Normal_ct: The Central Normal Distribution

In glmbayes: Bayesian Generalized Linear Models (IID Samples)

The Central Normal Distribution

Description

Distribution function and random generation for the center (between a lower and an upper bound) of the normal distribution with mean equal to mu and standard deviation equal to sigma.

Usage

pnorm_ct(a = -Inf, b = Inf, mu = 0, sigma = 1, log.p = TRUE, Diff = FALSE)

rnorm_ct(n, lgrt, lglt, mu = 0, sigma = 1)

Arguments

a	Lower bound for the interval. Numeric vector; must be finite when used in rnorm_ct.
b	Upper bound for the interval. Numeric vector; must be finite when used in rnorm_ct.
mu	mean parameter of the underlying normal distribution.
sigma	standard deviation of the underlying normal distribution.
log.p	Logical argument. If TRUE, the log probability is provided
Diff	Logical argument. If TRUE the second parameter is the difference between the lower and upper bound
n	number of draws to generate. If length(n) > 1, the length is taken to be the number required
lgrt	log of the distribution function between the lower bound and infinity. Numeric vectors of length n; used internally to avoid cancellation when b - a is small.
lglt	log of the distribution function between negative infinity and the upper bound. Numeric vectors of length n; used internally to avoid cancellation when b - a is small.

Details

The distribution function pnorm_ct finds the probability of the center of a normal density (the probability of the area between a lower bound a and an upper bound b) while the random number generator rnorm_ct samples from a restricted normal density where lgrt is the log of the distribution between the lower bound and infinity and lglt is the log of the distribution function between negative infinity and the upper bound. The sum of the exponentiated values for the two (exp(lgrt)+exp(lglt)) must sum to more than 1.

These functions are mainly used to handle cases where the differences between the upper and lower bounds b-a are small. In such cases, using pnorm(b)-pnorm(a) may result in 0 being returned even when the difference is supposed to be positive. They are used in envelope-based accept-reject sampling for Bayesian GLMs \insertCiteNygren2006glmbayes.

Value

For pnorm_ct, vector of length equal to length of a and for rnorm_ct, a vector with length determined by n containing draws from the center of the normal distribution.

References

\insertAllCited

See Also

Gamma_ct, EnvelopeBuild

Examples

pnorm_ct(0.2,0.4)
exp(pnorm_ct(0.2,0.4))
pnorm_ct(0.2,0.4,log.p=FALSE)
log(pnorm_ct(0.2,0.4,log.p=FALSE))
## Example where difference between two pnorm calls fail
## but call to pnorm_ct works
pnorm(0.5)-pnorm(0.4999999999999999)
pnorm_ct(0.4999999999999999,0.5,log.p=FALSE)

glmbayes documentation built on Aug. 5, 2026, 1:07 a.m.