CODEWITHSUNDEEP
r
stian
stian

Reputation: 1987

how to find upper limit of integral if area is known in R?

user, I am not so familiar with mathematics nor R, but I have a probability question, with a continues probability density. I should find the time where it is 50 % probable that a battery will fail. I believe that this can be expressed as setting the area of the probability density to 0.5 (50%), and it would be very cool if it was possible to say something like this in R; f = probability density function 0.5 = exp(f, lower = 0, upper = x), and R would calculate x.

Is there some easy way to calculate the range of the integral given a lower limit and the area in R?

Upvotes: 2

Views: 1988

Answers (1)

MrFlick
MrFlick

Reputation: 206401

This is pretty inefficient, but you it allows you to use an arbitrary density function

findprob <- function(f, interval, target) {
    optimize(function(x) {
        abs(integrate(f, -Inf, x)$value-target)
    }, interval)$minimum
}

mydensity <- function(x) dnorm(x)
findprob(mydensity, interval=c(-1,1), target=.5)

Here we use optimize to find a value for the integral where the distance from our target value is minimized. Note that optimize needs an interval in which to search for a solution so you'll want to have some idea of where the point might occur.

Upvotes: 3

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