Stochastic choice models differ in a number of ways from the other types of consumer choice behavior models. They also differ as to how they handle customer heterogeneity. Some models try to segment customer into homogeneous subsets and analyze them separately. Brand choice models are usually distinguished according to how they deal with population heterogeneity, purchase event feedback and exogenous market factors. Much of the information used in a number of popular brand choice models can be extracted from a brand-switching matrix. The elements in this matrix are obtained from purchase information on two occasions separated in time.
 In this paper we present the most popular methods that have been used until now in the analysis of brand switching matrix, giving emphasis to latent class models. Questions that are dealt with are the following: Which of these methods give us the best information about the consumer’s behavior? Assuming misclassification error is present, which technique best recovers the true market structure? Are there situations under which one model may fit the data better than another one?

PANAGIOTA ANASTASIOU
Department of Statistics, AUEB
Athens, Greece

Income arises from a number of different sources and in general it is not equally distributed. On the contrary the unequal distribution of income and wealth is one of the most prominent features of our society. The study of income distribution is the focus of the present paper which consists of two parts.
The first part covers a number of important theoretical aspects of the subject. Presentation of certain distributions that may be used to describe income distribution and discussion of the criteria that they should satisfy. Presentation of income distribution generation formulas. Identification of the factors affecting income inequality. Suggestion of measures for income inequality. Study of the relation between reported and true income. The second part is an application of the Pareto’s Law to Greek income data for the period 1960-1995.

XANTHI BALOGIANNI
Department of Statistics, AUEB
Athens, Greece
 
 

Autoregressive conditional heteroscedastic (ARCH) models, introduced by Engle (1982), have been widely used in financial time series analysis and particularly in analyzing the risk of holding an asset, evaluating the price of an option, forecasting time varying confidence intervals and obtaining more efficient estimators under the existence of heteroscedasticity. In the recent literature one can find several forms of ARCH models have been considered for the description of some of the characteristics of financial markets. The problem of selecting the model that describes best the movement of the series under study is therefore of practical importance.
Most of the methods used in the literature for selecting the appropriate model are based on evaluating the ability of the models to describe the data. Standard model selection criteria such as the Akaike Information Criterion (1973) and the Schwartz Bayesian Criterion (1978) have been widely used in the ARCH literature, despite the fact that their statistical properties in the ARCH context are unknown.
In this paper, an alternative model selection approach is examined based on the evaluation of the predictability of the models. Attention is focused on the behavior of the estimators of conditional means or of conditional variances. In both cases the Correlated Gamma Ratio Distribution (CGR) developed by Panaretos et al. (1997) in the context of linear models, is being considered to be applied in the context of ARCH models.

STAVROS DEGIANNAKIS
Department of Statistics, AUEB
Athens, Greece
 
 

We study the multivariate unobserved ARCH and the latent factor ARCH models which capture the cross-covariance changes commonly appearing in the financial time-series. We adopt Bayesian inference via Markov Chain Monte Carlo and we present easy to implement  algorithms which use only Gibbs sampling steps. We illustrate our methodology with data from four exhange rate series.

STEFANOS GIAKOUMATOS
Department of Statistics, AUEB
Athens, Greece
 
 

The most fundamental element of representative democracy is the Electoral System, as it translates vote totals into parliamentary seats. An important topic is the choice of the electoral system, which will be applied in an election, because parliamentary seats allocated to political parties differ when a different system is used.
In the present paper we focus attention on the Greek parliamentary electoral systems of the period 1974-1996. Our aim is to analyse statistically these electoral systems and compare them by using measures of disproportionality. We also examine the behaviour of electoral systems when one or more electoral parameters change. Sensitivity analysis is performed in order to find out which percentages of total votes give majority of parliamentary seats to a party, for the six electoral systems used in Greek elections in the period under study.

AIKATERINI KALOGIROU
Department of Statistics, AUEB
Athens, Greece
 
 

The compilation of a price index that truly reflects the present consumption patterns of the economy, is necessary for a number of reasons, the most important being the need to record changes linked to the value of money. Associated to the achievement of price stability by member states of the European Union, the Consumer Price Index is a statistical measure, which reflects the effects of price variations for a given quantitative and qualitative composition of the goods and services purchased by households during the period covered by the Household Budget Survey. The importance of the use of the CPI in the formulation of social and economic policies makes it obvious that predicting its value and as well as the values of its subdivisions is an interesting problem.
In this paper, the problem of forecasting future values of the basic groups of the Consumer Price Index is examined. For this purpose, 12 time series have been considered, that correspond to the indexes of the 12 basic subdivisions of the Consumer Price Index, for the period from January 1988 to September 1998. The forecast of the General consumer price index is obtained as a weighted average of the forecasts of the indexes of the basic groups. The source of the data is the National Statistical Service of Greece. The Box and Jenkins method is applied for the creation of appropriate forecasting models of the12 basic groups of the Consumer Price Index, using SPSS for the analysis of the time series, the estimation of the parameters of the models and for the diagnostic checking.

POLYXENI LIVA
Department of Statistics, AUEB
Athens, Greece
 
 

Process capability indices (PCI’s) aim to quantify the capability of a process to produce according to some given specifications. These specifications are determined through the lower specification limit, the upper specification limit and the target value. A variety of PCI’s can be found in the literature and the most prominent among them are Cp, Cpk, Cpm and Cpmk. The basic drawback of these four indices is that they have been developed under the somewhat restrictive assumption that the distribution of the examined process is normal. For this reason, some modifications of these indices have been proposed in the literature. However, the construction of confidence limits for these modifications without resorting to the method of bootstrap is extremely cumbersome. Moreover, some of these indices do not have a direct association to the proportion of conformance of the process, i.e. to the probability of producing within the specification area.
In this paper, a new PCI is proposed, which is based on the proportion of conformance of the examined process and has several appealing features. Indeed, this index is simple in its assessment and interpretation and is applicable to processes with normal or non-normal distributions. Further, it can be used under either unilateral or bilateral tolerances and the assessment of confidence limits for its true value is not very involved. Moreover, point estimators and confidence limits for the new index are constructed, under several distributional assumptions.

MICHAEL PERAKIS
Department of Statistics, AUEB
Athens, Greece
 
 

We consider queues with multiplexed On-Off fluid inputs under the assumption of exponential Off periods. Refined asymptotics based on the results of Willekens and Teugels (1992) are obtained for the workload distribution under the assumption of On periods with regularly varying tails. The analysis, based on the embedded M/G/1 queue, extends the results in Jelenkovic and Lazar (1999).

DIMITRA PINOTSI
Department of Statistics, AUEB
Athens, Greece
 
 

The increase of criminal activity worldwide calls for cooperation in order to combat crime. All over the world, scientists, including Statisticians, of many seemingly unrelated fields are cooperating in order to find methods to prevent or to reduce crime.
Kent S. Borowick (1997) in "Analysis of low probability count data with applications in crime analysis"(PhD thesis, Baylor University) has performed several statistical analyses on crime data. Using his approach, in this paper we analyze Greek crime data. The data are reported crimes per month or per year for the periods 1987-1997 (for the monthly data) and 1982-1997 (for the annual data). Some of the examined crimes are Commonly Dangerous Crimes, Robbery, Theft, Murder, Rape, Arson, Personal Vengeance, Drug Violations, Smuggling of Antiquities and Beggary. Data about the offenders are also examined.
Multivariate methods such as Principal Component Analysis (PCA), Multidimensional Scaling and Clustering methods are employed in order to map the crime activity in Greece and point out the areas where certain crimes seem to be on the increase. Quality Control is employed in order to make inferences about the months when different crimes are more possible to occur.

ALEXANDRA TSIAMTSIOURI
Department of Statistics, AUEB
Athens, Greece
 
 

An analysis of a class of multivariate ARCH and GARCH models is proposed consisting of parameter estimation and model comparison. We study some models that already exist in the literature, as well as propose a new multivariate GARCH model. Bayesian and classical techniques are used for the estimation of the parameters of the models analyzed, and model comparisons are addressed via predictive distributions. We provide implementation details and illustrations using daily exchange rates of the Athens exchange market.

I. D. VRONTOS
Department of Statistics, AUEB
Athens, Greece
 
 

Daily seizure counts are a prime tool in investigating epileptic disease and examining the effectiveness of certain drugs. Does an epileptic fit make the patient prone to have another fit in the near future? Do unobservable factors exist that may contribute to an epileptic fit? These are a few of many questions that arise in epileptic disease investigations.
 In this paper questions of this nature are investigated on the basis of data on epileptic fit occurrences. These are viewed as time series of counts, i.e. as non-negative, integer-valued stochastic processes in discrete time. We present models that are useful for the modeling of discrete-time dependent counting processes and pay special attention to the integer-valued autoregressive (INAR) and the switching integer-valued autoregressive (SINAR) models. The SINAR model is fitted to a series of daily counts of epileptic seizures of a patient. The EM-algorithm is used in order to estimate the parameters of this model.

NIKKIE YIOKARI
Department of Statistics, AUEB
Athens, Greece