The Extended Skew-Exponential Power Distribution and Its Derivation

We consider an extended family of asymmetric univariate distributions generated using a symmetric density, f, and the cumulative distribution function, G, of a symmetric distribution, which depends on two real-valued parameters λ and β and is such that when β = 0 it includes the entire class of distributions with densities of the form g(z | λ) = 2 G(λ z) f(z). A key element in the construction of random variables distributed according to the family is that they can be represented stochastically as the product of two random variables. From this representation we can readily derive theoretical properties, easy-to-implement simulation schemes, as well as extensions to the multivariate case and an explicit procedure for obtaining the moments. We give special attention to the extended skew-exponential power distribution. We derive its information matrix in order to obtain the asymptotic covariance matrix of the maximum likelihood estimators. Finally, an application to a real data set is reported, which shows that the extended skew-exponential power model can provide a better fit than the skew-exponential power distribution.     

Step-Down diagnostic analysis for monitoring the covariance matrix of bivariate normal processes

ABSTRACT

A comparison among VMIX, VMAX and the adapted step-down Sullivan et al. (SE) tests for covariance matrix under bivariate normal assumption is presented. The type I error and power estimates were obtained by using Monte Carlo simulation under different scenarios with respect to covariance and correlation structures. In general, VMIX was more powerful than VMAX being SE more powerful than both, with few exceptions. SE test is more general since it can be used for normal and non-normal data, with no restriction with respect to the pattern of the covariance matrix shifts, and for larger dimension than the bivariate case.     

Generalized skew-normal models: properties and inference [Statistics 40 (2006) 495–505]

In [H.W. Gómez, H.S. Salinas and H. Bolfarine, Generalized skew-normal models: Properties and inference, Statistics 40(6) (2006), pp. 495–505] introduces a new family of asymmetric distributions that depends on two parameters called, α and β, such as for the particular case β = 0 obtained skew-normal distribution. In this note we give a corrected version for the expression that is used in calculating the moments of such distribution.     

What population studies can do for business

Demographers have a fundamental role to play in planning for the future. They possess a wide range of skills concerning the number, diversity and spatial distribution of the population, which are of value to business concerns. The role of demographers in analysis of census data is of special value. This paper discusses the specific skills acquired by demographers and provides examples of how these skills can be very useful and important in planning in both the private and public sectors. Finally the future of demographic training in Australia is considered by contrasting the APA membership with that of the PAA and considering the need for developing more teaching in demography at Australian tertiary institutions. The role of the APA in improving the status of demography as an important tool for corporate planning for the future is also emphasized.     

Using census data to study elderly migration: problems and possibilities

Although the elderly are the fastest growing of all age groups in developed countries, their migration remains little studied. Elderly migration differs in several fundamental ways from that of other age groups, but many of the data collection and analysis procedures, as well as basic concepts used in censuses, have been developed with the working population in mind and are of limited utility in studying elderly migration. This article discusses some of the problems using census data to identify movers among the elderly population, and to analyze the characteristics of movers and the causes of migration. The author concludes that it is clear that what is needed with respect to census data on elderly migration is not necessarily new questions to be included. Instead, more appropriate decisions need to be made at the stages of deciding what variables to code and what categories are to be included. In addition, at the stage of determining tabulation programs there needs to be greater sensitivity to finer age breakdowns among elderly migrants and to the selection of cross-tabulation variables which are more relevant to issues and problems of the aged. Hugo suggests that an authoritative agency convene a working group to establish guidelines which address the following issues. 1) What are appropriate age breakdowns? 2) What are appropriate variables for detailed cross-tabulations? 3) Exactly what is an appropriate form for migration data to be prepared for multi-regional analysis? 4) What is the most appropriate way of formatting public use sample tapes to make analyses for assisting in the study of elderly migration? 5) How should the institutional population among the aged be dealt with? Another recommendation which arises out of the issues raised here is that, analysts should give a clear indication of what movers are actually missed by census data and which types of movers are included. Awareness of the limitations of particular data sources is of critical significance to meaningful interpretation of results if one is seeking a better understanding of the causes and consequences of important social phenomena.     

A process view of the population turnaround: an Australian rural case study

"This paper provides empirical evidence of local-level demographic and socio-economic changes during the 'population turnaround' decade of 1970 to 1980. The study covers a contiguous area occupied by five small country towns and their trade areas, centred around 80-90 km north of Adelaide [Australia]. These communities were surveyed in detail in 1968 and 1970 in order to make forecasts of demographic change by 1980. In 1980, a replicatory resurvey provided data on various processes of population change operating at grass roots level."     

Sexual Offenses Against Elderly People: Forensic Evaluation and Judicial Outcome

Forensic evaluation reports and judicial outcomes regarding older victims of suspected sexual offenses were retrospectively reviewed. During this period, a total of 14 cases were registered, corresponding to 0.3% of nonfatal crimes against elderly and 0.6% of the total of sexual crimes reported. All the victims were female. The majority lived alone and did not have limitations in communication, orientation, ambulation, or autonomy. The offenders were all male (17 to 81 years old); most were known to the victims and had history of previous disruptive behaviors. The majority of the sexual offenses occurred in the victims’ homes, and the offenders tended to use physical violence. Forensic evaluation was crucial for the identification of physical and biological evidence, and forensic conclusions were positively correlated with the judicial outcome of each case. High prosecution and conviction rates were also observed.