Quantile on normal and log-normal

[Jay YK Kim]

Hi, my name is Jay Kim and I was wondering if I can get some advice about the quantile on normal distribution and log-normal distribution.

According to one of the Coursera lecture I'm taking recently,

if

r ~ N(mean, SD^2)
and
R = exp(r) - 1

then

R ~ logN(mean, SD^2)

furthermore

Quantile on R with alpha = exp(Quantile on r with alpha) - 1

But I somehow intuitively thought that it is not correct,
and I checked myself the calculations using R.

And it turned out that the R function

plnorm(exp(Quantile on r with alpha) - 1, mean, SD)

does not give me alpha at all. The result is zero, not some positive value of alpha. (In this case, my alpha was 0.05)
But it should be alpha according to the lecture. I'm here very confused.

exp(qnorm(alpha, mean, SD)) - 1
and
qlnorm(alpha, mean, SD)
are not the same either, which is very opposite of what the lecturer said.

I was wondering what kinds of mistakes I've made here.
Quantile on R with alpha = exp(Quantile on r with alpha) - 1
Is above equation really correct?
Or should I conclude that the lecturer taught me something wrong?

I would appreciate you help.. Thank you.

 

[Jay YK Kim]

Sorry my mistake.

It was (1+R) ~ logN, not that R ~ logN.

 

[quotes]

I guess you want to generate a random variable on normal or log-normal distribution through a simple random variable on uniform distribution.

Let us just think it this way, you line up all your m classmates according to their height, from shortest to tallest. And then you get a quantile function. You know the knd lowest classmate's height. Now you draw a lot from 1 to m, get the result k, and pick up the knd lowest classmate, and write down the height. And these procedures have just enabled you to generate the random variable height from a uniform random variable from 1 to m, or from 1/m to m/m.

In general,

CDF- (U) passes the randomness of uniform r.v. U ~(0,1] to the r.v with the CDF.