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I'm trying to provide different parameters to the integrate function for various probability functions. I'm using dnorm as the simplest example here. For instance integrate(dnorm, -1.96, 1.96) produces the correct answer for a normal distribution with mean 0 and standard deviation 1. I've tried two ways to use mean=2.0 and standard deviation 1, but with no luck. The examples follow. > integrate(dnorm, -1.96, 1.96) 0.9500042 with absolute error < 1e-11 > mean = 2.0 > sd = 1.0 > integrate(dnorm, -1.96, 1.96) 0.9500042 with absolute error < 1e-11 > integrate(dnorm(mean=2.0,sd=1.0), -1.96, 1.96) Error in .Internal(dnorm(x, mean, sd, log)) : 'x' is missing Calls: integrate -> match.fun -> dnorm Execution halted How do I change the built in mean=0 and standard deviation=1 for dnorm using integrate? Thanks, Frank Chicago, IL [[alternative HTML version deleted]] ______________________________________________ [hidden email] 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. |
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Hi,
Check this link (https://stat.ethz.ch/pipermail/r-help/2010-February/227902.html). Hope it helps. A.K. ----- Original Message ----- From: FJ M <[hidden email]> To: R <[hidden email]> Cc: Sent: Monday, July 23, 2012 10:23 PM Subject: [R] Integrate(dnorm) with different mean and standard deviation help I'm trying to provide different parameters to the integrate function for various probability functions. I'm using dnorm as the simplest example here. For instance integrate(dnorm, -1.96, 1.96) produces the correct answer for a normal distribution with mean 0 and standard deviation 1. I've tried two ways to use mean=2.0 and standard deviation 1, but with no luck. The examples follow. > integrate(dnorm, -1.96, 1.96) 0.9500042 with absolute error < 1e-11 > mean = 2.0 > sd = 1.0 > integrate(dnorm, -1.96, 1.96) 0.9500042 with absolute error < 1e-11 > integrate(dnorm(mean=2.0,sd=1.0), -1.96, 1.96) Error in .Internal(dnorm(x, mean, sd, log)) : 'x' is missing Calls: integrate -> match.fun -> dnorm Execution halted How do I change the built in mean=0 and standard deviation=1 for dnorm using integrate? Thanks, Frank Chicago, IL [[alternative HTML version deleted]] ______________________________________________ [hidden email] 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. ______________________________________________ [hidden email] 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. |
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In reply to this post by FJ M
Hello,
Maybe the following could help: > f <- function(x) dnorm(x, mean=2, sd=1) > integrate(f, -1.96, 1.96) 0.4840091 with absolute error < 1.4e-12 HTH Regards. Le 24/07/2012 11:23, FJ M a écrit : > > I'm trying to provide different parameters to the integrate function for various probability functions. I'm using dnorm as the simplest example here. For instance integrate(dnorm, -1.96, 1.96) produces the correct answer for a normal distribution with mean 0 and standard deviation 1. I've tried two ways to use mean=2.0 and standard deviation 1, but with no luck. The examples follow. > > >> integrate(dnorm, -1.96, 1.96) > 0.9500042 with absolute error < 1e-11 >> mean = 2.0 >> sd = 1.0 >> integrate(dnorm, -1.96, 1.96) > 0.9500042 with absolute error < 1e-11 >> integrate(dnorm(mean=2.0,sd=1.0), -1.96, 1.96) > Error in .Internal(dnorm(x, mean, sd, log)) : 'x' is missing > Calls: integrate -> match.fun -> dnorm > Execution halted > > How do I change the built in mean=0 and standard deviation=1 for dnorm using integrate? > > Thanks, > > Frank > Chicago, IL > [[alternative HTML version deleted]] > > ______________________________________________ > [hidden email] 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. > ______________________________________________ [hidden email] 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. |
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In reply to this post by FJ M
Try
> integrate(dnorm, mean = 2, sd = 1, -1.96, 1.96) 0.4840091 with absolute error < 1.4e-12 HTH, Jorge.- On Mon, Jul 23, 2012 at 10:23 PM, FJ M <> wrote: > > I'm trying to provide different parameters to the integrate function for > various probability functions. I'm using dnorm as the simplest example > here. For instance integrate(dnorm, -1.96, 1.96) produces the correct > answer for a normal distribution with mean 0 and standard deviation 1. I've > tried two ways to use mean=2.0 and standard deviation 1, but with no luck. > The examples follow. > > > > integrate(dnorm, -1.96, 1.96) > 0.9500042 with absolute error < 1e-11 > > mean = 2.0 > > sd = 1.0 > > integrate(dnorm, -1.96, 1.96) > 0.9500042 with absolute error < 1e-11 > > integrate(dnorm(mean=2.0,sd=1.0), -1.96, 1.96) > Error in .Internal(dnorm(x, mean, sd, log)) : 'x' is missing > Calls: integrate -> match.fun -> dnorm > Execution halted > > How do I change the built in mean=0 and standard deviation=1 for dnorm > using integrate? > > Thanks, > > Frank > Chicago, IL > [[alternative HTML version deleted]] > > ______________________________________________ > [hidden email] 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. > [[alternative HTML version deleted]] ______________________________________________ [hidden email] 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. |
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In reply to this post by Pascal Oettli-2
On 2012-07-23 19:48, Pascal Oettli wrote:
> Hello, > > Maybe the following could help: > > > f <- function(x) dnorm(x, mean=2, sd=1) > > integrate(f, -1.96, 1.96) > 0.4840091 with absolute error < 1.4e-12 Or you could note the '...' argument indicated on the help page: integrate(dnorm, lower = -1.96, upper = 1.96, mean = 2, sd = 1) Peter Ehlers > > HTH > > Regards. > > > Le 24/07/2012 11:23, FJ M a écrit : >> >> I'm trying to provide different parameters to the integrate function for various probability functions. I'm using dnorm as the simplest example here. For instance integrate(dnorm, -1.96, 1.96) produces the correct answer for a normal distribution with mean 0 and standard deviation 1. I've tried two ways to use mean=2.0 and standard deviation 1, but with no luck. The examples follow. >> >> >>> integrate(dnorm, -1.96, 1.96) >> 0.9500042 with absolute error < 1e-11 >>> mean = 2.0 >>> sd = 1.0 >>> integrate(dnorm, -1.96, 1.96) >> 0.9500042 with absolute error < 1e-11 >>> integrate(dnorm(mean=2.0,sd=1.0), -1.96, 1.96) >> Error in .Internal(dnorm(x, mean, sd, log)) : 'x' is missing >> Calls: integrate -> match.fun -> dnorm >> Execution halted >> >> How do I change the built in mean=0 and standard deviation=1 for dnorm using integrate? >> >> Thanks, >> >> Frank >> Chicago, IL >> [[alternative HTML version deleted]] >> >> ______________________________________________ >> [hidden email] 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. >> > > ______________________________________________ > [hidden email] 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. > ______________________________________________ [hidden email] 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. |
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In reply to this post by FJ M
integrate(dnorm, -1.96, 1.96, mean=2, sd=1) Read the help for integrate! It tells you that the integrate function has a "..." argument which consists of "additional arguments to be passed to f". cheers, Rolf Turner On 24/07/12 14:23, FJ M wrote: > I'm trying to provide different parameters to the integrate function for various probability functions. I'm using dnorm as the simplest example here. For instance integrate(dnorm, -1.96, 1.96) produces the correct answer for a normal distribution with mean 0 and standard deviation 1. I've tried two ways to use mean=2.0 and standard deviation 1, but with no luck. The examples follow. > > >> integrate(dnorm, -1.96, 1.96) > 0.9500042 with absolute error < 1e-11 >> mean = 2.0 >> sd = 1.0 >> integrate(dnorm, -1.96, 1.96) > 0.9500042 with absolute error < 1e-11 >> integrate(dnorm(mean=2.0,sd=1.0), -1.96, 1.96) > Error in .Internal(dnorm(x, mean, sd, log)) : 'x' is missing > Calls: integrate -> match.fun -> dnorm > Execution halted > > How do I change the built in mean=0 and standard deviation=1 for dnorm using integrate? ______________________________________________ [hidden email] 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. |
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In reply to this post by Peter Ehlers
Hello,
Yes, I should learn to read. Regards Le 24/07/2012 11:54, Peter Ehlers a écrit : > On 2012-07-23 19:48, Pascal Oettli wrote: >> Hello, >> >> Maybe the following could help: >> >> > f <- function(x) dnorm(x, mean=2, sd=1) >> > integrate(f, -1.96, 1.96) >> 0.4840091 with absolute error < 1.4e-12 > > Or you could note the '...' argument indicated on the help page: > > integrate(dnorm, lower = -1.96, upper = 1.96, > mean = 2, sd = 1) > > Peter Ehlers > >> >> HTH >> >> Regards. >> >> >> Le 24/07/2012 11:23, FJ M a écrit : >>> >>> I'm trying to provide different parameters to the integrate function >>> for various probability functions. I'm using dnorm as the simplest >>> example here. For instance integrate(dnorm, -1.96, 1.96) produces the >>> correct answer for a normal distribution with mean 0 and standard >>> deviation 1. I've tried two ways to use mean=2.0 and standard >>> deviation 1, but with no luck. The examples follow. >>> >>> >>>> integrate(dnorm, -1.96, 1.96) >>> 0.9500042 with absolute error < 1e-11 >>>> mean = 2.0 >>>> sd = 1.0 >>>> integrate(dnorm, -1.96, 1.96) >>> 0.9500042 with absolute error < 1e-11 >>>> integrate(dnorm(mean=2.0,sd=1.0), -1.96, 1.96) >>> Error in .Internal(dnorm(x, mean, sd, log)) : 'x' is missing >>> Calls: integrate -> match.fun -> dnorm >>> Execution halted >>> >>> How do I change the built in mean=0 and standard deviation=1 for >>> dnorm using integrate? >>> >>> Thanks, >>> >>> Frank >>> Chicago, IL >>> [[alternative HTML version deleted]] >>> >>> ______________________________________________ >>> [hidden email] 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. >>> >> >> ______________________________________________ >> [hidden email] 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. >> > > ______________________________________________ [hidden email] 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. |
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In reply to this post by Peter Ehlers
It would be a useful additon to the help page to add integrate(dnorm, lower = -1.96, upper = 1.96, mean = 2, sd = 1) as an example. Thanks, Frank Chicago > Date: Mon, 23 Jul 2012 19:54:45 -0700 > From: [hidden email] > To: [hidden email] > CC: [hidden email]; [hidden email] > Subject: Re: [R] Integrate(dnorm) with different mean and standard deviation help > > On 2012-07-23 19:48, Pascal Oettli wrote: > > Hello, > > > > Maybe the following could help: > > > > > f <- function(x) dnorm(x, mean=2, sd=1) > > > integrate(f, -1.96, 1.96) > > 0.4840091 with absolute error < 1.4e-12 > > Or you could note the '...' argument indicated on the help page: > > integrate(dnorm, lower = -1.96, upper = 1.96, > mean = 2, sd = 1) > > Peter Ehlers > > > > > HTH > > > > Regards. > > > > > > Le 24/07/2012 11:23, FJ M a écrit : > >> > >> I'm trying to provide different parameters to the integrate function for various probability functions. I'm using dnorm as the simplest example here. For instance integrate(dnorm, -1.96, 1.96) produces the correct answer for a normal distribution with mean 0 and standard deviation 1. I've tried two ways to use mean=2.0 and standard deviation 1, but with no luck. The examples follow. > >> > >> > >>> integrate(dnorm, -1.96, 1.96) > >> 0.9500042 with absolute error < 1e-11 > >>> mean = 2.0 > >>> sd = 1.0 > >>> integrate(dnorm, -1.96, 1.96) > >> 0.9500042 with absolute error < 1e-11 > >>> integrate(dnorm(mean=2.0,sd=1.0), -1.96, 1.96) > >> Error in .Internal(dnorm(x, mean, sd, log)) : 'x' is missing > >> Calls: integrate -> match.fun -> dnorm > >> Execution halted > >> > >> How do I change the built in mean=0 and standard deviation=1 for dnorm using integrate? > >> > >> Thanks, > >> > >> Frank > >> Chicago, IL > >> [[alternative HTML version deleted]] > >> > >> ______________________________________________ > >> [hidden email] 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. > >> > > > > ______________________________________________ > > [hidden email] 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. > > > ______________________________________________ [hidden email] 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. |
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I might suggest:
integrate(dnorm, lower = -1.96 + 2 , upper = 1.96 + 2, mean = 2, sd = 1) instead. Incidentally, (and since I find this treatment of ... somewhat opaque) I think anonymous first class functions are much easier: integrate(function(x) dnorm(x, mean = 2, sd = 1), lower = -1.96, upper = 1.96) and I don't think you're any worse for performance. Best, Michael On Thu, Jul 26, 2012 at 12:06 PM, FJ M <[hidden email]> wrote: > > It would be a useful additon to the help page to add > > integrate(dnorm, lower = -1.96, upper = 1.96, mean = 2, sd = 1) > > as an example. > > Thanks, > > Frank > Chicago > > >> Date: Mon, 23 Jul 2012 19:54:45 -0700 >> From: [hidden email] >> To: [hidden email] >> CC: [hidden email]; [hidden email] >> Subject: Re: [R] Integrate(dnorm) with different mean and standard deviation help >> >> On 2012-07-23 19:48, Pascal Oettli wrote: >> > Hello, >> > >> > Maybe the following could help: >> > >> > > f <- function(x) dnorm(x, mean=2, sd=1) >> > > integrate(f, -1.96, 1.96) >> > 0.4840091 with absolute error < 1.4e-12 >> >> Or you could note the '...' argument indicated on the help page: >> >> integrate(dnorm, lower = -1.96, upper = 1.96, >> mean = 2, sd = 1) >> >> Peter Ehlers >> >> > >> > HTH >> > >> > Regards. >> > >> > >> > Le 24/07/2012 11:23, FJ M a écrit : >> >> >> >> I'm trying to provide different parameters to the integrate function for various probability functions. I'm using dnorm as the simplest example here. For instance integrate(dnorm, -1.96, 1.96) produces the correct answer for a normal distribution with mean 0 and standard deviation 1. I've tried two ways to use mean=2.0 and standard deviation 1, but with no luck. The examples follow. >> >> >> >> >> >>> integrate(dnorm, -1.96, 1.96) >> >> 0.9500042 with absolute error < 1e-11 >> >>> mean = 2.0 >> >>> sd = 1.0 >> >>> integrate(dnorm, -1.96, 1.96) >> >> 0.9500042 with absolute error < 1e-11 >> >>> integrate(dnorm(mean=2.0,sd=1.0), -1.96, 1.96) >> >> Error in .Internal(dnorm(x, mean, sd, log)) : 'x' is missing >> >> Calls: integrate -> match.fun -> dnorm >> >> Execution halted >> >> >> >> How do I change the built in mean=0 and standard deviation=1 for dnorm using integrate? >> >> >> >> Thanks, >> >> >> >> Frank >> >> Chicago, IL >> >> [[alternative HTML version deleted]] >> >> >> >> ______________________________________________ >> >> [hidden email] 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. >> >> >> > >> > ______________________________________________ >> > [hidden email] 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. >> > >> > > [[alternative HTML version deleted]] > > > ______________________________________________ > [hidden email] 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. > ______________________________________________ [hidden email] 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. |
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In reply to this post by FJ M
On Jul 26, 2012, at 10:06 AM, FJ M wrote: > > It would be a useful additon to the help page to add > > integrate(dnorm, lower = -1.96, upper = 1.96, mean = 2, sd = 1) Wouldn't most statisticians instead use the more accurate and undoubtedly faster: pnorm(1.96, mean=2, sd=1) - pnorm(-1.96, mean=2, sd=1) ... or p_xxx where _xxx is distribution of interest? (And I do not see that every help page needs a worked example of the proper use of the 'dots' argument. That is a basic R lesson and it is only by chance that you have needed to learn it in the context of integrate(). A large fraction of other functions offer that facility. You might review the material you used when learning R to see at what point you skimmed over that crucial topic too quickly. ) -- David Alameda. > > as an example. > > Thanks, > > Frank > Chicago > > >> Date: Mon, 23 Jul 2012 19:54:45 -0700 >> From: [hidden email] >> To: [hidden email] >> CC: [hidden email]; [hidden email] >> Subject: Re: [R] Integrate(dnorm) with different mean and standard >> deviation help >> >> On 2012-07-23 19:48, Pascal Oettli wrote: >>> Hello, >>> >>> Maybe the following could help: >>> >>>> f <- function(x) dnorm(x, mean=2, sd=1) >>>> integrate(f, -1.96, 1.96) >>> 0.4840091 with absolute error < 1.4e-12 >> >> Or you could note the '...' argument indicated on the help page: >> >> integrate(dnorm, lower = -1.96, upper = 1.96, >> mean = 2, sd = 1) >> >> Peter Ehlers >> >>> >>> HTH >>> >>> Regards. >>> >>> >>> Le 24/07/2012 11:23, FJ M a écrit : >>>> >>>> I'm trying to provide different parameters to the integrate >>>> function for various probability functions. I'm using dnorm as >>>> the simplest example here. For instance integrate(dnorm, -1.96, >>>> 1.96) produces the correct answer for a normal distribution with >>>> mean 0 and standard deviation 1. I've tried two ways to use >>>> mean=2.0 and standard deviation 1, but with no luck. The examples >>>> follow. >>>> >>>> >>>>> integrate(dnorm, -1.96, 1.96) >>>> 0.9500042 with absolute error < 1e-11 >>>>> mean = 2.0 >>>>> sd = 1.0 >>>>> integrate(dnorm, -1.96, 1.96) >>>> 0.9500042 with absolute error < 1e-11 >>>>> integrate(dnorm(mean=2.0,sd=1.0), -1.96, 1.96) >>>> Error in .Internal(dnorm(x, mean, sd, log)) : 'x' is missing >>>> Calls: integrate -> match.fun -> dnorm >>>> Execution halted >>>> >>>> How do I change the built in mean=0 and standard deviation=1 for >>>> dnorm using integrate? >>>> >>>> Thanks, >>>> >>>> Frank >>>> Chicago, IL >>>> [[alternative HTML version deleted]] >>>> >>>> ______________________________________________ >>>> [hidden email] 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. >>>> >>> >>> ______________________________________________ >>> [hidden email] 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. >>> >> > > [[alternative HTML version deleted]] > > ______________________________________________ > [hidden email] 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. David Winsemius, MD Alameda, CA, USA ______________________________________________ [hidden email] 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. |
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On 27/07/12 20:55, David Winsemius wrote:
> > On Jul 26, 2012, at 10:06 AM, FJ M wrote: > >> >> It would be a useful additon to the help page to add >> >> integrate(dnorm, lower = -1.96, upper = 1.96, mean = 2, sd = 1) > > Wouldn't most statisticians instead use the more accurate and > undoubtedly faster: > > pnorm(1.96, mean=2, sd=1) - pnorm(-1.96, mean=2, sd=1) > > ... or p_xxx where _xxx is distribution of interest? I conjecture that the OP was just using "dnorm" as an easily reproducible example, and was really interested in a function or functions for which no built-in "indefinite integral" exists. > > (And I do not see that every help page needs a worked example of the > proper use of the 'dots' argument. That is a basic R lesson and it is > only by chance that you have needed to learn it in the context of > integrate(). A large fraction of other functions offer that facility. > You might review the material you used when learning R to see at what > point you skimmed over that crucial topic too quickly. ) > Well, yes, but ................. the use of the "..." argument to pass arguments to another function (which itself is an argument) is a bit subtle. At least initially, to those of us who are Bears of Very Little Brain. A wee example would be redundant, as your discussion implies, but a little redundancy rarely hurts and tends to add robustness. We can't expect the documentation to explain "..." every time it appears as a function argument, but giving an example in "important" instances (with important being defined as when someone requests an example) seems to me to be a good idea. cheers, Rolf P. S. My Thunderbird mailer does not recognise the word "Winsemius" as a word and suggests "inseminates" as a possible alternative. :-) R. P^2. S. Strangely enough, Thunderbird does not recognise ***Thunderbird*** as a word!!! R. ______________________________________________ [hidden email] 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. |
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