Large sample validity of the binomial distribution for lives with unequal mortality rates

Abstract

Let us consider a group of n lives which are observed during some time or age interval. Suppose that the following conditions are satisfied: 1. The probability of death within the interval considered has the same value q for each person of the group.

2. These lives represent statistically independent observations (with respect to mortality).

     

Derivation of the Wishart distribution of the second order sample moments by straightforward integration of a multiple integral

1. Introduction.

In his textbook of statistics Kendall classifies the methods of deducing exact sampling distributions into four groups:

• (a) straightforward evaluation of the integral in question by ordinary analytical processes such as a convenient change of variable;

• (b) the use of geometrical terminology;

• (c) the use of characteristic functions; and

• (d) other analytical methods.

     

Book Reviews

Organized Uncertainty: Designing a World of Risk Management. Michael Power. Oxford University Press, 2007. xviii and 248pp. ISBN 978–0–9–925394–4. £24.99.

Intellectual Capital Reporting: Lessons from Hong Kong and Australia. J. Guthrie, R. Petty and F. Ricceri. The Institute of Chartered Accountants of Scotland, 2007, vii and 118pp. ISBN 978–1–904574–27–9. £15

The Routledge Companion to Fair Value and Financial Reporting. P. Walton (ed.). Routledge, 2007. xviii and 404 pp. ISBN 978–0–415–42356–4. £95.

UK Reporting of Intellectual Capital. Jeffrey Unerman, James Guthrie and Ludmila Striukova. ICAEW Centre for Business Performance, 2007. 68 pp. ISBN 978 1 84152 507 5. £20.     

The Sickness Experience of the Valkyrian Insurance Company, 1929-48

Abstract

1. Introduction.     

Application de la théorie collective du risque à la réassurance « Excess-Loss »

Abstract

Introduction.

Les méthodes de calcul de la prime de réassurance Excess-Loss utilisées jusqu'à présent ou bien avaient un caractère purement empirique, ou bien présumaient que les écarts entre le montant des sinistres constatés et le montant des sinistres attendus se répartissent suivant la loi de Laplace-Gauss.     

Book reviews

Working with Developers in Urban Renewal

Francis Terry (Ed.). Public Finance Foundation London (1989). Discussion Paper 26, 78 pp. £10.00. ISBN 0 85299 445 1.

Councils in Conflict

S. Lansley, S. Goss and C. Wolmar. Macmillan, London (1989). x + 216 pp. £8.99. ISBN 0 333 454 138.

The Future of Housing Allowances

J. Hills, R. Berthoud and P. Kemp. Policy Studies Institute (1989). 71 pp. £5.95. ISBN 0 85374 461 0.     

CALL FOR PAPERS

Organized Uncertainty: Designing a World of Risk Management. Michael Power. Oxford University Press, 2007. xviii and 248pp. ISBN 978–0–9–925394–4. £24.99.

Intellectual Capital Reporting: Lessons from Hong Kong and Australia. J. Guthrie, R. Petty and F. Ricceri. The Institute of Chartered Accountants of Scotland, 2007, vii and 118pp. ISBN 978–1–904574–27–9. £15

The Routledge Companion to Fair Value and Financial Reporting. P. Walton (ed.). Routledge, 2007. xviii and 404 pp. ISBN 978–0–415–42356–4. £95.

UK Reporting of Intellectual Capital. Jeffrey Unerman, James Guthrie and Ludmila Striukova. ICAEW Centre for Business Performance, 2007. 68 pp. ISBN 978 1 84152 507 5. £20.     

Insurance economics

Abstract

Background

Insurance accounting is generally speaking based upon the idea that a comparison shall be made between “premiums earned” and “claims incurred”. Even if there are exceptions in different countries and in different classes of business the method where premiums earned and claims incurred are compared is so widely used that we will take this method as our starting point for a discussion of the shortcomings, if any, of insurance accounting.     

Basic concepts in life assurance mathematics

Abstract

1. Introduction.

In this paper the basic concepts of the life insurance mathematics will be discussed. Due to the fact that the importance of the probability calculus as a hasis for the actuarial science has repeatedly been disclaimed in recent literature (See e.g. Ernst ZWinggi (1]), the present author feels that there is a justification for reconsidering the fundamental ideas of the actuarial science.     

Remarks on “A note on compound generalized distributions”

Abstract

1. INTRODUCTION

In [1] the authors derive recursion formulae for computing total claim probabilities for a general class of modified power series distributions. Such formulae provide an important tool for computing total claim size probabilities in risk-theory. As it turns out, two of their recursions (Theorem 3.2 and Theorem 3.4) need modifications. Unfortunately, these modifications have the effect that the recursions break down. In the following, we will state the modified theorems and show how these obstacles can be overcome.     

Eksamen i Forsikringsvidenskab og Statistik ved Københavns Universitet

abstract

Ved et Sporvognsstoppested pas serer Linje 1 hvert 6. Minut, Linje 15 hvert 7 ½ Minut; mellem de to Linjers Afgangstider antages der ikke at bestaa nogen Forbindelse. Find Sandsynligheden for:

1^p0. At en tilfældig Passager maa vente kortere paa Linje 1 end paa Linje 15.

2^p0. At han højst maa vente 2 Minutter for at komme med en af de to Linjer.     

Withdrawal among Norwegian Life Assured 1910–1935

Introduction.

In the series of statistical experiences of the Norwegian life assurance companies report No. IV was issued some time ago. ¹ “Frivillig avgang blant norske livsforsikrede og dödeligheten blant forsikrede med fripolise 1910–1935”. Oslo 1943. The report, which was prepared at the Statistical Bureau of the Norwegian Life Assurance Companies, comprises 2 subjects: 1. Withdrawal among Norwegian life assured

2. Mortality among assured with paid-up policies (free policies) both during the period 1910–1935.

     

Integration of Financial Services

Abstract

Integration financial services is a term with many meanings. Definitions might include:

• ownership of different segments of financial services,

• the distribution of products of one segment by another, and

• a consumer-centric strategy driven to satisfy the needs of the customer regardless of organizational structures.

For the purposes of my paper, I will define it as the erasing of boundaries leading to consumers receiving value propositions that are not restricted by traditional industry segment barriers.     

An inequality satisfied by the Gamma function

Abstract

1. Summary

For all real values of α and λ satisfying α + λ > 0, α ≠ 0, α ≠ 1, λ > 0 the following inequality involving the Gamma function holds:

This follows from a general inequality for the variance of regular unbiased estimators given by Cramér [1].     

Facts & figures: Public sector pay: The last ten years

Next Steps: Improving Management in Government? Edited by Barry J. O'Toole and Grant Jordan (Dartmouth Publishing Company, Aldershot, 1995). £37.50. ISBN 1 855 21491 1.

The Myth of Democratic Failure. By Donald Wittman (University of Chicago Press, Chicago; distributed by John Wiley, Chichester, 1995). £23.95. ISBN 0 226 90422 9.

Managing Change in the New Public Sector. Edited by Roger Lovell (Pearson Professional, Southport, 1995). £32.50. ISBN 0 582 23893 5.     

Oversikt av utländska aktuarietidskrifter

Abstract

Under Makehami's law, life annuities are expressed by incomplete gamma functions.     

Book reviews

Public Sector Management Norman Flynn. Harvester Wheatsheaf, Hemel Hempstead, UK (1990). 201 pp. £9.95. ISBN 0–7450–0594–2.

CIPFA Guide to the Community Charge R. Hale and C. Stewart (Eds). Longman, Harlow, UK (1990). Price £225. ISBN 0–582–063–54X.

Ethics in the British Civil Service Richard A. Chapman. Routledge, London ( 1988). pp. xix + 338. £30.     

Facts & figures: Public sector and GDP: Some international comparisons; Local authorities and the law: Selected legal precedents

We are indebted to Alastair Gray, of the Open University, for much of the statistical analysis on which this article is based.     

Financial & economic review

This is an expanded version of an article by Sue Ward in TRANSPORT UK 1985.     

The choice of stratification points

Abstract

Extract

The importance of the problem of the optimum choice of stratification points, when conducting stratified sampling on a univariate population, has been pointed out by Dalenius (1950, 1957) In a simplified form, this problem may be given the following mathematical formulation.