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Tables and Formulae for the Computation of Life Contingencies: With Copious ...
Oliver Peter Gray
No preview available - 2016
according adding addition advantage already amount annuity application argument assurance balls becomes benefit called columns combination commence compared complementary complete computation consequently constant construction contains continuous corresponding deduced denote depends determined Diff differences direct employed entered equal error example existence expectation expression extension fail figures formation formed formula function give given greater happen Hence increased initial values interest joint known labour less lives Log 1+x Log Log log.v logarithm manner mean duration method mode Morgan's multiplication namely necessary obtained obviously operation payments portion present value previously probability PROBLEM proportional quantity question received reference regard relation remaining remarks requisite respect shown single specified subsist successive survivorship tabular taken tion unit unity usual verification whole
Page 36 - ... the application of the theory of computing the average duration of human life after any given age is founded on two assumptions. " Of these the first is that the experience of the future will accord with that of the past ; that is to say, that what ratio soever may have been found to exist in times past between the number surviving and the number dying in a given time, out of a specified number of individuals observed upon, the same ratio will be found to subsist in time to come between the number...
Page 80 - B dedepends ; if, moreover, TT denote the probability of a payment of B being received in the first year, and II the probability of the single life, or of all the lives, on which that benefit depends, surviving a year ; — then will the following equation always subsist : — For, if the benefit...
Page 69 - Expec." at a specified age, considered as a term of years, is more likely than any other term to be the actual duration of that life ; and another is that it denotes a term of years which the life in question is as likely to survive as not. Neither of these notions is correct. The first would imply that the year in which a life is most likely to fail is that in which its
Page 19 - All the entries of the same kind — direct and inverse — are brought together, the whole of the logarithms being found before a single natural number is taken out. We consequently proceed right through the table; and as we proceed, we find two, three, four, and even as many as six and eight entries on the same opening. At the close, moreover, the taking out of the numbers may, if necessary, be turned over to an assistant. On the other hand, when the common tables are used, direct and inverse entries...
Page 90 - I.) the present value of £1 to be received at the same time provided (x) be then alive, the difference between these two is evidently the present value of £l to be received a year hence if (x) be then dead.
Page 1 - All mathematical tables consist of two series of corresponding values, each value in either series having a value corresponding to it in the other.
Page 119 - XI. —To find the present value of a life assurance of £ 1 on (x) ; that is, of £1 to be received at the end of the year in which (x) dies, whenever that event may happen.
Page 101 - ... to be paid at the end of the year in which (x) dies, provided he shall have been survived by (y). This is the benefit whose present value is denoted by h^—, (192).
Page 69 - ... term, to be the actual duration of that life; and another is, that it denotes a term of years which the life in question is as likely to survive as not. Neither of these notions is correct. The first would imply that the year in which a life is most likely to fail is that in which its " expectation