plnorm and log scale parameters

Question

I have expenditure data in several regions, and for each of them i know mean expenditure, standard deviation and skewness in original scale. Since data are skewed i want to compute probability of being below certain expenditure level (for example 1500$) with log normal distribution. For example in one region i have mean expenditure m=2000$, sd=1000, and skweness=1.1. in that case can i use

plnorm(1500,2000,1000)

or i need to transform evertything in log scale first? In plnorm parameters are described "mean and standard deviation of the distribution on the log scale with default values of 0 and 1 respectively." If i need to transform it first, is the following correct:

m=2000
s=1000
lsm=log(m)-(1/2)*log((s/m)^2+1)
lssd=sqrt(log((s/m)^2+1))
plnorm(log(1500),lsm,lssd)

I guess this is very related to post How to calculate log-normal parameters using the mean and std of the given distribution but in my case i also need to be sure i am using plnorm/pnorm correctly.

Answer 1

You need to transform first.

You can check with

dat <- rlnorm(10^6, lsm, lssd) 
mean(dat) 
sd(dat)

which should give you values near $2000$ and $1000$

You can then use either

plnorm(1500, lsm, lssd)

or

pnorm(log(1500), lsm, lssd)

to give about $0.35$ (your version of plnorm(log(1500),lsm,lssd) would be wrong)

I think the skewness could be rather higher, perhaps about $1.625$ rather than the question's $1.1$