Local Powers of Optimal One‐sample and Multi‐sample Tests for the Concentration of Fisher‐von Mises‐Langevin Distributions

One‐sample and multi‐sample tests on the concentration parameter of Fisher‐von Mises‐Langevin distributions on (hyper‐)spheres have been well studied in the literature. However, only little is known about their behaviour under local alternatives, which is due to complications inherent to the curved nature of the parameter space. The aim of the present paper therefore consists in filling that gap by having recourse to the Le Cam methodology, which has recently been adapted from the linear to the spherical setup. We obtain explicit expressions of the powers for the most efficient one‐ and multi‐sample tests. As a nice by‐product, we are also able to write down the powers (against local Fisher‐von Mises‐Langevin alternatives) of the celebrated Rayleigh test of uniformity. A Monte Carlo simulation study confirms our theoretical findings and shows the empirical powers of the above‐mentioned procedures.     

GRADING JOURNALS IN ECONOMICS: THE ABCS OF THE ABDC

Many institutions and governments grade academic journals for the evaluation of research. In this paper, we implement a multi-bibliometric methodology for the evaluation of such a list of journal grades. We examine the grades assigned by the Australian Business Deans Council (ABDC) for over 750 journals in the fields of economics and statistics. Firstly, we generate up to 48 bibliometric-based grades for each journal based on the grade distribution implied by the ABDC. Secondly, we categorize the bibliometrics employing a cluster analysis of an interrater agreement statistic. Thirdly, we present a visualization of the consistency of the grading by journal. Finally, we list those journals where the majority of the matched bibliometrics indicate a higher or lower grade than their ABDC grade.     

An Empirical Investigation of the Effects of Rounding on the SPF Probabilities of Decline and Output Growth Histograms

I consider the possibility that respondents to the Survey of Professional Forecasters round their probability forecasts of the event that real output will decline in the future, as well as their reported output growth probability distributions. I make various plausible assumptions about respondents’ rounding practices, and show how these impinge upon the apparent mismatch between probability forecasts of a decline in output and the probabilities of this event implied by the annual output growth histograms. I find that rounding accounts for about a quarter of the inconsistent pairs of forecasts.     

Too Good to be True? An Analysis of the Options Market's Reactions to Earnings Releases

Using option implied risk neutral return distributions before and after earnings announcements, we study the option market's reaction to extreme events over earnings announcements. While earnings announcements generally reduce short‐term uncertainty about the stock price, very good news does not reduce uncertainty and slightly bad news actually increases uncertainty. We also find that left tail probabilities decrease over earnings releases while right tail probabilities increase. We interpret these findings as evidence of maintained investor expectations that very good news is generally not released during earnings announcements, combined with skepticism in the form of lingering uncertainty at the release of such very good news.     

Bayesian and Bühlmann credibility for phase-type distributions with a univariate risk parameter

Credibility theory is a statistical tool to calculate the premium for the next period based on past claims experience and the manual rate. Each contract is characterized by a risk parameter. A phase-type (or PH) random variable, which is defined as the time until absorption in a continuous-time Markov chain, is fully characterized by two sets of parameters from that Markov chain: the initial probability vector and transition intensity matrix. In this article, we identify an interpretable univariate risk parameter from amongst the many candidate parameters, by means of uniformization. The resulting density form is then expressed as an infinite mixture of Erlang distributions. These results are used to obtain a tractable likelihood function by a recursive formula. Then the best estimator for the next premium, i.e. the Bayesian premium, as well as its approximation by the Bühlmann credibility premium are calculated. Finally, actuarial calculations for the Bühlmann and Bayesian premiums are investigated in the context of a gamma prior, and illustrated by simulated data in a series of examples.     

An alternative interpretation of the discontinuity in earnings distributions

We show that the asymmetric effects of income taxes and special items for profit and loss firms contribute to a discontinuity at zero in the distribution of earnings. Income taxes draw profit observations towards zero while negative special items pull loss observations away from zero. These earnings components are thus expected to contribute to a discontinuity even in the absence of discretion. We show our results are not an artifact of deflation and that other common components of earnings do not have similar effects on the earnings distribution around zero.

Forward-neutral valuation relationships for options on zero coupon bonds

This paper extends the literature on Risk-Neutral Valuation Relationships (RNVRs) to derive valuation formulae for options on zero coupon bonds when interest rates are stochastic. We develop Forward-Neutral Valuation Relationships (FNVRs) for the transformed-bounded random walk class. Our transformed-bounded random walk family of forward bond price processes implies that (i) the prices of the zero coupon bonds are bounded below at zero and above at one, and (ii) negative continuously compounded interest rates are ruled out. FNVRs are frameworks for option pricing, where the forward prices of the options are martingales independent of the market prices of risk. We illustrate the generality and flexibility of our approach with models that yield several new closed-form solutions for call and put options on discount bonds.     

Bivariate income distributions for assessing inequality and poverty under dependent samples

As indicators of social welfare, the incidence of inequality and poverty is of ongoing concern to policy makers and researchers alike. Of particular interest are the changes in inequality and poverty over time, which are typically assessed through the estimation of income distributions. From this, income inequality and poverty measures, along with their differences and standard errors, can be derived and compared. With panel data becoming more frequently used to make such comparisons, traditional methods which treat income distributions from different years independently and estimate them on a univariate basis, fail to capture the dependence inherent in a sample taken from a panel study. Consequently, parameter estimates are likely to be less efficient, and the standard errors for between-year differences in various inequality and poverty measures will be incorrect. This paper addresses the issue of sample dependence by suggesting a number of bivariate distributions, with Singh–Maddala or Dagum marginals, for a partially dependent sample of household income for two years. Specifically, the distributions considered are the bivariate Singh–Maddala distribution, proposed by Takahasi (1965), and bivariate distributions belonging to the copula class of multivariate distributions, which are an increasingly popular approach to modelling joint distributions. Each bivariate income distribution is estimated via full information maximum likelihood using data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey for 2001 and 2005. Parameter estimates for each bivariate income distribution are used to obtain values for mean income and modal income, the Gini inequality coefficient and the headcount ratio poverty measure, along with their differences, enabling the assessment of changes in such measures over time. In addition, the standard errors of each summary measure and their differences, which are of particular interest in this analysis, are calculated using the delta method.     

A practical solution to the problem of ultimate ruin probability

Abstract

It was the Swiss actuary Chr. Moser who, in lectures at Bern University at the turn of the century, gave the name “self-renewing aggregate” to what Vajda (1947) has called the “unstationary community” of lives, namely where deaths at any epoch are immediately replaced by an equivalent number of births. It was Moser too (1926) who coined the expression “steady state” for the stationary community in which the age distribution at any time follows the life table (King, 1887). With such a distinguished actuarial history, excellently summarized by Saxer (1958, Ch. IV), it behoves every actuary to know at least the definitions and modus operandi of today's so-called renewal (point), or recurrent event, processes.     

Distribution of parallel exchange rates in African countries

This paper investigates the distribution of parallel exchange rates in African countries using exploratory data analysis techniques and model fitting. Stable laws are fitted to empirical distributions using the maximum likelihood estimation method. Empirical evidence supports the stable hypothesis these distributions are positively skewed and have tails that are much heavier than Gaussian counterparts. The stable hypothesis is further supported by the “converging variance test,” which suggests that these distributions have infinite variance.