R help - Jun 2010 - question in R

Dear all,
   I am trying to calculate certain critical values from bivariate normal
distribution (please see the
function below).

m <- 10
rho <- 0.1
k <- 2
alpha <- 0.05
## calculate critical constants
cc_z <- numeric(m)
var <- matrix(c(1,rho,rho,1), nrow=2, ncol=2, byrow=T)
for (i in 1:m){
   if (i <= k) {cc_z[i] <- qmvnorm((k*(k-1))/(m*(m-1))*alpha,
tail="upper",
sigma=var)$quantile} else
               {cc_z[i] <- qmvnorm((k*(k-1))/((m-i+k)*(m-i+k-1))*alpha,
tail="upper", sigma=var)$quantile}
               }



After the critical constants cc_z is calculated, I wanted to check whether
they are correct.

> ##check whether cc_z is correct
>  pmvnorm(lower=c(cc_z[1], cc_z[1]),
upper=Inf,sigma=var)-(k*(k-1))/(n*(n-1))
[1] 0.001111025
attr(,"error")
[1] 1e-15
attr(,"msg")
[1] "Normal Completion"
>   pmvnorm(lower=c(cc_z[3], cc_z[3]),
upper=Inf,sigma=var)-(k*(k-1))/((n-1)*(n-2))
[1] 0.001388974
attr(,"error")
[1] 1e-15
attr(,"msg")
[1] "Normal Completion"


As you can see, there is some error. Supposedly, the answer should be zero
for all cc_z[i]
in the above checking function.

Is there something wrong with my code? Can someone give some help?
Thank you very much!

                                        Hannah

	[[alternative HTML version deleted]]

See below.

On Fri, Jun 18, 2010 at 7:11 PM, li li <hannah.hlx at gmail.com>
wrote:
> Dear all,
> ? I am trying to calculate certain critical values from bivariate normal
> distribution (please see the
> function below).
>
> m <- 10
> rho <- 0.1
> k <- 2
> alpha <- 0.05
> ## calculate critical constants
> cc_z <- numeric(m)
> var <- matrix(c(1,rho,rho,1), nrow=2, ncol=2, byrow=T)
> for (i in 1:m){
> ? if (i <= k) {cc_z[i] <- qmvnorm((k*(k-1))/(m*(m-1))*alpha,
tail="upper",
> sigma=var)$quantile} else
> ? ? ? ? ? ? ? {cc_z[i] <- qmvnorm((k*(k-1))/((m-i+k)*(m-i+k-1))*alpha,
> tail="upper", sigma=var)$quantile}
> ? ? ? ? ? ? ? }
>
>
>
> After the critical constants cc_z is calculated, I wanted to check whether
> they are correct.
>
>
>> ##check whether cc_z is correct
>> ?pmvnorm(lower=c(cc_z[1], cc_z[1]),
> upper=Inf,sigma=var)-(k*(k-1))/(n*(n-1))
Shouldn't this be
> pmvnorm(lower=c(cc_z[1], cc_z[1]),
+ upper=Inf,sigma=var)-(k*(k-1))/(m*(m-1))*alpha
[1] -5.87e-09
attr(,"error")
[1] 1e-15
attr(,"msg")
[1] "Normal Completion"

This still gives a bit of an error, but you have to take into account
as well that the underlying algorithms use randomized quasi-MC
methods, and that floating point issues can play here as well. So it
looks to me that your calculations are correct.

Cheers
Joris


-- 
Joris Meys
Statistical consultant

Ghent University
Faculty of Bioscience Engineering
Department of Applied mathematics, biometrics and process control

tel : +32 9 264 59 87
Joris.Meys at Ugent.be
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