Apr 8, 2017 · But when using Claude's eqtn(1) for erf(X) his adjusted cdf curve and your adjusted cdf curve are not coincident. $\endgroup$ – steveOw Commented May 12, 2022 at 23:01

The CDF of a standard normal random variable is never actually 0 or 1, they only approach 0 and 1, correct?

Just to check on this, the R code for the standard normal CDF is pnorm, and the statement pnorm(0.8416212) returns 0.8 exactly. Here's how it looks in Minitab: MTB > invcdf .8; SUBC> …

$\begingroup$ I have rolled back the edit made by Thor H. Jonsson who claimed that "integration by parts was wrong as the author forgot to differentiate the latter part of the integrand."

I think that the expected value of a CDF is $0.5$ but since $\Phi$ is the CDF of a standard normal CDF and $\frac{a-bX}{c}$ is not standard normal I do not think the expected value should be …

Dec 13, 2016 · $\begingroup$ Thanks; great point. I guess my actual question is: Does the distribution of $\Phi(X)$ coincide with that of (perhaps a function of) another random variable …

Oct 22, 2018 · Let $\Phi(x)$ denote the cdf of the standard normal distribution. What are the asymptotics of $\Phi^{-1}(p ...

Integrating a special skew normal -- the CDF of a convolution of a normal with a truncated normal. 3.

Jul 16, 2021 · An interesting inequality about the cdf of the normal distribution. 0. Integral of a bivariate normal cdf. 3.

Apr 25, 2017 · Find the cdf and quantile function for the truncated (at a) normal random variable given that $$\frac{\varphi(x) I_{x>a}}{1-\Phi(a)}$$ where $\varphi(x)$ is the density for standard …