# question with integrate function

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## question with integrate function

 Hi all,   The function h below is a function of c and it should be a monotone increasing function since the integrand is nonnegative and integral is taken from c to infinity. However, as we can see from the plot, it is not shown to be monotone. Something wrong with the usage of integrate function? Thanks so much for your help.     Hanna h <- function(c){     g <- function(x){pnorm(x-8.8, mean=0.4, sd=0.3, lower.tail=TRUE)*dnorm(x, mean=9,sd=0.15)}     integrate(g, lower=c, upper=Inf)\$value} xx <- seq(-20,20,by=0.001) y <- xx for (i in 1:length(xx)){y[i] <- h(xx[i])} plot(xx, y)         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: question with integrate function

 Sorry. I meant in the previous email that the function h() is a monotone decreasing function. Thanks very much. 2018-02-06 13:32 GMT-05:00 li li <[hidden email]>: > Hi all, >   The function h below is a function of c and it should be a monotone > increasing function since the integrand is nonnegative and integral is > taken from c to infinity. However, as we can see from the plot, it is not > shown to be monotone. Something wrong with the usage of integrate function? > Thanks so much for your help. >     Hanna > > > > h <- function(c){ >     g <- function(x){pnorm(x-8.8, mean=0.4, sd=0.3, > lower.tail=TRUE)*dnorm(x, mean=9,sd=0.15)} >     integrate(g, lower=c, upper=Inf)\$value} > > xx <- seq(-20,20,by=0.001) > y <- xx > for (i in 1:length(xx)){y[i] <- h(xx[i])} > plot(xx, y) > >         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: question with integrate function

 Hi Hanna, your function is essentially zero outside a short interval around 9. And the help page states: "If the function is approximately constant (in particular, zero) over nearly all its range it is possible that the result and error estimate may be seriously wrong." You could try to integrate over a finite interval, say (7, 12). Göran Broström On 2018-02-06 19:40, li li wrote: > Sorry. I meant in the previous email that the function h() is a monotone > decreasing function. Thanks very much. > > 2018-02-06 13:32 GMT-05:00 li li <[hidden email]>: > >> Hi all, >>    The function h below is a function of c and it should be a monotone >> increasing function since the integrand is nonnegative and integral is >> taken from c to infinity. However, as we can see from the plot, it is not >> shown to be monotone. Something wrong with the usage of integrate function? >> Thanks so much for your help. >>      Hanna >> >> >> >> h <- function(c){ >>      g <- function(x){pnorm(x-8.8, mean=0.4, sd=0.3, >> lower.tail=TRUE)*dnorm(x, mean=9,sd=0.15)} >>      integrate(g, lower=c, upper=Inf)\$value} >> >> xx <- seq(-20,20,by=0.001) >> y <- xx >> for (i in 1:length(xx)){y[i] <- h(xx[i])} >> plot(xx, y) >> >> > > [[alternative HTML version deleted]] > > ______________________________________________ > [hidden email] mailing list -- To UNSUBSCRIBE and more, see > 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 -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: question with integrate function

 Oh ok. Thanks very much. I will have to restrict to a shorter interval.     Hanna 2018-02-06 14:33 GMT-05:00 Göran Broström <[hidden email]>: > Hi Hanna, > > your function is essentially zero outside a short interval around 9. And > the help page states: "If the function is approximately constant (in > particular, zero) over nearly all its range it is possible that the result > and error estimate may be seriously wrong." > > You could try to integrate over a finite interval, say (7, 12). > > Göran Broström > > > On 2018-02-06 19:40, li li wrote: > >> Sorry. I meant in the previous email that the function h() is a monotone >> decreasing function. Thanks very much. >> >> 2018-02-06 13:32 GMT-05:00 li li <[hidden email]>: >> >> Hi all, >>>    The function h below is a function of c and it should be a monotone >>> increasing function since the integrand is nonnegative and integral is >>> taken from c to infinity. However, as we can see from the plot, it is not >>> shown to be monotone. Something wrong with the usage of integrate >>> function? >>> Thanks so much for your help. >>>      Hanna >>> >>> >>> >>> h <- function(c){ >>>      g <- function(x){pnorm(x-8.8, mean=0.4, sd=0.3, >>> lower.tail=TRUE)*dnorm(x, mean=9,sd=0.15)} >>>      integrate(g, lower=c, upper=Inf)\$value} >>> >>> xx <- seq(-20,20,by=0.001) >>> y <- xx >>> for (i in 1:length(xx)){y[i] <- h(xx[i])} >>> plot(xx, y) >>> >>> >>> >>         [[alternative HTML version deleted]] >> >> ______________________________________________ >> [hidden email] mailing list -- To UNSUBSCRIBE and more, see >> https://stat.ethz.ch/mailman/listinfo/r-help>> PLEASE do read the posting guide http://www.R-project.org/posti>> ng-guide.html >> and provide commented, minimal, self-contained, reproducible code. >> >>         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.