Performs a computer simulation of the confidence interval performance for a population mean. Sample data can be generated from five different population distributions. All distributions are scaled to have a standard deviation of 1.0.
Arguments
- alpha
alpha level for 1-alpha confidence
- n
sample size
- dist
type of distribution (1, 2, 3, 4,or 5)
1 = Gaussian (skewness = 0 and excess kurtosis = 0)
2 = platykurtic (skewness = 0 and excess kurtosis = -1.2)
3 = leptokurtic (skewness = 0 and excess kurtosis = 6)
4 = moderate skew (skewness = 1 and excess kurtosis = 1.5)
5 = large skew (skewness = 2 and excess kurtosis = 6)
- rep
number of Monte Carlo samples
Value
Returns a 1-row matrix. The columns are:
Coverage - probability of confidence interval including population mean
Lower Error - probability of lower limit greater than population mean
Upper Error - probability of upper limit less than population mean
Ave CI Width - average confidence interval width
Examples
sim.ci.mean(.05, 10, 1, 5000)
#> Coverage Lower Error Upper Error Ave CI Width
#> 0.9498 0.0234 0.0268 1.388709
# Should return (within sampling error):
# Coverage Lower Error Upper Error Ave CI Width
# 0.9484 0.0264 0.0252 1.392041
sim.ci.mean(.05, 40, 4, 1000)
#> Coverage Lower Error Upper Error Ave CI Width
#> 0.928 0.018 0.054 0.6319032
# Should return (within sampling error):
# Coverage Lower Error Upper Error Ave CI Width
# 0.94722 0.01738 0.0354 0.6333067