Goodness-of-fit testing for Weibull-type behavior

In the process of analyzing data, testing the fit of a model under consideration is a prerequisite for performing inference about the model parameters. In this paper we examine the goodness-of-fit testing problem for assessing whether a sample is consistent with the Weibull-type model. Inspired by the Jackson and the Lewis test statistics, originally proposed as goodness-of-fit tests for the exponential distribution, we introduce two new statistics for testing Weibull-type behavior, and study their asymptotic properties. Moreover, given that the statistics are ratios of estimators for the Weibull-tail coefficient, we obtain new estimators for the latter, and establish their consistency and asymptotic normality. The small sample behavior of our statistics and estimators is evaluated on the basis of a simulation study.     

The Impact of Societal Instability on Demographic Behavior (The Case of Soviet and Post-Soviet Russia)

Population Research and Policy Review - This paper investigates the impact of sociopolitical instability on fertility. We develop a model linking macro-level instability with its perceptions as...     

Sleep patterns and sleepiness of working college students

The double journey (work and study) may result or aggravate health problems, including sleep disturbances, as observed in previous studies with high school students. The aim of this study is to analyze the sleep-wake cycle and perceived sleepiness of working college students during weekdays. Twenty-three healthy college male students, 21-24 years old, working during the day and attending classes in the evening, participated in this study. During five consecutive days, the students filled out daily activities logs and wore actigraphs. Mean sleeping time was lower than 6 hours per night. No significant differences were observed in the sleep-wake cycle during the weekdays. The observed lack of changes in the sleepwake cycle of these college students might occur as participants were not on a free schedule, but exposed to social constraints, as was the regular attendance to evening college and day work activities. Sleepiness worsened over the evening school hours. Those results show the burden carried by College students who perform double activities - work and study.     

Generalized functions in the qualitative study of heterogeneous populations

ABSTRACT

Solutions from non-smooth functional spaces, including generalized functions and measures, often appear in optimal control theory but are avoided in applications. They are however useful in finding the optimal distribution of investments into new and old capital equipment under improving technology. The corresponding economic problem involves optimal control in a linear Lotka-McKendrik model of age-structured population. Optimal solutions do not exist in normal functional classes and, so, generalized functions are used to construct the solutions. The optimal age-distributions of capital and investment include the Dirac function and are interpreted as instantaneous investment in equipment of certain age. A numerical simulation completes the presentation of the dynamics.     

Approximations of the Distributions of Test Statistics for Homogeneity of a Product Multinomial Model

Statistics R ^a based on power divergence can be used for testing the homogeneity of a product multinomial model. All R ^a have the same chi-square limiting distribution under the null hypothesis of homogeneity. R ⁰ is the log likelihood ratio statistic and R ¹ is Pearson's X ² statistic. In this article, we consider improvement of approximation of the distribution of R ^a under the homogeneity hypothesis. The expression of the asymptotic expansion of distribution of R ^a under the homogeneity hypothesis is investigated. The expression consists of continuous and discontinuous terms. Using the continuous term of the expression, a new approximation of the distribution of R ^a is proposed. A moment-corrected type of chi-square approximation is also derived. By numerical comparison, we show that both of the approximations perform much better than that of usual chi-square approximation for the statistics R ^a when a ≤ 0, which include the log likelihood ratio statistic.     

Generalized Kernel Estimators for the Weibull-Tail Coefficient

We introduce new families of estimators for the Weibull-tail coefficient, obtained from a weighted sum of a power transformation of excesses over a high random threshold. Asymptotic normality of the estimators is proven for an intermediate sequence of upper order statistics, and under classical regularity conditions for L-statistics and a second-order condition on the tail behavior of the underlying distribution. The small sample performance of two specific examples of kernel functions is evaluated in a simulation study.     

Testing monotonicity of pricing kernels

The behaviour of market agents has been extensively covered in the literature. Risk averse behaviour, described by Von Neumann and Morgenstern (Theory of games and economic behavior. Princeton University Press, Princeton, 1944) via a concave utility function, is considered to be a cornerstone of classical economics. Agents prefer a fixed profit over an uncertain choice with the same expected value, however, lately there has been a lot of discussion about the empirical evidence of such risk averse behaviour. Some authors have shown that there are regions where market utility functions are locally convex. In this paper we construct a test to verify uncertainty about the concavity of agents’ utility function by testing the monotonicity of empirical pricing kernels (EPKs). A monotonically decreasing EPK corresponds to a concave utility function while a not monotonically decreasing EPK means non-averse pattern on one or more intervals of the utility function. We investigate the EPKs for German DAX data for the years 2000, 2002 and 2004 and find evidence of non-concave utility functions: the null hypothesis of a monotonically decreasing pricing kernel is rejected for the data under consideration. The test is based on approximations of spacings through exponential random variables. In a simulation we investigate its performance and calculate the critical values (surface).     

A Bidimensional Model of Acculturation for Korean American Older Adults

With the growth of immigrant populations and the increasing awareness and appreciation for the cultural diversity in the U.S., the present study assessed a model of acculturation with a sample of Korean American older adults. We addressed a bidimensional model of acculturation, considering both orientations toward home and host-cultures, and assessed the relevance of Berry's four-cell typology of acculturation (integration, assimilation, separation, and marginalization). Based on the unique characteristics of the present sample, including that they were all born in Korea and had been exposed to their home culture for a substantial amount of time, we hypothesized that their orientation towards original culture would be strong and that simple application of Berry's four-cell typology would not be relevant. As expected, scores on Korean orientation were distributed toward the high end of the scale, suggesting a high level of familiarity and adherence to the original culture; scores on American orientation were correspondingly low. Cluster analysis showed that a two-cluster model was an optimal group classification in the sample used in this investigation. The groups were identified as "integrated group" and "separated group." Compared to the separated group, integrated group was more likely to be younger, married, and educated. More years of residence in the U.S. and better physical and mental health were observed among those who were integrated. The findings call attention to the needs to consider the unique nature of immigrant samples in order to adequately apply the acculturation typologies.     

Optimal Dynamic Pricing of Perishable Items by a Monopolist Facing Strategic Consumers

We introduce a dynamic pricing model for a monopolistic company selling a perishable product to a finite population of strategic consumers (customers who are aware that pricing is dynamic and may time their purchases strategically). This problem is modeled as a stochastic dynamic game in which the company's objective is to maximize total expected revenues, and each customer maximizes the expected present value of utility. We prove the existence of a unique subgame‐perfect equilibrium pricing policy, provide equilibrium optimality conditions for both customer and seller, and prove monotonicity results for special cases. We demonstrate through numerical examples that a company that ignores strategic consumer behavior may receive much lower total revenues than one that uses the strategic equilibrium pricing policy. We also show that, when the initial capacity is a decision variable, it can be used together with the appropriate pricing policy to effectively reduce the impact of strategic consumer behavior. The proposed model is computationally tractable for problems of realistic size.