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

Ratio distribution is a probability distribution representing the ratio of two random variables, each usually having a known 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.

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