Simplify the division of Normals cumulatives functions

Question

I'm struggling on how I can simplify the quotient of two normal probability functions in R. Actually, I'm calculating a conditional skew-Normal density, them I have the division between this two function:

pnorm(alpha0+t(alpha2)%*%chol2inv(chol(omega2))%*%t(y2-xi2.1))/pnorm(tau2.1)

where alpha0+t(alpha2)%*%chol2inv(chol(omega2))%*%t(y2-xi2.1) and tau2.1 result in real numbers. For example, sometimes I have pnorm(-50)/pnorm(-40), e.g. an inconsistency 0/0. But these values are not zero, R is just approximating. I tried to use the erf function, but I got the same problem (0/0).

Any hint on how can I overcome this issue?

score 1 · Accepted Answer · answered Sep 10 '20 at 12:13

1

pnorm has a log parameter, which makes it return log(p). Change your equation to exp(log(p1) - log(p2)):

exp(pnorm(-50, log = TRUE) - pnorm(-40, log = TRUE))
#[1] 2.95577e-196

answered Sep 10 '20 at 12:13

Roland

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works perfectly for me! I didin't know about this parameter. – DR15 Sep 10 '20 at 12:16
You are not the first one with this issue. It is very common in statistics. – Roland Sep 10 '20 at 12:17
Actually, we need to apply the `exp` separately. – DR15 Sep 10 '20 at 12:20
I don't understand. – Roland Sep 10 '20 at 13:36

Simplify the division of Normals cumulatives functions

1 Answers1