A method of deriving valid approximate expressions for bias in ratio estimation

The expectation of a ratio of two statistics is usually obtained by the method in which the denominator is expanded into a binomial series around its mean. However, this method can less generally be employed because the expansion of the denominator is not always valid. This paper presents a device in which the expectation of a ratio of two statistics can more generally be obtained. The device is to adopt a positive value as ‘catalyzer’. It can be applied not only to the ratio of estimates based on samples but also to ratio of any two statistics, if the denominator is positive and finite.