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Mean and variance of ratios of proportions from categories of a multinomial distribution

Author

Listed:
  • Frantisek Duris

    (Geneton s.r.o.
    Slovak Centre of Scientific and Technical Information)

  • Juraj Gazdarica

    (Comenius University, Faculty of Natural Sciences)

  • Iveta Gazdaricova

    (Comenius University, Faculty of Natural Sciences)

  • Lucia Strieskova

    (Comenius University, Faculty of Natural Sciences)

  • Jaroslav Budis

    (Comenius University Faculty of Mathematics, Physics and Informatics)

  • Jan Turna

    (Comenius University, Science Park)

  • Tomas Szemes

    (Geneton s.r.o.
    Comenius University, Faculty of Natural Sciences
    Comenius University, Science Park)

Abstract

Ratio distribution is a probability distribution representing the ratio of two random variables, each usually having a known distribution. Currently, there are results when the random variables in the ratio follow (not necessarily the same) Gaussian, Cauchy, binomial or uniform distributions. In this paper we consider a case, where the random variables in the ratio are joint binomial components of a multinomial distribution. We derived formulae for mean and variance of this ratio distribution using a simple Taylor-series approach and also a more complex approach which uses a slight modification of the original ratio. We showed that the more complex approach yields better results with simulated data. The presented results can be directly applied in the computation of confidence intervals for ratios of multinomial proportions. AMS Subject Classification: 62E20

Suggested Citation

  • Frantisek Duris & Juraj Gazdarica & Iveta Gazdaricova & Lucia Strieskova & Jaroslav Budis & Jan Turna & Tomas Szemes, 2018. "Mean and variance of ratios of proportions from categories of a multinomial distribution," Journal of Statistical Distributions and Applications, Springer, vol. 5(1), pages 1-20, December.
    • Handle: RePEc:spr:jstada:v:5:y:2018:i:1:d:10.1186_s40488-018-0083-x
    DOI: 10.1186/s40488-018-0083-x
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    References listed on IDEAS

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    1. Nadarajah, Saralees & Kotz, Samuel, 2006. "On The Product And Ratio Of Gamma And Weibull Random Variables," Econometric Theory, Cambridge University Press, vol. 22(2), pages 338-344, April.
    2. Marsaglia, George, 2006. "Ratios of Normal Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 16(i04).
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