# Comparing Exact and Approximate Censored Normal Likelihoods

Comparing Exact and Approximate Censored Normal Likelihoods

A random sample of size is simulated from a left-censored standard normal distribution with censor point , where is the censor rate and is the inverse cumulative distribution function of the standard normal distribution. The Demonstration shows the exact relative likelihood function for the mean of the underlying distribution (blue curve) as well as a crude approximation (red curve) that ignores censoring. When is close to zero, the crude approximation is reasonable, but as increases, the exact method becomes more and more accurate. The blue and red lines show corresponding point estimates for the exact and approximate estimates. while the gray line shows the true parameter value. By varying the random seed, you see the stochastic nature of estimates; for example, sometimes the crude estimator may be more accurate, even though overall, on average, it is less accurate when .

n

c=Φ(r)

-1

r

Φ

-1

r

r

r>0