lik.ci: Likelihood Confidence Intervals for Scalar Parameter
In SMPracticals: Practicals for Use with Davison (2003) Statistical Models

Description Usage Arguments Value Note Author(s) References Examples

A simple function for computing confidence intervals from the values of a likelihood function for a scalar parameter. It prints the maximum likelihood estimate (MLE) and its standard error, and confidence intervals based on normal approximation to the distribution of the MLE and on the chi-squared approximation to the distribution of the likelihood ratio statistic.

1	lik.ci(psi, logL, conf = c(0.975, 0.025))

`psi`	Vector containing parameter values, the range of which contains the MLE
`logL`	Vector containing corresponding log likelihood values
`conf`	Vector containing levels for which confidence interval limits needed

See above

This uses the spline functions in library(modreg).

Anthony Davison (Anthony.Davison@epfl.ch)

Davison, A. C. (2003) Statistical Models. Cambridge University Press. Sections 4.4.2, 4.5.1.

# likelihood analysis for mean of truncated Poisson data
y <- c(1:6)
n <- c(1486,694,195,37,10,1)
logL <- function(x, y, n.obs)      # x is theta
{  f <- dpois(y,x)/(1-dpois(0,x))  # dpois is Poisson PDF
   sum(n*log(f))  }                # log likelihood
theta <- seq(from=0.8, to=1, length=200)
L <- rep(NA, 200)
for (i in 1:200) L[i] <- logL(theta[i], y, n)
plot(theta, L, type="l", ylab="Log likelihood")
lik.ci(theta, L)