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## Economic and Financial Modeling with Mathematica®

### Economic and Financial Modeling with Mathematica® (1993-01-01) , January 01, 1993

## The lattice structure of nonlinear congruential pseudorandom numbers

### Metrika (1993-12-01) 40: 115-120 , December 01, 1993

Several known deficiencies of the classical linear congruential method for generating uniform pseudorandom numbers led to the development of nonlinear congruential pseudorandom number generators. In the present paper a general class of nonlinear congruential methods with prime power modulus is considered. It is proved that these generators show certain undesirable linear structures, too, which stem from the composite nature of the modulus.

## Back Matter - Statistical Design and Analysis for Intercropping Experiments

### Statistical Design and Analysis for Intercropping Experiments (1993-01-01) , January 01, 1993

## On some important statistical problems

### Statistics and Computing (1993-12-01) 3: 185-187 , December 01, 1993

## Spherical symmetry: An elementary justification

### Journal of the Italian Statistical Society (1993-04-01) 2: 1-16 , April 01, 1993

### Summary

The present paper includes characterizations of the conditions of spherical symmetry and of centered spherical symmetry. These characterizations provide an empirical justification for the above mentioned conditions of symmetry.

## Bayesian Econometrics: Conjugate Analysis and Rejection Sampling

### Economic and Financial Modeling with Mathematica® (1993-01-01): 344-367 , January 01, 1993

In real-world problems we are invariably faced with making decisions in an environment of uncertainty (see also the chapter by R. Korsan in this volume). A statistical paradigm then becomes essential for extracting information from observed data and using this to improve our knowledge about the world (inference), and thus guiding us in the decision problem at hand. The underlying probability interpretation for a Bayesian is a subjective one, referring to a personal degree of belief. The rules of probability calculus are used to examine how prior beliefs are transformed to posterior beliefs by incorporating data information. The sampling model is a “window” [see Poirier (1988)] through which the researcher views the world. Here we only consider cases where such a model is parameterized by a parameter vector *θ* of finite dimension. A Bayesian then focuses on the inference on *θ* (treated as a random variable) given the observed data *Y* (fixed), summarized in the posterior density *p*(*θ*|*Y*). The observations in *Y* define a mapping from the prior *p*(*θ*) into *p*(*θ*|*Y*). This posterior distribution can also be used to integrate out the parameters when we are interested in forecasting future values, say, *Ỹ*, leading to the post-sample predictive density *p*(*Ỹ*|*Y*) = *∫**p*(*Ỹ*|*Y*, *θ*)*p*(*θ*|*Y*)*d**θ* where *p*(*Ỹ*|*Y*, *θ*) is obtained from the sampling model.

## Some characterizations of distributions of the exponential-type

### Statistical Papers (1993-12-01) 34: 175-180 , December 01, 1993

We consider a particular subclass of the two-parameter exponential family with natural parameters γ_{1}, γ_{2} and characterize those distributions of the family having a ratio of the mean value and the variance that is a linear function of γ_{1} by the form of the moment generating function. As special cases we find the normal and the gamma distributions.

## Useful matrix transformations for panel data analysis: a survey

### Statistical Papers (1993-12-01) 34: 281-301 , December 01, 1993

This paper surveys some useful matrix transformations which simplify the derivation of GLS as WLS in an error component model. This is particularly important for large panel data applications where brute force inversion of large data matrices may not be feasible. This WLS transformation is known in the literature as the Fuller and Baltese (1974) transformation and its extension to error component models with heteroscedasticity, serial correlation, unbalancedness as well as a set of seemingly unrelated regressions are considered.

## Tomáš Havránek

### Computational Aspects of Model Choice (1993-01-01): 1-5 , January 01, 1993

Tomáš Havránek was born in Prague in the family of well known bohemist academician B. Havránek. His carrier started in 1972 just after finishing Charles University and fulfilling military service. The first job has been that of statistician — consultant in the Institute of Microbiology of the Czechoslovak Academy of Sciences. Here he split interests into the two parts, the routine statistical analysis of biological data and his own scientific problems. And on this place he has found a lot of ideas for books, papers and lectures which followed soon.