# skew normal computation

I want to compute probabilities assuming data have log skew normal distribution (in R). As I couldn't find any package that directly computes log skew normal (as plnorm does log normal), I am wondering, if I can get log normal with pnorm, for example to compute log normal probability at point 2 with mean=2 and sd=3:

plnorm(2,2,3)
pnorm(log(2),2,3)


can I use psn to compute skew-log-normal probability at point 2 with mean=2, sd=3 and skewness=1:

psn(log(2), xi=2, omega=3, alpha=1, tau=0, dp=NULL)


or I need some other transformations of the mean/sd/skewness before I apply it? In case I need to transform it first, didnt I need some transformations also in plnorm, instead of just putting mean and sd?

• What does psn do? What do its arguments represent? Could you be explicit about what you mean by a "log skew normal" distribution?
– whuber
Feb 21, 2019 at 21:58
• psn is part of 'sn' package in r for skew normal distribution, and psn computes its distribution function with xi being location parameter, omega scale parameters, alpha slant etc... I am not very sure how do they relate to the mean, sd and skewness. Here is the link cran.r-project.org/web/packages/sn/sn.pdf . Log skew normal i found for example here ncbi.nlm.nih.gov/pmc/articles/PMC2758628
Feb 21, 2019 at 22:07
• Why not take the logarithm of the data and fit regular normal and skew normal distributions? Feb 21, 2019 at 23:21

Let $$X$$ be a skew normal random variable (or really, what is used here is only that it is some random variable on the real line.) Of interest is the distribution of $$e^X$$. Then, as usual, $$F_{e^X}(Z)= F_X(\log z) \quad \text{for z>0.}$$ and by differentiation (assuming $$X$$ has a density) we find $$f_{e^X}(z)= f_X(\log z)/z.$$ Assuming you have functions psn, dsn in R available, you can define

library(sn)
plsn <-  function(x, ...) sn::psn(log(x), ...)


And for the density:

dlsn <- function(x, ..., log=FALSE) {
d <- x;  ind0 <- ifelse(x <= 0,1L,0L) ; ind1 <- 1-ind0
d[ind0] <- 0
d[ind1] <- sn::dsn(log(x[ind1]), ..., log=TRUE) - log(x[ind1])
if (log=FALSE)  d[ind1] <- exp(d[ind1])
d


}

(not tested)