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Chapter 76: Quantile Estimators

Quantile Estimators
Quantile estimators
Introduction

Questions of what is the level, within a population, below which a random value from that population can be attained with a given probability are very common. Such levels are known as distribution quantiles or percentiles and they are very frequently used in several scientific fields such as risk management, economics, biology, medicine, etc. Assuming that X is a random variable with cumulative density function (CDF) F, the pth quantile of that distribution is the Qp that satisfies

The quantile estimators are formulas that try to estimate the quantiles of a distribution using a sample of the parent distribution. Let X be a random variable and X1, X2, …, Xn a random sample of size n from X if the parent distribution is ...