Re: [R] Looking for simpler solution to probabilistic question
Dear Rainer, If X1 is random on 1:20 with probabilities proportional to dnorm(,10,2), and X2 is random on 10:30 with probs proportional to dnorm(,15,1), and the object is to find out the probability distribution of X1 + X2, then a very quick way is with package distr: library(distr) X1 <- DiscreteDistribution(1:20, prob = dnorm(1:20,10,2)) X2 <- DiscreteDistribution(10:30, prob = dnorm(10:30,15,1)) X <- X1 + X2 plot(X) # plot the probabilites d(X)(11:50) # look at probs individually Notice that the answer from distr is different from the answers posted previously. The answers will be the same if the line p <- matrix(p1, ncol=length(p1), nrow=length(p2), byrow=TRUE) + p2 is replaced with p <- matrix(p1, ncol=length(p1), nrow=length(p2), byrow=TRUE) * p2 (the only difference is the multiplication by p2 instead of addition with p2). This is following from an assumption of independence between X1 and X2. Otherwise, you would seem to need to know the joint distribution of X1 and X2, which isn't mentioned in your problem description. Is there additional information about the problem that would suggest adding p2 rather than multiplying? I hope this helps, Jay On Jan 15, 2008 8:33 AM, Rainer M Krug <[EMAIL PROTECTED]> wrote: > Berwin A Turlach wrote: > > G'day Rainer, > > > > On Tue, 15 Jan 2008 14:24:08 +0200 > > Rainer M Krug <[EMAIL PROTECTED]> wrote: > > > > > > >> ager <- range(age1) + range(age2) > >> ager <- ager[1]:ager[2] > >> pp1 <- c(cumsum(p1), rev(cumsum(rev(p1 > >> pp2 <- c(cumsum(p2[-21]), rev(cumsum(rev(p2)))[-1]) > >> pr <- pp1+pp2 > >> pr <- pr/sum(pr) > > > >> all.equal(p, pr) > > [1] TRUE > >> all.equal(age, ager) > > [1] TRUE > > > > > > If this is more elegant is probably in the eye of the beholder, but it > > should definitely use less memory. :) > > Thanks - interesting approach which is different to using the outer() > > > > > BTW, I am intrigued, in which situation does this problem arise? The > > time it takes the second process to finish seems to depend in a curious > > way on the time it took the first process to complete. > > These are two growth processes, where the first one is seedling growth > up to a certain X and the second one is adult growth from size X onwards > until it reaches a given final size. > > I hope my calculations fit the process... > > > > > > > Cheers, > > > > Berwin > > > > === Full address = > > Berwin A TurlachTel.: +65 6516 4416 (secr) > > Dept of Statistics and Applied Probability+65 6516 6650 (self) > > Faculty of Science FAX : +65 6872 3919 > > National University of Singapore > > 6 Science Drive 2, Blk S16, Level 7 e-mail: [EMAIL PROTECTED] > > Singapore 117546http://www.stat.nus.edu.sg/~statba > > __ > R-help@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. > -- *** G. Jay Kerns, Ph.D. Assistant Professor / Statistics Coordinator Department of Mathematics & Statistics Youngstown State University Youngstown, OH 44555-0002 USA Office: 1035 Cushwa Hall Phone: (330) 941-3310 Office (voice mail) -3302 Department -3170 FAX E-mail: [EMAIL PROTECTED] http://www.cc.ysu.edu/~gjkerns/ __ R-help@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.
Re: [R] Looking for simpler solution to probabilistic question
Berwin A Turlach wrote: > G'day Rainer, > > On Tue, 15 Jan 2008 14:24:08 +0200 > Rainer M Krug <[EMAIL PROTECTED]> wrote: > > >> ager <- range(age1) + range(age2) >> ager <- ager[1]:ager[2] >> pp1 <- c(cumsum(p1), rev(cumsum(rev(p1 >> pp2 <- c(cumsum(p2[-21]), rev(cumsum(rev(p2)))[-1]) >> pr <- pp1+pp2 >> pr <- pr/sum(pr) > >> all.equal(p, pr) > [1] TRUE >> all.equal(age, ager) > [1] TRUE > > > If this is more elegant is probably in the eye of the beholder, but it > should definitely use less memory. :) Thanks - interesting approach which is different to using the outer() > > BTW, I am intrigued, in which situation does this problem arise? The > time it takes the second process to finish seems to depend in a curious > way on the time it took the first process to complete. These are two growth processes, where the first one is seedling growth up to a certain X and the second one is adult growth from size X onwards until it reaches a given final size. I hope my calculations fit the process... > > Cheers, > > Berwin > > === Full address = > Berwin A TurlachTel.: +65 6516 4416 (secr) > Dept of Statistics and Applied Probability+65 6516 6650 (self) > Faculty of Science FAX : +65 6872 3919 > National University of Singapore > 6 Science Drive 2, Blk S16, Level 7 e-mail: [EMAIL PROTECTED] > Singapore 117546http://www.stat.nus.edu.sg/~statba __ R-help@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.
Re: [R] Looking for simpler solution to probabilistic question
G'day Rainer, On Tue, 15 Jan 2008 14:24:08 +0200 Rainer M Krug <[EMAIL PROTECTED]> wrote: > I have two processes which take with a certain probability (p1 and > p2) x number of years to complete (age1 and age2). As soon as thge > first process is completed, the second one begins. I want to > calculate the time it takes for the both processes to be completed. > > I have the following script which gives me the answer, butI think > there must be a more elegant way of doing the calculations between > the # The code between the together with the first line after the second could be just shortened to: > ager <- range(age1) + range(age2) > ager <- ager[1]:ager[2] > pp1 <- c(cumsum(p1), rev(cumsum(rev(p1 > pp2 <- c(cumsum(p2[-21]), rev(cumsum(rev(p2)))[-1]) > pr <- pp1+pp2 > pr <- pr/sum(pr) > all.equal(p, pr) [1] TRUE > all.equal(age, ager) [1] TRUE If this is more elegant is probably in the eye of the beholder, but it should definitely use less memory. :) BTW, I am intrigued, in which situation does this problem arise? The time it takes the second process to finish seems to depend in a curious way on the time it took the first process to complete. Cheers, Berwin === Full address = Berwin A TurlachTel.: +65 6516 4416 (secr) Dept of Statistics and Applied Probability+65 6516 6650 (self) Faculty of Science FAX : +65 6872 3919 National University of Singapore 6 Science Drive 2, Blk S16, Level 7 e-mail: [EMAIL PROTECTED] Singapore 117546http://www.stat.nus.edu.sg/~statba __ R-help@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.
Re: [R] Looking for simpler solution to probabilistic question
Hi Dimitris that was EXACTLY what I was looking for Thanks Rainer Dimitris Rizopoulos wrote: > matrix(age1, ncol=length(age1), nrow=length(age2), byrow=TRUE) + age2 > > can be replaced by > > outer(age2, age1, "+") > > and the same for 'p'. > > > Best, > Dimitris > > > Dimitris Rizopoulos > Ph.D. Student > Biostatistical Centre > School of Public Health > Catholic University of Leuven > > Address: Kapucijnenvoer 35, Leuven, Belgium > Tel: +32/(0)16/336899 > Fax: +32/(0)16/337015 > Web: http://med.kuleuven.be/biostat/ > http://www.student.kuleuven.be/~m0390867/dimitris.htm > > > - Original Message - From: "Rainer M Krug" <[EMAIL PROTECTED]> > To: "r-help" <[EMAIL PROTECTED]> > Sent: Tuesday, January 15, 2008 1:24 PM > Subject: [R] Looking for simpler solution to probabilistic question > > >> Hi >> >> I have two processes which take with a certain probability (p1 and p2) x >> number of years to complete (age1 and age2). As soon as thge first >> process is completed, the second one begins. I want to calculate the >> time it takes for the both processes to be completed. >> >> I have the following script which gives me the answer, butI think there >> must be a more elegant way of doing the calculations between the # >> >> Any ideas welcom, >> >> Rainer >> >> >> age1 <- 1:20 >> p1 <- dnorm(age1,10,2) >> >> age2 <- 10:30 >> p2 <- dnorm(age2,15,1) >> >> ## >> age <- matrix(age1, ncol=length(age1), nrow=length(age2), byrow=TRUE) >> + age2 >> >> p <- matrix(p1, ncol=length(p1), nrow=length(p2), byrow=TRUE) + p2 >> p <- as.numeric(tapply(p, age, sum)) >> p <- p / sum(p) >> # >> >> age <- sort(unique(as.numeric(age))) >> >> plot(age, p) >> >> lines(age1, p1) >> lines(age2, p2) >> >> __ >> R-help@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. >> > > > Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm > __ R-help@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.
Re: [R] Looking for simpler solution to probabilistic question
matrix(age1, ncol=length(age1), nrow=length(age2), byrow=TRUE) + age2 can be replaced by outer(age2, age1, "+") and the same for 'p'. Best, Dimitris Dimitris Rizopoulos Ph.D. Student Biostatistical Centre School of Public Health Catholic University of Leuven Address: Kapucijnenvoer 35, Leuven, Belgium Tel: +32/(0)16/336899 Fax: +32/(0)16/337015 Web: http://med.kuleuven.be/biostat/ http://www.student.kuleuven.be/~m0390867/dimitris.htm - Original Message - From: "Rainer M Krug" <[EMAIL PROTECTED]> To: "r-help" <[EMAIL PROTECTED]> Sent: Tuesday, January 15, 2008 1:24 PM Subject: [R] Looking for simpler solution to probabilistic question > Hi > > I have two processes which take with a certain probability (p1 and > p2) x > number of years to complete (age1 and age2). As soon as thge first > process is completed, the second one begins. I want to calculate the > time it takes for the both processes to be completed. > > I have the following script which gives me the answer, butI think > there > must be a more elegant way of doing the calculations between the > # > > Any ideas welcom, > > Rainer > > > age1 <- 1:20 > p1 <- dnorm(age1,10,2) > > age2 <- 10:30 > p2 <- dnorm(age2,15,1) > > ## > age <- matrix(age1, ncol=length(age1), nrow=length(age2), > byrow=TRUE) + age2 > > p <- matrix(p1, ncol=length(p1), nrow=length(p2), byrow=TRUE) + p2 > p <- as.numeric(tapply(p, age, sum)) > p <- p / sum(p) > # > > age <- sort(unique(as.numeric(age))) > > plot(age, p) > > lines(age1, p1) > lines(age2, p2) > > __ > R-help@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. > Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm __ R-help@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.
[R] Looking for simpler solution to probabilistic question
Hi I have two processes which take with a certain probability (p1 and p2) x number of years to complete (age1 and age2). As soon as thge first process is completed, the second one begins. I want to calculate the time it takes for the both processes to be completed. I have the following script which gives me the answer, butI think there must be a more elegant way of doing the calculations between the # Any ideas welcom, Rainer age1 <- 1:20 p1 <- dnorm(age1,10,2) age2 <- 10:30 p2 <- dnorm(age2,15,1) ## age <- matrix(age1, ncol=length(age1), nrow=length(age2), byrow=TRUE) + age2 p <- matrix(p1, ncol=length(p1), nrow=length(p2), byrow=TRUE) + p2 p <- as.numeric(tapply(p, age, sum)) p <- p / sum(p) # age <- sort(unique(as.numeric(age))) plot(age, p) lines(age1, p1) lines(age2, p2) __ R-help@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.
