gets to approximately 0.46 the
> intervals I provide no longer have the opposite signs (both -ve).
> 
> I have tried various different upper limits but I still can't seem to find a
> root.
> 
> Does anyone have any suggestions?

Hi.

The expression for BV.FV() contains only one occurrence of x and it may be
separated from the equation. The solution for x may be expressed as

  get.x <- function(y,a,A)
  ((A/(y^(a-1/a))/(exp(-((1^(-a^-1)+y^(-a^-1))^a)+y^-1)))^(1/(a-1))-y^(-a^-1))^(-a)

  a <- 0.703
  A <- 0.45
  y <-  - 1/log(A)

  uniroot(BV.FV, c(1, 20), y=y, a=a, A=A)$root
  [1] 3.477799

  get.x(y, a, A)
  [1] 3.477794

As pointed out in another reply, the equation does not always have
a solution. It seems to tend to infinity in the following

  for (A in seq(0.45, 0.4677, length=20)) {
  	y <-  - 1/log(A)
  	cat(get.x(y, a, A), uniroot(BV.FV, c(1, 1000), y=y, a=a, A=A)$root, "\n")
  }

  3.477794 3.477791 
  3.637566 3.637565 
  3.812851 3.812851 
  4.006213 4.006214 
  4.220838 4.220834 
  4.460738 4.460739 
  4.731048 4.731052 
  5.038453 5.038473 
  5.391845 5.391843 
  5.803329 5.803329 
  6.289873 6.28988 
  6.876084 6.876084 
  7.5992 7.599201 
  8.518665 8.518683 
  9.736212 9.736212 
  11.44329 11.44328 
  14.05345 14.05345 
  18.68155 18.68155 
  29.97659 29.9766 
  219.3156 219.3155 

Hope this helps.

Petr Savicky.