R help - Feb 2018 - 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]]

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 <hannah.hlx at gmail.com>:
> 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]]

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).

G?ran Brostr?m

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 <hannah.hlx at gmail.com>:
> 
>> 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]]
> 
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