Some results on moments and cumulants

Abstract

In the present paper we discuss various results related to moments and cumulants of probability distributions and approximations to probability distributions. As the approximations are not necessarily probability distributions themselves, we shall apply the concept of moments and cumulants to more general functions. Recursions are deduced for moments and cumulants of functions in the form R_k [a, b] as defined by Dhaene & Sundt (1996). We deduce a simple relation between the De Pril transform and the cumulants of a function. This relation is applied to some classes of approximations to probability distributions, in particular the approximations of Hipp and De Pril.     

Customer loyalty to food retailers in Northern Ireland: ‘devoted loyals’ or ‘promiscuous switchers’?

Store loyalty is a major challenge for food retailers, and the food retail market in Northern Ireland has been subject to considerable change in the past decade. Although shoppers will often patronize many stores, they typically have a primary affiliation to a ‘main’ food store that captures the majority of their food purchases. This study uses a unique approach to segmenting customers into groups based on loyalty in terms of both the type of data used to generate a loyalty score and the data collection techniques used. Innovative projective techniques have been used alongside traditional questioning techniques to reveal ‘behavioural’ and ‘emotional’ loyalty indicators, and in doing so create a holistic measure of customer loyalty to a main food store, allowing customers to be segmented into groups based on loyalty. A paper‐based questionnaire was administered to 152 food shoppers from throughout Northern Ireland. Responses to traditional questioning formats and projective techniques (cartoon friends and mini case studies) were analysed and used to generate a loyalty score for each respondent. The first group of customers nearly always visit the same store, are willing to recommend the store to others and are less likely to switch to a competitor, even when offered an incentive to do so. They also rate the ‘hard’ attributes of this store highly. As a result of these characteristics, customers in this segment were termed ‘devoted loyals’. The second group of customers may occasionally use a different supermarket for food shopping, some would consider switching to a competitor if offered an incentive, and they rate ‘hard’ store attributes at a slightly lower level than the ‘devoted loyals’. Based on their group profile, these customers were assigned the title of ‘susceptibles’. The third group of customers are less willing to actively encourage friends and family to shop at a specific store. Many in this group did not consider their current store as their number one choice in the next few years. An incentive to switch to a competitor store is more likely to trigger a transfer of loyalty by this group. These customers were termed ‘promiscuous switchers’.     

Testing for mean reversion in heteroskedastic data II: Autoregression tests based on Gibbs-sampling-augmented randomization

A decade ago Fama and French [Fama, E.G., French, K.R., 1988. Permanent and temporary components of stock prices. J. Political Econ. 96 (2) 246–273] estimated that 40% of variation in stock returns was predictable over horizons of 3–5 yr, which they attributed to a mean reverting stationary component in prices. While it has been clear that the Depression and war years exert a strong influence on these estimates, it has not been clear whether the large returns of that period contribute to the information in the data or rather are a source of noise to be discounted in estimation. This paper uses the Gibbs-sampling-augmented randomization methodology to address the problem of heteroskedasticity in estimation of multi-period return autoregressions. Extending the sample period to 1995, we find little evidence of mean reversion. Examining subsamples, only 1926–1946 provides any evidence of mean reversion, while the post war period is characterized by mean aversion. A test of structural change suggests that this difference between pre and post war periods is significant.     

What do schools produce? Implications of multiple outputs in education

This article introduces the hypothesis that secondary schools create at least two competing 'outputs' standardized test scores and high school completion - which may be seen as substitutes. This hypothesis provides an explanation for the decrease in standardized test scores that occurred over the last 40 years along with an often overlooked increase in high school graduation rates. The article presents evidence supporting this hypothesis as well as evidence that different schools face different tradeoffs and discusses the policy implications of such trade-offs.     

An error-correction model of the demand for equity mutual funds in the U.S. 1973–1994

The purpose of this paper is to estimate an error-correction model of the U.S. demand for equity mutual funds. Using annual data for the period 1973–1994, this study finds that changes in the demand for equity mutual funds have been significantly influenced by the changes in the rate of return on equity mutual funds and savings deposits, as well as by the growth in income over the long run. The authors would like to thank an anonymous referee of this journal for many useful comments and suggestions.     

Experience matters in principal preparation

An act of leadership is always an act of practical theory. We lead because we hold visions of the world as it ought to be, because of the not yet, because of the potential that we see in ideas and people. Yet, there still exists a perceived binary between leadership theory (in the strong sense) and leadership practice, a binary that divides organizations, classrooms, and the differing bodies of leadership literature. In this Symposium, Duncan Waite and his colleagues discuss the barriers they have faced in bringing theory to the educational leadership classroom, as well as the promise they feel theory holds for more productive, equitable, and humane schooling organizations.     

PSM system upgrade in response to an Occupational Safety and Health Administration NEP inspection

This article presents a brief analysis of the Occupational Safety and Health Administration (OSHA) Petroleum Refinery Process Safety Management National Emphasis Program (NEP) citation results as of early 2009. It includes trends distilled from the OSHA inspections performed to date. Recommendations for preparing for PSM NEP level inspections are provided. A proven approach to designing and implementing an upgrade project for OSHA process safety management systems and EPA risk management program is described. The model presented can be targeted to a facility's NEP specific citations or used for a general PSM system effectiveness upgrade. This article includes recommendations for improving PSM as a result of an NEP inspection. The recommendations are for the PSM elements that routinely have major OSHA citations; that is: Operating Procedures, Mechanical Integrity, Process Hazards Analysis, Process Safety Information, Management of Change, and Incident Investigations. © 2009 American Institute of Chemical Engineers Process Saf Prog 2009     

SUSTAINING THE GOOSE THAT LAYS THE GOLDEN EGG: A CONTINUOUS TREATMENT OF TECHNOLOGICAL TRANSFER

This paper proposes a simple model of the trade-offs perceived by innovating firms when investing in countries with limited intellectual property rights (IPR). The model allows for a continuous treatment of technology transfer and production cost gains occurring through FDI. While it does not consider possible changes in rates of innovation caused by changes in IPR in developing countries, it allows one to uncover a potentially non-monotonic relationship between welfare and IPR in the recipient country.     

Endogenous discounting, the world saving glut and the U.S. current account

We study the evolution of the U.S. current account in a two-country dynamic stochastic endowment model in which a single non-state contingent bond is the only internationally traded asset. The paper focuses on the world ‘saving glut’ as the primary cause of continual deterioration in the current account and departs from the standard framework by introducing a three-parameter model of the subjective discount factor that depends on societal (per capita) variables that are external to household choices. When agents in the model are presented with U.S. and rest-of-world endowment data as the realization of the exogenous state vector, endogenously driven short-run international differences in subjective discounting that display increasing relative U.S. impatience create saving and current account imbalances that matches patterns observed in the data.