288 Group Discussion 



of mortality for the populations, so that at a different age an addi- 

 tional factor seems to be interjected into the mortality picture. 

 Perhaps Mr. Perks would comment on these tables [not printed]. 



Perks: First, I find it rather strange that you have such a large 

 number of "ages" in your life-tables. We actuaries, of course, string 

 out the rates of mortality for each year of age, but that is for the 

 practical purposes of life assurance. For understanding the mortality 

 that underlies the life-table we would certainly compress it, and we 

 would not have 67 values of the independent variable. We would 

 probably group these in fives and show the values of qx for five 

 intervals at a time. That is a general question of presentation, and 

 of trying not to confuse the reader with too many figures. 



The next point is that the distribution of dx for male houseflies 

 gave me the impression of a curve very much like the Karl Pearson 

 type 3 frequency curve, that is the gamma distribution, that comes 

 up to a peak fairly quickly and has a long tail away to the right. The 

 mortality curves for electric light bulbs that E. G. Pearson published 

 25 to 30 years ago had very much of that characteristic ; they were 

 fitted fairly well by the type 3 distribution. If we are actually to 

 understand anything about the underlying mathematical processes 

 of mortality curves, we should start with the simpler organisms, or 

 simple physical objects, and electric light bulbs are particularly 

 suitable for this purpose. You can get them fairly homogeneous, 

 and put them on a uniform circuit, so cutting down much of the 

 extraneous variation. It certainly is interesting to see a death 

 curve with a long tail to the right. The human death curve tends to 

 have the tail to the left — coming up slowly to the peak, and then 

 coming down very sharply. Beard has fitted incomplete gamma 

 functions to a number of human life-tables, but he had to do a bit of 

 manipulation with the data first, to remove the accident and 

 infectious diseases mortality, otherwise the tail on the left-hand side 

 would not asymptote to zero. There is a mathematical model that 

 provides some analogy with the death process. Imagine that a 

 population of objects are put on a wall, and shot at at regular 

 intervals so that each is equally likely to be hit. Then suppose you 

 define death as when a particular object has been hit n times; then 

 the death distribution is in fact the type 3 distribution. Thinking 

 along those lines may help us to get mathematical representations of 

 the death curves of more complicated objects. I am particularly 

 interested to see that the housefly appears to give a relatively simple 

 distribution. 



My impression of the female table is that it is rather similar to the 

 male, except that the peak is much flatter. So far as the so-called 



