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Chapter 77: Quantile Estimators – Bootstrap Confidence Intervals
The pth quantile of a distribution is the number below which a random value following that distribution can be attained with a probability p. Assuming that X is a random variable with cumulative density function (CDF) D, the pth quantile of that distribution is the Qp that satisfies
Quantiles are estimated using quantile estimators, which are formulas that utilize a sample of the parent distribution. If the parent distribution is normal and the sample size is n, then the well-known eqn (2) is used for estimating the pth quantile:
where m is the sample mean, s is the sample standard deviation and zp is the pth quantile of N (0,1).
When no assumptions for D are posted, nonparametric ...