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Unformatted text preview: 1.017/1.010 Class 18 Small Sample Statistics Small Samples When sample size N is small the estimator of a distributional property a (mean, variance, 90 percentile, etc.) is generally not normal. In this case, the CDFs of the estimate a and standardized statistic z (used to derive confidence intervals and hypothesis tests) can be approximated with stochastic simulation . In order to generate random replicates in the stochastic simulation we need to specify the property a (or parameters that are related to it): For estimating confidence intervals we assume a a = (the estimate computed from the actual data). For testing hypotheses we assume a a = (the hypothesized parameter value). The stochastic simulation uses many N rep random sample replicates, each of length N , to generate N rep estimates. The desired estimate and standardized statistic CDFs are derived from this ensemble of estimates. Example Small-sample two-sided confidence Intervals for the mean of an exponential distribution Consider a small sample that is thought to be drawn from an exponential distribution with unknown parameter a : [ x 1 , x 2 , x 3 , x 4 , x 5 ] = [0.05 1.46 0.50 0.72 0.11 ] The sample mean is an unbiased estimator of...
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This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.
- Spring '05