Note on a new method of construction of mortality tables when the number of lives exposed to risk is unknown

Abstract

Abstract It has been known for some time that the dbx column in a mortality table can be considered as a compound frequency curve with a limited number of maxima and minima. From a theoretical point of view this is of course a self evident conclusion which follows directly from the so-called genetic theory of frequency originally introduced by Laplace. He showed that any frequency distribution can be considered or generated as the sum of a very large number of elementary errors, referrable to several sources of error, each group or error having its own peculiar law of error. While the pure theory of the generation of frequency curves from such secondary sources of elementary errors is simple enough, the inverse and essentially practical problem of decomposing a compound frequency curve into its component or constituent elements is by no means simple and often presents great difficulties, especially if certain restrictions are imposed upon the component curves. An example of such restrictions would be the requirement that all the component curves should be normal Laplacean probability curves.