Literatur

1. A simplified method for the deduction of Sheppard's correction formulae for ordinary and factorial moments, and for semi-invariants, together with more general results than those previously known, especially with regard to the remainder term, has recently been given ¹ H. Wold: Sulla correzione di Sheppard. Giornale dell' Istituto Italiano degli Attuari IV 1934, pp. 304–314. The methods used in the note referred to are similar to those used by W. F. Sheppard in his paper “The Calculation of Moments of a Frequency Distribution”, Biometrika V 1907, pp. 450–459. However, Sheppard's results are not valid under equally general conditions. . The method is based upon a very simple application of Euler—MacLaurin's formula, and the usual corrections are thereby shown to be valid for very general frequency curves, even for those without high contact in one or both directions. The note referred to deals with the case of one variable; the use of the method employed there can, however, easily be extended to an arbitrary number of variables, which extension it is the purpose of this paper to carry through. For the sake of formal simplicity the deductions are performed with two variables; the results can then immediately be generalized.     

Notes on some present day Questions regarding Mortality

Abstract

In the absence of any definite development of actuarial science in Great Britain which would be a suitable subject for this paper I considered that the most useful course would be to discuss some of the problems which are at present exercising my own mind, and no doubt the minds of many of my colleagues. Probably, many of these questions are akin to others which arise in other countries, so that their discussion at a meeting such as this may prove of mutual interest, while even if they are peculiar to ourselves, a disclosure of our doubts and difficulties will indicate the directions in which future developments may be expected. I must, however, emphasize that any views expressed are purely personal, and do not in any way pretend to represent a consensus of British actuarial opinion. Throughout this paper only Ordinary (as opposed to Industrial) business in considered.     

The probability of decrements from a population. A study in discrete random processes

Abstract

The statistician, whether he be biologist, actuary, or worker III the social sciences, often requires to measure the intensity of some decremental force, or forces, acting on an observed body of individuals. The latter may be human beings, animals, or even inanimate objects (e. g. aircraft), and the decrements considered may range from marriage to‘write-off’. N evertheless the assumptions made are, for the most part, analogous and the technique adopted is broadly the same in every case: the decrements are assumed to be random (in the technical sense) and they are related to the body in which they have occurred (the so-called‘exposed to risk’) in order to obtain a relative frequency, or‘rate’, of decrement.     

On the independence of system life distribution and cause of failure

Abstract

Under the competing risks model, we obtain conditions for and consequences of the independence of the system life length and the cause of failure. When the survival distributions are continuous, we consider the situations where the risks are independent as well as they are dependent. In the dependent case, the discussion is limited to two risks with some special bivariate survival distributions. The discussion of discrete model where we assume the survival distributions to be discrete, is limited to two independent risks. This results in two characterizations of geometric distribution. Finally some generalizations of our results to k out of m systems are considered.