264 Gradnation and Anali/sis of a Siclness Table 



latter mothod, aiui, as we wish to graduate oiir rates as nearly as possible to the 

 end of the table, the poiut is worth bearing in niind. 



The first inethod I havc dcscribed gavc the best graduation aiid it could bc 

 improved by calculatiiig the fij^ures f^r the sickness to a few inore places of 

 dccimals and usiug everj' teriu for finding the inoinents instead of groups of five. 

 We inight also treat the rate of sickness beyond age 100 as 52167*; for by usiug 

 an infinite-range curve as the exposed we assume that some live beyond the hust 

 age oecurring in the experience and it is not unreasonable to suppose that they 

 would be perrnanently sick. The rates for the last ten er fifteen ages if unsatis- 

 factory might be altered by graduating the end of the experience by a parabolic 

 curve or thov niight bc supplied by drawing a straight line such as the dotted one 

 shewn in the figure. I niay remark, however, that for practical purposes it is 

 unnecessary to obtaiu graduated rates of sickness right up to the limit of old age ; 

 in fact Bowser's tabiesf end (a-s regards sickness) at age 80 and he says on 

 p. XV. of bis Introdiiction that " if the rules of a society perniit ' sick pay ' to be 

 " continued für the whole of life the valucr should rcgard the sickness benefit 

 "after age SO, or still better age 7ö, in tiie light of a Pension for li/e" and bis 

 peusion tables provide for the chronic sickness of old age. 



For the present purpose it seems unnecessary to discuss the advantages of the 

 method of graduation as it would involve a somewhat lengthy comparison with 

 other methods wliich would liave to be explained for non-actuarial readers ; but it is 

 obvious that the graduated rates nuist run evenlyand will agree with the observed 

 rates closely if the araount of sickness can be represented accurately by a frequency 

 curve. 



II. 



Analysis of Sickness Table. 



My object in continuing the work beyond a niere graduation of Sutton's Table 

 was to see if sickness niay bc referred to certaiu broadly inarked periods of life 

 corresponding to those wbich Professor Pearson shewed were characteristic of 

 mortality. 



Before giving the work doni^ in conuection with sickness it will be well to 

 recall the rcsults obtained by Professor Pearson from bis iiivestigation of mortality. 

 'Die l'nnction on whicb he wcirked was that kiiown to actuaries as the "deaths" or 

 " dx" colunin i>f the mortality table:!;. This colunin gives the nuinber of persons 



• 521(!7 wceks whh taken as n füll jonr by Sutton; on p. xii. he says "it should be addcd that I 

 "hftve invariably considcred as regnrils brokcii wecks that thcrc aro six workinR days in a weck." 



t " Friendly Socicties' Valuation and other tables deducod from the experience of the Independent 

 " Order of OddfcUows, Manchester Unity l'ricndly Society, IStlll — 1.S70" by Wilfred .\. Bo\v.«er. London, 

 C. and E. Layton, 18'.I6. The Manchester Unity table i» tho Standard for Friendly Society Vahmtions. 



X The rcader must be careful to distinguish betwcen the d culunin of the mortality table and the 

 nuinber of deaths in a mortality experience ; the lattcr is the actual uumber who die, the forraer is a 



