Bayes, Neyman and Neyman-Bayes Inference for Queueing Systems

In this paper we will use the Bayesian inference for the parameters that appear in the queueing systems. We will estimate these parameters and we will build confidence intervals and significance tests for them, considering the parameters of the exponential Poisson and geometric distribution. We will also use the Neyman and the Neyman-Bayes inference for the exponential and Poisson distribution.parameters estimation, confidence intervals, statistical tests, Bayes

Modeling the fraud-like investment founds by Petri nets

In this paper we model the fraud-like investment founds using place-transition Petri nets. We will also classify the business using regression line in order to find the possible fraud-like investment founds. In these regression lines we compute analytical the mark of a place in function of some other elements of the Petri net, and next we express this value in function of the same elements using regression. From the identity of the coefficients we find a ratio between two weights of arcs. We make also a program where the marks and transitions are implemented as classes for Petri nets, and, using the heritage mechanism we extend the Petri net to Petri net with priorities.Petri nets, fraud-like investment founds, objects programming.

Pattern classification using polynomial and linear regression

In this paper we will classify patterns using an algorithm analogous to the k-means algorithm and the regression polynomial of the degree k (for instance, if k=1 we obtain the regression line, and if k=2 we obtain the regression parable), and the regression hyper-plane. We will also present a financial application in which we apply these regressions if the points represent the interests for accounts with different terms.Regression, pattern classification, k-means

Simulation of queueing systems with many stations and of queueing networks using copulas

In this paper we will generate queueing systems with c stations where the inter-arrival time and the c service times depend through a c+1 copula C. We will consider two models: first when the customer does not know the order of service times for the free service channels (he/she chooses the service channel randomly), and the second when he/she knows this order (he/she chooses the fastest free service channel). The marginals can be exponential, Erlang or hyper-exponential.Queueing systems, copula, simulation.

Linear Programming by Solving Systems of Differential Equations Using Game Theory

In this paper we will solve some linear programming problems by solving systems of differential equations using game theory. The linear programming problem must be a classical constraints problem or a classical menu problem, i.e. a maximization/minimization problem in the canonical form with all the coefficients (from objective function, constraints matrix and right sides) positive. Firstly we will transform the linear programming problem such that the new problem and its dual have to be solved in order to find the Nash equilibrium of a matriceal game. Next we find the Nash equilibrium by solving a system of differential equations as we know from evolutionary game theory, and we express the solution of the obtained linear programming problem (by the above transformation of the initial problem) using the Nash equilibrium and the corresponding mixed optimal strategies. Finally, we transform the solution of the obtained problem to obtain the solution of the initial problem. We make also a program to implement the algorithm presented in the paper.Linear programming, evolutionary game theory, Nash equilibrium.

Pattern classification using principal components regression

In this paper we will classify patterns using an algorithm analogous to the k-means algorithm and the principal components regression (PCR). We will also present a financial application in which we apply PCR if the points represent the interests for accounts with different terms.Principal components regression, pattern classification, k-means

Gordon and Newell queueing networks and copulas

In this paper we have found an analytical formula for a copula that connects the numbers Ni of customers in the nodes of a Gordon and Newell queueing network. We have considered two cases: the first one is the case of the network with 2 nodes, and the second one is the case of the network with at least 3 nodes. The analytical formula for the second case has been found for the most general case (none of the constants from a list is equal to a given value), and the other particular cases have been obtained by limit.Gordon and Newell queueing networks, copulas.

Informational Criteria for the Homoscedasticity of Errors

In this paper we will test the homoscedasticity of errors using the Goldfeld-Quandt test and we will classify the points using the explanatory variable by which we sort them. We will also use the Hartley test for the equality of the class error variances (if we have at least two classes). For all the points (only one class) and all the possible classifications for which we have homoscedasticity we will compute some informational criteria like Akaike ( AIC=Akaike Informational Criterion) and Schwartz ( BIC=Bayes Informational Criterion). Of course, from these classifications we will choose that classification with the minimum of the considered criterion. As application, we have monthly data from November 1990 to November 2008 concerning the price indexes for services, the price indexes for food and for the price indexes of non-food goods.homoscedasticity, classification, informational criteria, price indexes

Pattern Classification Using Secondary Components Perceptron and Economic Applications

In this paper we will classify patterns using a modified Perceptron algorithm (Dumitrache et al., 1999). The generalization uses the eigenvalues and the eigenvectors of the sample covariance matrix, as we did for classifying patterns using PCR (Ciuiu 2007b).We shall also define measurements for the cohesion of the obtained classes and of the separation between them. The first economic application considered in the paper is a consumer behavior model (Jula 2003), and the second is the same financial application for classifying banks (Ciuiu, 2007a, Ciuiu, 2007b), where we have used regression for classification.Perceptron, principal and secondary components, consumption, banks

Gordon and Newell queueing networks and copulas

In this paper we have found an analytical formula for a copula that connects the numbers Ni of customers in the nodes of a Gordon and Newell queueing network. We have considered two cases: the first one is the case of the network with 2 nodes, and the second one is the case of the network with at least 3 nodes. The analytical formula for the second case has been found for the most general case (none of the constants from a list is equal to a given value), and the other particular cases have been obtained by limit