On Shifted Geometric INAR(1) Models Based on Geometric Counting Series

Two types of shifted geometric integer valued autoregressive models of order one (SGINAR(1)) are proposed. Both are based on the thinning operator generated by counting series of i.i.d. geometric random variables. Their correlation properties are derived and compared. Also, regression and conditional variance are considered. Nonparametric estimators of model parameters are obtained and their asymptotic characterizations are given. Finally, these two models are applied to a real-life data set and they are compared to some referent INAR(1) models.     

The Marshall-Olkin Fréchet Distribution

We introduce a new distribution, namely Marshall–Olkin Fréchet distribution. The probability density and hazard rate functions are derived and their shape properties are considered. Expressions for the nth moments are given. Various results with respect to quantiles, Rényi entropy and order statistics are obtained. The unknown parameters of the new distribution are estimated using the maximum likelihood estimation method adopting three different iterative procedures. The model is applied on a real data set on survival times.

[Supplementary materials are available for this article. Go to the publisher's online edition of Communications in Statistics—Theory and Methods for the following free supplemental resource: A file that will allow the random variables from MOF distribution to be generated.]     

Estimation in a bivariate integer-valued autoregressive process

ABSTRACT

A bivariate integer-valued autoregressive time series model is presented. The model structure is based on binomial thinning. The unconditional and conditional first and second moments are considered. Correlation structure of marginal processes is shown to be analogous to the ARMA(2, 1) model. Some estimation methods such as the Yule–Walker and conditional least squares are considered and the asymptotic distributions of the obtained estimators are derived. Comparison between bivariate model with binomial thinning and bivariate model with negative binomial thinning is given.     

On some moving-average processes with exponentially distributed innovations

Summary In this paper we discusse the stationary sequence of random variables which are formed from an independent identically distributed sequence, according to the moving-average model of ordern. Some properties of the process are considered. The joint bivariate exponential distribution is given, as well as the distribution of the sum.     

Sustainable Development of Maritime Tourism in Croatia 2007–2015

This paper’s objective has been an analysis of the sustainable development of Croatia’s maritime tourism. In order to define the main characteristics and determinants of the maritime tourism, a model of growth has been used. The evaluation and analysis of the relevant variables and the resulting growth rates have been aimed at a scientific formulation of the results of the sustainable development analysis of the maritime tourism in the Republic of Croatia. Combinations of a number of scientific methods have been used, among which the most relevant are statistical and mathematical methods, method of model drawing, analysis and synthesis, induction and deduction. The basic hypothesis has been confirmed through the direct growth rates of the chosen model variables. It has been confirmed that, based on scientific insights into the sustainable development of the maritime tourism, it is possible to suggest a new model of its sustainable development in Croatia for the period 2007–2015.      

A generalized semi-Pareto minification process

In this paper a generalization of the semi-Pareto autoregressive minification process of the first order is given. The necessary and sufficient condition for stationarity of the process is determined. It is shown that the process is ergodic and uniformly mixing. The joint survival function and the joint density function of the random variables X _n+h and X _n are determined. The extremes of the random variables X ₁, X ₂, ..., X _n and the geometric extremes of random variables X ₁, X ₂, ..., X _N are derived and their asymptotic distributions are discussed. The estimation of the parameters is discussed and some numerical results are given.     

Sexual and Reproductive Strategies Among Serbian Gypsies

This paper deals with a full range of sexual and reproductive behaviors among different tribes of Gypsies in Serbia. The examined traits include rates of fertility, mortality, age distribution, education, crime rates, and parental care. In addition, Gypsy traditions of culturally prescribed sexual behavior are also studied. It is found that Gypsy tribes employ different reproductive strategies, ranging from an extreme, for humans, r (reproductive) strategy to a more typical K (parental) strategy. The reasons bringing about these differences come from the Gypsies' readiness to adjust their behavior and reproduction in order to create the most favorable strategy in a given environment. This paper elucidates and contrasts the more typical r-selected Gypsies with a group of K-selected Gypsies living in a Serbian village.     

Streamlining for democracy: Intercultural predispositions of the Croatian secondary school population

This work interprets the results of empirical research conducted into the intercultural predispositions of secondary school students in Croatia. Data were collected in 1993 and in 1998, using specially constructed questionnaires in which, for a variety of democratic values, a Likert-type battery of questions, were given to respondents. In 1993 the stratified research sample consisted only of secondary school students, while in 1998 the research sample also included students, parents and teachers. An analysis of the results shows that: (1) students had, generally speaking, affirmative attitudes both in 1993 and 1998 and that the hierarchy of support for these values remained the same; and (2) all three groups examined in 1998 shared a common hierarchy of values. However, they differed in the degree to which they accepted democratic values; teachers ranked the highest, students the lowest. The fact that students' attitudes were much closer to their parents' than to their teachers' leads to the conclusion that schools are not the major factor in the "political" socialization of young people in Croatia. This indicates a need for the introduction of new curriculum in all secondary schools. This curriculum should include educational content that emphasizes democratic values and intercultural relations, and methods that stress students' participation through action, reciprocity, dialogue, and solidarity, led by well-trained teachers.