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Statistical methods for astronomical data with upper limits. I - Univariate distributions
Feigelson, E. D.; Nelson, P. I.
AA(Pennsylvania State University, University Park, PA), AB(Kansas State University of Agriculture and Applied Science, Manhattan, KS)
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 293, June 1, 1985, p. 192-206. (ApJ Homepage)
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NASA/STI Keywords:
Multivariate Statistical Analysis, Radio Astronomy, X Ray Astronomy, Error Analysis, Galaxies, Maximum Likelihood Estimates, Radio Sources (Astronomy)
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The authors discuss statistical techniques applicable when a portion of an object sample is not detected; i.e., when upper limits, or left-censored data, are present. An extensive field of statistics called "survival analysis" of "lifetime data" exists to address these problems. This paper presents the foundations of nonparametric univariate survival analysis and discusses its application to astronomical data. The Kaplan-Meier product-limit estimator, its variance, mean, and standard deviation are presented. It provides a maximum-likelihood-type reconstruction of the true distribution function when upper limits are present. Three nonparametric procedures for testing whether or not two censored samples are drawn from the same distribution - the Gehan, logrank, and Peto-Prentice tests - are described. Some illustrative examples using astronomical data sets are included.

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