Feng Zhang
2002-Nov-07 19:27 UTC
[R]The integration of the square of the c.d.f of normal distribution
Assume F(x) is the cdf of stardard normal c.d.f, and want to get the integration of F(x)^2 over (-infinite, +infinite). So whats the value of this integration? And is there some function to achieve this? Thanks. -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
Chin-Shan Chuang
2002-Nov-07 22:22 UTC
[R]The integration of the square of the c.d.f of normal distribution
Infinity, no? The integrand doesn't die at +infinity. In fact it's 1 there. Maybe I missed something. "Feng Zhang" <f0z6305 at labs.tamu.edu> wrote: Assume F(x) is the cdf of stardard normal c.d.f, and want to get the integration of F(x)^2 over (-infinite, +infinite). So whats the value of this integration? And is there some function to achieve this? Thanks. ____________________________________________________________________ -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
Roger Peng
2002-Nov-07 23:09 UTC
[R]The integration of the square of the c.d.f of normal distribution
I believe that the integral of F(x)^2 in this case is infinite. Do you mean the normal _density_ squared? Either way, you can use the integrate() function to check:> f <- function(x) pnorm(x)^2 > integrate(f, -Inf, Inf)Error in integrate(f, -Inf, Inf) : the integral is probably divergent>-roger _______________________________ UCLA Department of Statistics rpeng at stat.ucla.edu http://www.stat.ucla.edu/~rpeng On Thu, 7 Nov 2002, Feng Zhang wrote:> Assume F(x) is the cdf of stardard normal c.d.f, > and want to get the integration of F(x)^2 over > (-infinite, +infinite). > > So whats the value of this integration? > And is there some function to achieve this? > > Thanks. > > > > -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- > r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html > Send "info", "help", or "[un]subscribe" > (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch > _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._ >-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._