Journal of Official Statistics, Vol.6, No.1, 1990. pp. 7587

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Graduation Models for the Age-Specific Marital Fertility Rates: The Hungarian Example

In this paper we have proposed two models that express the age-specific marital fertility rate m(x) as a function of age x. Specifically, linear functions of ln x and ln (50 − x) have been suggested as possible estimators of ln m(x) and ln (−ln m(x)). These models have been fitted on Hungarian data covering a twenty year period from 1960. Both of these models have three parameters which have been estimated by the method of least squares and by solving a set of three simultaneous equations generated by three data points. We have compared these models and methods with another model based on a Pearsonian Type I distribution fitted earlier by the method of moments. Using the square of the correlation coefficient between the observed and the model values as a measure of goodness of fit, we have found that the model based on ln (−ln m(x)) fits the data very well by both methods.

Age-specific marital fertility rates; linear model; logarithmic transformation; method of least squares; solutions of simultaneous equations.

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