1. I assume you are looking at the cumulative DISTRIBUTION function
(cdf), F(x), which is the probability that a random variable X is less
than or equal to x; the cdf is the integral of the density function.
2. The maximum likelihood nonparametric estimate of the cdf is the
"empirical cdf" (ecdf) in library(stepfun). However, this is NOT a
function appropriate for "integrate". The following looks like it
gives
me the correct answer:
pecdf <- function(x, y=1:3, lower.tail=TRUE){
nx <- length(x)
F. <- rep(NA, nx)
for(i in 1:nx){
F.[i] <- sum(y<=x[i])
}
F. <- F./length(y)
if(lower.tail) F. else (1-F.)
}
pecdf(0:4)
pecdf(0:4, lower.tail=FALSE)
Omega <-
function(r){
numerator <- integrate(pecdf, 1, r)
denominator <- integrate(pecdf, r, 3, lower.tail=FALSE)
numerator$value/denominator$value
}
Omega(2)
3. For "data" y = 1:3, I get the following expressions for the
numerator and denominator:
numerator(r) = ((ifelse(r<=2, (5-2*r), (3-r))/3)
denominator(r) = ((ifelse(r<=2, (r-1), (2*r-3))/3)
One could probably develop a more general form of this for arbitrary
"y".
hope this helps. spencer graves
s viswanath wrote:
>Hi,
>
>I am interested in looking at cumulative density functions. If F(x) is a
cumulative density of monthly fund returns over the interval of a to b, and I am
interested in returns above and below a specified point r, then I would like to
find the number that is made up of
>
>1.(integral from r to b)(1-F(x))dx
>2. (integral from a to r)(F(x)dx)
>
>3. the ratio of #1/#2 above
>
>
>In financial literature this ratio has been called the Omega function.
>
>My first guess in obtaining this equation using R
>is to use the integrate function but I am have two problems:
>
>I. can I use a nonparametric density in the integrate function(how?),
>II. how can i get the ratio of #3 above as the integrate function gives the
number plus the absolute error
>
>
>>integrate(dnorm,-4,1.96)
>>
>>
>0.9749704 with absolute error < 2.1e-07
>so using a ratio in #3 above i get the following error:
> : non-numeric argument to binary operator
>
>
>
>Thank you in advance.
>Sri Viswanath
>
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