How do you find unknowns inside distribution functions in R?

Question

I need to find the mean in for example 0.02 <- pnorm(400, mean = x, sd = 4)

how do I find x? Is R capable of solving equations?

Hint: have a look at `?qnorm` – user20650 Apr 24 '20 at 09:48 — user20650, Apr 24 '20 at 09:48
@user20650 I guess you need a known mean to apply `qnorm` – ThomasIsCoding Apr 24 '20 at 09:54 — ThomasIsCoding, Apr 24 '20 at 09:54
`qnorm(0.02, 400, 4, FALSE)` – user20650 Apr 24 '20 at 10:03 — user20650, Apr 24 '20 at 10:03
@user20650 Thanks! Good to know the magic of `qnorm` – ThomasIsCoding Apr 24 '20 at 10:32 — ThomasIsCoding, Apr 24 '20 at 10:32

ThomasIsCoding · Answer 1 · 2020-04-24T14:50:08.360

3

You might need erfinv from pracma to get the mean value mu, e.g.,

p <- 0.02
x <- 400
sgm <- 4
mu <- x - sgm*sqrt(2)*pracma::erfinv(2*p-1)

such that

> mu
[1] 408.215

> pnorm(400,mu,sgm) # check the obtained value of mu
[1] 0.02

A smarter approach is via qnorm (thanks to @user20650)

mu <- qnorm(p,x,sgm,FALSE)

edited Apr 24 '20 at 14:50

answered Apr 24 '20 at 09:48

ThomasIsCoding

1 Answers1