The arcsine transformation converts a binomial random variable into one that is nearly normal and whose variance depends very little on the parameter
. If
is a binomial random variable with parameters
and
(so
models the number of heads in
tosses of a coin that is weighted to have probability
of landing heads), then
is the arcsine transformation of
. The distribution of
is nearly normal with mean
and variance
. The histogram in the image is the distribution of
with the rectangle heights scaled so that the sum of their areas is one, and the black curve is the approximating normal density function.
