An Introduction to Probability Theory and Its Applications, by William Feller

By William Feller

Significant alterations during this variation comprise the substitution of probabilistic arguments for combinatorial artifices, and the addition of recent sections on branching methods, Markov chains, and the De Moivre-Laplace theorem.

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Sample text

Knowing that for one data set, three quarters of the data are below the detection limit, while a second data set has only 10% below the same limit, strongly indicates that the first data set contains lower values than the second. This is evident without any knowledge of values above the detection limit. Efficient procedures for censored data combine the values above the detection limit(s) with the information contained in the proportion of data below the detection limit(s) in order to reach a result.

It is a limit above which data values are reported as single numbers without qualification by the analytical laboratory. Unfortunately, the terms “detection limit,” “detected value,” and “nondetect” are ubiquitous and used in both a specific and general sense. In this edition of the book I have attempted to be specific in meaning whenever possible. I have reserved the term “detection limit” for its more specific meaning described in this chapter, and used “reporting limit” whenever I refer to a censoring limit that might be either a detection or quantitation limit.

Specific capacity is affected by the well, resulting in an estimated transmissivity (T) that is lower than the true value in the aquifer. T is “greater than” the estimate, but the amount greater is unknown. For these right-censored examples, survival analysis software can be used directly. The situation is a little more complicated for left-censored data with censored observations, the focus of this book. Nonparametric survival analysis software is often hard-wired for right-censored data. Left-censored environmental data must be transformed into right-censored data before these routines can be used.

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