[R] Finding proportion of observations that are outliers from the left tail of the normal distribution

[Thomas Frööjd]

Hi fellow users

I have a new R problem i am hoping to get some pointers on. I have a
dataset that is approximately normally distributed but with a fat left
tail. I am interested in a good measurement on how much fatter the
left tail is than can be expected from a normal distribution. One
thing I'll  tried was fitting a two component mixture model with the
Rmix package but i am also interested in other ideas. Now to my
question.

I would like to calculate how many observations are "outside" the
normal distribution on the left side. I want to do this by fitting a
normal distributions and then use the proportion of observations not
inside the bell curve on the left side as a statistic. Since I am
relatively new to R I dont have very much success so far and would
love any pointers or code examples. Bonus points are given for ideas
on how to estimate standard errors.

Happy for any help.