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Computes the cdf and/or the pmf of the ratio of two independent Poisson random variables



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PoissRatioCdf computes the cumulative distribution function (cdf) and/or the probability mass function (pmf) of the random variable X which is proportional to the ratio of two independent Poisson random variables, X = constant * (Y_lambdaNum / Y_lambdaDen), where constant is given constant, Y_lambdaNum is a random variable with Poisson distribution with parameter lambdaNum, and Y_lambdaDen follows the 1-displaced Poisson distribution (shifted by 1 to the right), with parameter lambdaDen, respectively.

The cumulative distribution function is given by
cdf = Prob( X <= x) = Prob(constant * (Y_lambdaNum / Y_lambdaDen) <= x).

This could be a useful modeling concentration measurements based on spectrometric methods. For more details on the method and its application for evaluation of the concentration measurements based on PTR-MS (Proton Transfer Reaction Mass Spectrometry) see e.g. Arendacka etal. (JBR 2008).

ARENDACKÁ, B. - SCHWARZ, K. - ŠTOLC JR, S. - WIMMER, G. - WITKOVSKÝ, V.: Variability issues in determining concentration of isoprene in human breath by PTR-MS. Journal of Breath Research 2, 2008, 037007 (8pp), doi:10.1088/1752-7155/2/3/037007.

The PoissRatioCdf distribution icludesthe following m-files:
PoissRatioCdf.m, PoissRatioPmf.m, PoissRatioStat.m, SetValuesX.m

Revised: 14-Nov-2009 15:36:29

Contact Address:
Viktor Witkovsky
Institute of Measurement Science
Slovak Academy of Sciences
Dubravska cesta 9
84104 Bratislava, Slovakia

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