The help for the pnorm function states:
It says that pnorm gives the "distribution function", but it seems that it gives the quantile,
for example, pnorm(q = 0, 0, 1) returns 0.5, which suggests that q=0 refers to the 50th quantile of a N(0,1). I understand what the "normal probability density function" is, but not why pnorm is called a 'distribution function'.
The R help says that the q argument is a "vector of quantiles", but it appears in practice that q represents an observed value.
What I want to know is, if I observe '2', what does pnorm(2) say about my assumption that it came from a N(0,1) distribution?
Best Answer
pnormis giving you the cumulative probability distribution at a specified value of $x$. This is the cumulative probability for a standard normal distribution. So in your example the quantity I call $x$ is specified as $0$ and $0.5$ as the answer is $P[X\leq 0]$ for a random variable $X$ with a $N(0,1)$ distribution.If you took $x=1.96$ you would get $0.975$ because a standard normal distribution has probability $0.025$ in the upper right tail above $1.96$.