1.
M/M/1 Queues under N-policy involving Batches - Böhm, Walter; Mohanty, Sri Gopal
In this paper the transient solutions of MR/M/1 M/MR/1 models are derived in discrete and continuous time. (author's abstract)

2.
Simple Random Walk Statistics. Part I: Discrete Time Results - Katzenbeisser, Walter; Panny, Wolfgang
In a famous paper Dwass [I9671 proposed a method to deal with rank order statistics, which constitutes a unifying framework to derive various distributional results. In the present paper an alternative method is presented, which allows to extend Dwass's results in several ways, viz. arbitrary endpoints, horizontal steps, and arbitrary probabilities for the three step types. Regarding these extensions the pertaining rank order statistics are extended as well to simple random walk statistics. This method has proved appropriate to generalize all results given by Dwass. Moreover, these discrete time results can be taken as a starting point to derive the...

3.
Some further Results on the Height of Lattice Path - Katzenbeisser, Walter; Panny, Wolfgang
This paper deals with the joint and conditional distributions concerning the maximum of random walk paths and the number of times this maximum is achieved. This joint distribution was studied first by Dwass [1967]. Based on his result, the correlation and some conditional moments are derived. The main contributions are however asymptotic expansions concerning the conditional distribution and conditional moments. (author's abstract)

4.
On the Number of Times where a simple Random Walk reaches its Maximum - Katzenbeisser, Walter; Panny, Wolfgang
Let Q, denote the number of times where a simple random walk reaches its maximum, where the random walk starts at the origin and returns to the origin after 2n steps. Such random walks play an important r6le in probability and statistics. In this paper the distribution and the moments of Q, are considered and their asymptotic behavior is studied. (author's abstract)

5.
Diagnostics in some Discrete Choice Models - Nagel, Herbert; Hatzinger, Reinhold
Discrete choice models form a class of models widely used in econometrics for modelling the individual choice from a finite set of alternatives. The most widely used model is the multinomial logit model, implicitly assuming independence of irrelevant alternatives. A generalization is the nested multinomial logit model, relaxing this strong assurnp tion. Viewing both models as nonlinear regression models a set of diagnostics is derived. This includes a hat matrix, measures of leverage, influence and residuals and an approximation to the parameters for case deletion. In an example for the multinomid logit model a good performance of these diagnostics is...

6.
On Fuzzy Bayesian Inference - Frühwirth-Schnatter, Sylvia
In the paper at hand we apply it to Bayesian statistics to obtain "Fuzzy Bayesian Inference". In the subsequent sections we will discuss a fuzzy valued likelihood function, Bayes' theorem for both fuzzy data and fuzzy priors, a fuzzy Bayes' estimator, fuzzy predictive densities and distributions, and fuzzy H.P.D .-Regions. (author's abstract)

7.
Concentration of Multivariate Statistical Tables - Strasser, Helmut
In this paper we lay the foundation of the concentration measurement for statistical tables with more than two columns. A concentration function and a coefficient of concentration are defined which can be used in a similar way as the Lorenz diagram and the Gini coefficient in case of tables with two columns. For computational purposes we derive an explicit formula and give an algorithm. The mathematics behind our approach is formally equivalent to the statistical theory of the comparison of experiments. (authors' abstract)

8.
Discretization of Markovian Queueing Systems - Böhm, Walter; Mohanty, Sri Gopal
Recently it turned out, that discretizing the time in a markovian queueing model makes it possible to apply powerfull combinatorid methods which often yield surprisingly simple answeres to complicated questions. In this paper we show that the continuous time solution of a markovian queueing model may be obtain from the solution of its discrete time analogue by a simple limiting procedure. Under mild regularity conditions these limiting forms can be shown to be the unique solutions of Kolmogorov's backward differential equations. Furthermore some additional methodological results concerning taboo probabilities and first passage densities are obtained. In a final section some...

9.
Estimation and Experimental Design for Second Kind Regression Models - Fedorov, Valery V.; Hackl, Peter; Müller, Werner
Estimation procedures and optimal designs for estimation of the individual parameters and of the global parameters are discussed under various conditions of prior knowledge. The extension to nonlinear parametrization of the response function ís based on the asymptotical validity of the results for the linear parametrization. For the case where the error variance and the dispersion matrix are unknown, an iterative estimation procedure is suggested. An example based on dental plaque pH profiles demonstrates the improvement that is achieved (a) through using the optimal design or a design that ís close to the optimal, and (b) through taking into account...

10.
Estimation and Experimental Design for Second Kind Regression Models - Fedorov, Valery V.; Hackl, Peter; Müller, Werner
Estimation procedures and optimal designs for estimation of the individual parameters and of the global parameters are discussed under various conditions of prior knowledge. The extension to nonlinear parametrization of the response function ís based on the asymptotical validity of the results for the linear parametrization. For the case where the error variance and the dispersion matrix are unknown, an iterative estimation procedure is suggested. An example based on dental plaque pH profiles demonstrates the improvement that is achieved (a) through using the optimal design or a design that ís close to the optimal, and (b) through taking into account...

11.
Diagnostics in some Discrete Choice Models - Nagel, Herbert; Hatzinger, Reinhold
Discrete choice models form a class of models widely used in econometrics for modelling the individual choice from a finite set of alternatives. The most widely used model is the multinomial logit model, implicitly assuming independence of irrelevant alternatives. A generalization is the nested multinomial logit model, relaxing this strong assurnp tion. Viewing both models as nonlinear regression models a set of diagnostics is derived. This includes a hat matrix, measures of leverage, influence and residuals and an approximation to the parameters for case deletion. In an example for the multinomid logit model a good performance of these diagnostics is...

12.
M/M/1 Queues under N-policy involving Batches - Böhm, Walter; Mohanty, Sri Gopal
In this paper the transient solutions of MR/M/1 M/MR/1 models are derived in discrete and continuous time. (author's abstract)

13.
Discretization of Markovian Queueing Systems - Böhm, Walter; Mohanty, Sri Gopal
Recently it turned out, that discretizing the time in a markovian queueing model makes it possible to apply powerfull combinatorid methods which often yield surprisingly simple answeres to complicated questions. In this paper we show that the continuous time solution of a markovian queueing model may be obtain from the solution of its discrete time analogue by a simple limiting procedure. Under mild regularity conditions these limiting forms can be shown to be the unique solutions of Kolmogorov's backward differential equations. Furthermore some additional methodological results concerning taboo probabilities and first passage densities are obtained. In a final section some...

14.
Some further Results on the Height of Lattice Path - Katzenbeisser, Walter; Panny, Wolfgang
This paper deals with the joint and conditional distributions concerning the maximum of random walk paths and the number of times this maximum is achieved. This joint distribution was studied first by Dwass [1967]. Based on his result, the correlation and some conditional moments are derived. The main contributions are however asymptotic expansions concerning the conditional distribution and conditional moments. (author's abstract)

15.
On the Number of Times where a simple Random Walk reaches its Maximum - Katzenbeisser, Walter; Panny, Wolfgang
Let Q, denote the number of times where a simple random walk reaches its maximum, where the random walk starts at the origin and returns to the origin after 2n steps. Such random walks play an important r6le in probability and statistics. In this paper the distribution and the moments of Q, are considered and their asymptotic behavior is studied. (author's abstract)

16.
Simple Random Walk Statistics. Part I: Discrete Time Results - Katzenbeisser, Walter; Panny, Wolfgang
In a famous paper Dwass [I9671 proposed a method to deal with rank order statistics, which constitutes a unifying framework to derive various distributional results. In the present paper an alternative method is presented, which allows to extend Dwass's results in several ways, viz. arbitrary endpoints, horizontal steps, and arbitrary probabilities for the three step types. Regarding these extensions the pertaining rank order statistics are extended as well to simple random walk statistics. This method has proved appropriate to generalize all results given by Dwass. Moreover, these discrete time results can be taken as a starting point to derive the...

17.
Concentration of Multivariate Statistical Tables - Strasser, Helmut
In this paper we lay the foundation of the concentration measurement for statistical tables with more than two columns. A concentration function and a coefficient of concentration are defined which can be used in a similar way as the Lorenz diagram and the Gini coefficient in case of tables with two columns. For computational purposes we derive an explicit formula and give an algorithm. The mathematics behind our approach is formally equivalent to the statistical theory of the comparison of experiments. (authors' abstract)