Distribution of some maximum norm summary sets of quantile estimators
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Authors
Read, Robert R.
Subjects
Probability distributions
quantile plots
goodness-of-fit testing
Markov Chains
quantile plots
goodness-of-fit testing
Markov Chains
Advisors
Date of Issue
2015-07
Date
July 2015
Publisher
Monterey, California. Naval Postgraduate School
Language
Abstract
This report introduces an expanded class of quantile level sets {(j-α)/(n+c), j = 1, ⋯, n} to augment the popular ones, i.e., (α = ½, c = 0) used in q-q probability plots and (α = 0, c = 1) known as the Pyke alternative, for use in data analysis graphical studies of order statistics and for tests of distribution hypotheses. The expanded class can be useful in small sample studies in which their effects can be the greatest. The corresponding test statistics have the form Tn = (max |uj ‒ (j-α)/(n+c)|, j = 1, ⋯, n) where the {uj} are the order statistics of a random sample of size n from a Uniform (0, 1) population. A sub family, called tail symmetric, is described and shown to have greater efficacy than the other members of the family. The small sample distributions of these statistics are developed using Markov Chain methodology.
The computational aspects are illustrated, with n = 5 using a selected set of featured statistics. Some computational idiosyncrasies are attended to and some behavioral properties are illustrated graphically. A number of side issues are discussed.
Type
Technical Report
Description
Series/Report No
Department
Operations Research
Identifiers
NPS Report Number
NPS-OR-15-007
Sponsors
Funder
Format
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.