Open AccessEstimation and prediction for mixtures of the exponential distribution
Author(s) -
Herbert Robbins
Publication year - 1980
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.77.5.2382
Subject(s) - exponential distribution , exponential function , mathematics , random variable , statistics , distribution (mathematics) , sample (material) , variable (mathematics) , statistical physics , chromatography , mathematical analysis , physics , chemistry
Letx be a random variable whose distribution is an unknown mixture of exponentials with different means θ. From a random samplex 1 ,...,xn ofx values we show thatE (θǀx >a ) can be estimated for any givena > 0. We can therefore predict the average of all future observations taken on thosex values in the sample that exceeda .