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A TWO STAGE PROCEDURE FOR ESTIMATING THE SIZE OF A TRUNCATED EXPONENTIAL SAMPLE
Author(s) -
Watson Dan A.,
Blumenthal Saul
Publication year - 1980
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1980.tb01180.x
Subject(s) - mathematics , exponential function , bounded function , variance (accounting) , scale (ratio) , statistics , combinatorics , sample size determination , mathematical analysis , physics , accounting , quantum mechanics , business
Summary Let X 1 , …, X N be i.i.d. exponential random variables with unknown scale parameter θ. If one can observe only those X i in (0, T 0 ), an estimate of N based on the J observations obtained has a variance which explodes as θ→θC. Using θC based on the observations in (0, T 0 ) T is computed and all X i in (0, T̂) are observed. An estimate of N based on all observations in (0, T̂) has a bounded variance where the bound can be adjusted by proper choice of T̂.