Sample size | Mean ( ) | SD ( ) | θ in C.I. | ρ in C.I. | ρ/θ in C.I. | ||||
---|---|---|---|---|---|---|---|---|---|
50 | 0.99 | 0.54 | 96 | 0.55 | 0.23 | 100 | 0.67 | 0.24 | 99 |
100 | 0.95 | 0.41 | 96 | 0.65 | 0.20 | 99 | 0.48 | 0.13 | 99 |
200 | 1.00 | 0.44 | 97 | 0.2 | 0.22 | 100 | 0.25 | 0.25 | 99 |
Shown are estimated means and standard deviations of the maximum-likelihood estimates of θ; estimated median of maximum-likelihood estimates of ρ and ρ/θ; g, the proportion of times that the MLE is within a factor of 2 of the truth; and coverage properties of an ~95% confidence interval (calculated using a chi-square approximation to the likelihood ratio statistic). Results are based on 100 samples (simulated with ρ = θ = 1.0) for each of three sample sizes.