yearly 8% drift, 25% sd why are x and y so different (x and z look ok)? Does this have something to do with biases due to the relationship between population and sample-estimates as a function of n samples and sd? Or am I doing something wrong? ----------------------------------------------------------------------- set.seed( 1 ); x <- mean( rnorm( 100000, mean=0.08, sd=0.25 )); set.seed( 1 ); y <- mean( rnorm( 100000, mean=(0.08/252), sd=(0.25/sqrt(252)) )) * 252; set.seed( 1 ); z <- mean( rnorm( 100000, mean=(0.08/252), sd=0.001 )) * 252; # ----------------------------------------------------------------------- x # 0.07943898 y # 0.07109407 z # 0.07943449 -- View this message in context: http://www.nabble.com/rnorm%28%29-converted-to-daily-tp23092444p23092444.html Sent from the R help mailing list archive at Nabble.com.
Ken-JP:> Does this have something to do with biases due to the relationship between > population and sample-estimates as a function of n samples and sd? Or am > I doing something wrong? > > ----------------------------------------------------------------------- > > set.seed( 1 ); > x <- mean( rnorm( 100000, mean=0.08, sd=0.25 )); > set.seed( 1 ); > y <- mean( rnorm( 100000, mean=(0.08/252), sd=(0.25/sqrt(252)) )) * 252; > set.seed( 1 ); > z <- mean( rnorm( 100000, mean=(0.08/252), sd=0.001 )) * 252;Yes, you?re doing something wrong. While it is true? that rnorm(n, a, b) will give the same results as rnorm(n, 0, 1) * b + a, it is *not* true that the above calculations would return the same numbers. That?s the reason the the means differ. ? True in practice, but not documented as far as I can see, so you should not depend on it. -- Karl Ove Hufthammer
I think I got it... I assumed that n=100000 would be big enough to give me a sample mean which converges on the population mean, but this was a bad assumption. Using sigma / sqrt(n) for the standard error of the sample mean, I get... ----------------------------------------------------- se.x.mean.as.perc.of.pop.mean <- (0.25 / sqrt(100000)) /0.08; se.y.mean.as.perc.of.pop.mean <- (0.25/sqrt(252)) / sqrt(100000) /(0.08/252); se.x.mean.as.perc.of.pop.mean # 0.0098821 se.y.mean.as.perc.of.pop.mean # 0.1568738 -- View this message in context: http://www.nabble.com/rnorm%28%29-converted-to-daily-tp23092444p23093105.html Sent from the R help mailing list archive at Nabble.com.
Meyners, Michael, LAUSANNE, AppliedMathematics
2009-Apr-17 08:21 UTC
[R] rnorm() converted to daily
SD in y is more than 15 times (!!!) larger than in x and z, respectively, and hence SD of the mean y is also larger. 100,000 values are not enough to stabilize this. You could have obtained 0.09 or even larger as well. Try y with different seeds, y varies much more than x and z do. Or check the variances: var.x <- var(replicate(100, mean( rnorm( 100000, mean=0.08, sd=0.25 )))) var.y <- var(replicate(100, mean( rnorm( 100000, mean=(0.08/252), sd=(0.25/sqrt(252)) )) * 252)) var.z <- var(replicate(100, mean( rnorm( 100000, mean=(0.08/252), sd=0.001 )) * 252)) I guess what you are doing wrong is assuming that 0.25/sqrt(252) is similar to 0.25/252, the latter being close so 0.001, while the former is obviously not. Try to replace 0.25 in y by 0.0158, than you should be close enough. HTH, Michael -----Original Message----- From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Ken-JP Sent: Freitag, 17. April 2009 09:26 To: r-help at r-project.org Subject: [R] rnorm() converted to daily yearly 8% drift, 25% sd why are x and y so different (x and z look ok)? Does this have something to do with biases due to the relationship between population and sample-estimates as a function of n samples and sd? Or am I doing something wrong? ----------------------------------------------------------------------- set.seed( 1 ); x <- mean( rnorm( 100000, mean=0.08, sd=0.25 )); set.seed( 1 ); y <- mean( rnorm( 100000, mean=(0.08/252), sd=(0.25/sqrt(252)) )) * 252; set.seed( 1 ); z <- mean( rnorm( 100000, mean=(0.08/252), sd=0.001 )) * 252; # ----------------------------------------------------------------------- x # 0.07943898 y # 0.07109407 z # 0.07943449 -- View this message in context: http://www.nabble.com/rnorm%28%29-converted-to-daily-tp23092444p23092444 .html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.