A new generalized Weibull distribution in income economic inequality curves

Researchers have been developing various extensions and modified forms of the Weibull distribution to enhance its capability for modeling and fitting different data sets. In this note, we investigate the potential usefulness of the new modification to the standard Weibull distribution called odd Weibull distribution in income economic inequality studies. Some mathematical and statistical properties of this model are proposed. We obtain explicit expressions for the first incomplete moment, quantile function, Lorenz and Zenga curves and related inequality indices. In addition to the well-known stochastic order based on Lorenz curve, the stochastic order based on Zenga curve is considered. Since the new generalized Weibull distribution seems to be suitable to model wealth, financial, actuarial and especially income distributions, these findings are fundamental in the understanding of how parameter values are related to inequality. Also, the estimation of parameters by maximum likelihood and moment methods is discussed. Finally, this distribution has been fitted to United States and Austrian income data sets and has been found to fit remarkably well in compare with the other widely used income models.     

The context of employment discrimination: interpreting the findings of a field experiment

Although field experiments have documented the contemporary relevance of discrimination in employment, theories developed to explain the dynamics of differential treatment cannot account for differences across organizational and institutional contexts. In this article, I address this shortcoming by presenting the main empirical findings from a multi‐method research project, in which a field experiment of ethnic discrimination in the Norwegian labour market was complemented with forty‐two in‐depth interviews with employers who were observed in the first stage of the study. While the experimental data support earlier findings in documenting that ethnic discrimination indeed takes place, the qualitative material suggests that theorizing in the field experiment literature have been too concerned with individual and intra‐psychic explanations. Discriminatory outcomes in employment processes seems to be more dependent on contextual factors such as the number of applications received, whether requirements are specified, and the degree to which recruitment procedures are formalized. I argue that different contexts of employment provide different opportunity structures for discrimination, a finding with important theoretical and methodological implications.     

TEACHING PROFESSIONAL WRITING TO FAMILY THERAPISTS: THREE APPROACHES

The authors present three educational approaches designed to demystify the writing process and to support better writing skills among family therapists. One framework is an academic course in professional writing, another is a writing seminar for family therapy and physician trainees within a medical school setting, and the third is a 2-hour continuing education writing workshop for family therapists. Each is replicable within a variety of settings.     

Design optimization using ANOVA

This paper describes the design optimization of a robot sensor used for locating 3-D objects employing the Taguchi method in a computer simulation scenario. The location information from the sensor is to be utilized to control the movements of an industrial robot in a 'pick-and-place' or assembly operation. The Taguchi method, which is based on the Analysis-of-Variance (ANOVA) approach, is utilized to improve the performance of the sensor over a wider operating range. A review of the Taguchi method is presented along with step-by-step implementation details to identify and optimize the design parameters of the sensor. The method allows us to gauge the impact of various interactions present in the sensor system exclusively and permits us to single out those factors that have a dominant influence on the overall performance of the sensor. The investigation suggests that the Taguchi method is a more structured and efficient approach for achieving a robust design compared with the classical full factorial design approach.     

LOG-PERIODOGRAM ESTIMATION OF LONG MEMORY VOLATILITY DEPENDENCIES WITH CONDITIONALLY HEAVY TAILED RETURNS

Many recent papers have used semiparametric methods, especially the log-periodogram regression, to detect and estimate long memory in the volatility of asset returns. In these papers, the volatility is proxied by measures such as squared, log-squared, and absolute returns. While the evidence for the existence of long memory is strong using any of these measures, the actual long memory parameter estimates can be sensitive to which measure is used. In Monte-Carlo simulations, I find that if the data is conditionally leptokurtic, the log-periodogram regression estimator using squared returns has a large downward bias, which is avoided by using other volatility measures. In United States stock return data, I find that squared returns give much lower estimates of the long memory parameter than the alternative volatility measures, which is consistent with the simulation results. I conclude that researchers should avoid using the squared returns in the semiparametric estimation of long memory volatility dependencies.     

Type I error rates from likelihood‐based repeated measures analyses of incomplete longitudinal data

The last observation carried forward (LOCF) approach is commonly utilized to handle missing values in the primary analysis of clinical trials. However, recent evidence suggests that likelihood‐based analyses developed under the missing at random (MAR) framework are sensible alternatives. The objective of this study was to assess the Type I error rates from a likelihood‐based MAR approach – mixed‐model repeated measures (MMRM) – compared with LOCF when estimating treatment contrasts for mean change from baseline to endpoint (Δ). Data emulating neuropsychiatric clinical trials were simulated in a 4 × 4 factorial arrangement of scenarios, using four patterns of mean changes over time and four strategies for deleting data to generate subject dropout via an MAR mechanism. In data with no dropout, estimates of Δ and SE_Δ from MMRM and LOCF were identical. In data with dropout, the Type I error rates (averaged across all scenarios) for MMRM and LOCF were 5.49% and 16.76%, respectively. In 11 of the 16 scenarios, the Type I error rate from MMRM was at least 1.00% closer to the expected rate of 5.00% than the corresponding rate from LOCF. In no scenario did LOCF yield a Type I error rate that was at least 1.00% closer to the expected rate than the corresponding rate from MMRM. The average estimate of SE_Δ from MMRM was greater in data with dropout than in complete data, whereas the average estimate of SE_Δ from LOCF was smaller in data with dropout than in complete data, suggesting that standard errors from MMRM better reflected the uncertainty in the data. The results from this investigation support those from previous studies, which found that MMRM provided reasonable control of Type I error even in the presence of MNAR missingness. No universally best approach to analysis of longitudinal data exists. However, likelihood‐based MAR approaches have been shown to perform well in a variety of situations and are a sensible alternative to the LOCF approach. MNAR methods can be used within a sensitivity analysis framework to test the potential presence and impact of MNAR data, thereby assessing robustness of results from an MAR method. Copyright © 2004 John Wiley & Sons, Ltd.