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On the derivation of expected value and variance of ratios without the use of infinite series expansions

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The introductory part of the paper discusses the implications underlying the use of infinite series expansions for determining expected value and variance of ratios of discrete variates. The basic initial step in deriving such expected values and variances, without, the use of infinite series expansions, lies in the establishment of an identity by the simple division of unity by a binomial expression which is a linear function of the random variable in the denominator of the ratio. The method leads to exact expressions. Some applications are considered.

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Authors and Affiliations

  1. Sampling and Survey Research Staff, Dominion Bureau of Statistics, Ottawa

    J. C. Koop

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  1. J. C. Koop
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Koop, J.C. On the derivation of expected value and variance of ratios without the use of infinite series expansions. Metrika 19, 156–170 (1972). https://doi.org/10.1007/BF01893291

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  • DOI: https://doi.org/10.1007/BF01893291

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