DSpace Collection: 2009 Volume 19
http://hdl.handle.net/10525/2108
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Optimum Chemical Balance Weighing Design under Certain Condition
http://hdl.handle.net/10525/2244
Title: Optimum Chemical Balance Weighing Design under Certain Condition<br/><br/>Authors: Ceranka, Bronislaw; Graczyk, Malgorzata<br/><br/>Abstract: The problem of estimation of unknown weights of p objects is considered. The experiment is carried out according to the standard Gauss-Markoff model of the chemical balance weighing design. Existence conditions of the optimum design are given. New construction method of the optimum design based on the set of the incidence matrices of the ternary balanced block designs is presented.<br/><br/>Description: 2000 Mathematics Subject Classification: 62K05, 05B05.Some Bounds for Almost Absorbing Birth and Death Processes with Catastrophes
http://hdl.handle.net/10525/2243
Title: Some Bounds for Almost Absorbing Birth and Death Processes with Catastrophes<br/><br/>Authors: Zeifman, Alexander; Chegodaev, Alexander; Satin, Yakov<br/><br/>Abstract: We consider nonstationary almost absorbing birth and death processes (BDPs) with catastrophes. The bounds of the rate of convergence to the limit regime and the estimates of the limit probabilities are obtained. We also study the bounds for the mean of the process and consider a queuing example.<br/><br/>Description: 2000 Mathematics Subject Classification: 60J27.Suboptimal Nonparametric Hypotheses Discriminating from Small Dependent Observations
http://hdl.handle.net/10525/2242
Title: Suboptimal Nonparametric Hypotheses Discriminating from Small Dependent Observations<br/><br/>Authors: Tsitovich, Ivan<br/><br/>Abstract: It is considered a discriminating of nonparametric hypotheses generated a small dependence of data. The suboptimal test with a guaranteed decision is proposed and numerical results illustrated the procedure suboptimality properties are presented.<br/><br/>Description: 2000 Mathematics Subject Classification: 62L10.Suboptimal Multistage Nonparametric Hypotheses Test
http://hdl.handle.net/10525/2241
Title: Suboptimal Multistage Nonparametric Hypotheses Test<br/><br/>Authors: Tsitovich, Fedor<br/><br/>Abstract: At the paper it is considered a discriminating of nonparametric hypotheses that are neighborhoods of given distributions. The suboptimal test means that distributions from the same neighborhoods are indistinguishable. Multistage hypotheses tests have practical advantages over fully-sequential tests in many situations. The suboptimal test with a guaranteed decision is generalized to the multistage case. Using a loss function that is a linear combination of sampling costs and error probabilities, the suboptimal multistage test of nonparametric hypotheses is constructed.<br/><br/>Description: 2000 Mathematics Subject Classification: 62L10, 62L15.Direction Finding Estimators of Cyclostationary Signals in Array Processing for Microwave Power Transmission
http://hdl.handle.net/10525/2240
Title: Direction Finding Estimators of Cyclostationary Signals in Array Processing for Microwave Power Transmission<br/><br/>Authors: Shishkov, B.; Hashimoto, K.; Matsumoto, H.; Shinohara, N.; Mitani, T.<br/><br/>Abstract: A solar power satellite is paid attention to as a clean, inexhaustible large- scale base-load power supply. The following technology related to beam control is used: A pilot signal is sent from the power receiving site and after direction of arrival estimation the beam is directed back to the earth by same direction. A novel direction-finding algorithm based on linear prediction technique for exploiting cyclostationary statistical information (spatial and temporal) is explored. Many modulated communication signals exhibit a cyclostationarity (or periodic correlation) property, corresponding to the underlying periodicity arising from carrier frequencies or baud rates. The problem was solved by using both cyclic second-order statistics and cyclic higher-order statistics. By evaluating the corresponding cyclic statistics of the received data at certain cycle frequencies, we can extract the cyclic correlations of only signals with the same cycle frequency and null out the cyclic correlations of stationary additive noise and all other co-channel interferences with different cycle frequencies. Thus, the signal detection capability can be significantly improved. The proposed algorithms employ cyclic higher-order statistics of the array output and suppress additive Gaussian noise of unknown spectral content, even when the noise shares common cycle frequencies with the non-Gaussian signals of interest. The proposed method completely exploits temporal information (multiple lag ), and also can correctly estimate direction of arrival of desired signals by suppressing undesired signals. Our approach was generalized over direction of arrival estimation of cyclostationary coherent signals. In this paper, we propose a new approach for exploiting cyclostationarity that seems to be more advanced in comparison with the other existing direction finding algorithms.Bootstrap for Critical Branching Process with Non-Stationary Immigration
http://hdl.handle.net/10525/2238
Title: Bootstrap for Critical Branching Process with Non-Stationary Immigration<br/><br/>Authors: Rahimov, I.; H. Omar, M.<br/><br/>Abstract: In the critical branching process with a stationary immigration the standard parametric bootstrap for an estimator of the offspring mean is invalid. We consider the process with non-stationary immigration, whose mean and variance α(n) and β(n) are finite for each n ≥ 1 and are regularly varying sequences with nonnegative exponents α and β, respectively. It turns out that if α(n) → ∞ and β(n) = o(nα2(n)) as n → ∞, then the standard parametric bootstrap procedure leads to a valid approximation for the distribution of the conditional least squares estimator. We state a theorem which justifies the validity of the bootstrap. By Monte-Carlo and bootstrap simulations for the process we confirm the theoretical findings. The simulation study highlights the validity and utility of the bootstrap in this model as it mimics the Monte-Carlo pivots even when generation size is small.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 60J80, Secondary 62F12, 60G99.Branching Processes in Autoregressive Random Environment
http://hdl.handle.net/10525/2237
Title: Branching Processes in Autoregressive Random Environment<br/><br/>Authors: Mayster, Penka<br/><br/>Abstract: We consider the model of alternating branching processes where two Markov branching processes act alternately at random observation and treatment times. The sequences of cycles (observation, treatment) = (δn, τn) constitute a random environment for branching mechanisms. We suppose in addition that the lengths of the cycles σ n = δn + τn are generated by the linear additive first order autoregressive schema EAR(1).<br/><br/>Description: 2000 Mathematics Subject Classification: 60J80, 60K05.A Note on Bayesian Estimation for the Negative-Binomial Model
http://hdl.handle.net/10525/2235
Title: A Note on Bayesian Estimation for the Negative-Binomial Model<br/><br/>Authors: L. Lio, Y.<br/><br/>Abstract: The Negative Binomial model, which is generated by a simple mixture model, has been widely applied in the social, health and economic market prediction. The most commonly used methods were the maximum likelihood estimate (MLE) and the moment method estimate (MME). Bradlow et al. (2002) proposed a Bayesian inference with beta-prime and Pearson Type VI as priors for the negative binomial distribution. It is due to the complicated posterior densities of interest not amenable to closed-form integration. A polynomial type expansion for the gamma function had been used to derive approximations for posterior densities by Bradlow et al. (2002). In this note, different parameters of interest are used to re-parameterize the model. Beta and gamma priors are introduced for the parameters and a sampling procedure is proposed to evaluate the Bayes estimates of the parameters. Through the computer simulation, the Bayesian estimates for the parameters of interest are studied via mean squared error and variance. Finally, the proposed Bayesian estimate is applied to model two real data sets.<br/><br/>Description: 2000 Mathematics Subject Classification: 62F15.Multiresponse Robust Engineering: Case with Errors in Factor Levels
http://hdl.handle.net/10525/2234
Title: Multiresponse Robust Engineering: Case with Errors in Factor Levels<br/><br/>Authors: Koleva, Elena; Vuchkov, Ivan; Velev, Kamen<br/><br/>Abstract: The model-based robust approach for improving the quality of the process is successfully applied to different industrial processes. In the case of multiple correlated responses the estimation of the mean and variance models of the quality characteristics in production conditions, taking into account the correlation between the multiple responses, together with the heteroscedasticity of the observations due to errors in the factor levels is considered at multivariate regression fit, robust engineering modeling and the optimization stages. The application of the proposed method gives the possibility to use raw industrial data for mean and variance models estimation and leads to reduction of the predicted variance of the responses in production conditions. The proposed approach is applied for electron beam melting and refining experiments.<br/><br/>Description: 2000 Mathematics Subject Classification: 62J05, 62J10, 62F35, 62H12, 62P30.Functional Transfer Theorems for Maxima of Stationary Processes
http://hdl.handle.net/10525/2232
Title: Functional Transfer Theorems for Maxima of Stationary Processes<br/><br/>Authors: Kalcheva Jordanova, Pavlina<br/><br/>Abstract: In this paper we discuss the problem of finding the limit process of sequences of continuous time random processes, which are constructed as properly affine transformed maxima of random number identically distributed random variables. The max-increments of these processes are dependent. First we work under the well known conditions D (un) and D' (un) of Leadbetter, Lindgren and Rootzen, (1983). Further we investigate the case of moving average sequence. The distribution function of the noise components is assumed to have regularly varying tails or is subexponential and belongs to the max-domain of attraction of Gumbel distribution or belongs to the max-domain of attraction of Weibull distribution. We work with random time-components which are a.s. strictly increasing to infinity. In particular their counting process is a mixed Poisson process or a renewal process with regularly varying tails with parameter β ∈ (0, 1). Here is proved that such sequences of random processes converges weakly to a compound extremal process.<br/><br/>Description: 2000 Mathematics Subject Classification: 60G70, 60F12, 60G10.Early Detection of Emergent Events Based on an Extremal Process Approach
http://hdl.handle.net/10525/2231
Title: Early Detection of Emergent Events Based on an Extremal Process Approach<br/><br/>Authors: Jacob, Christine; Khraibani, Zaher; Pancheva, Elisaveta<br/><br/>Abstract: We explore a real renewal process representing the successive arrival times of some event (ex.: clinical case of an infectious disease). We wish to test that the first observed events are sporadic, and not emergent. We also compare this distribution to the one got under the independency of standard setting. We finally illustrate this approach by testing on the first observations of a simulation of a slowly emergent phenomenon that this phenomenon is a sporadic one, and we show that the statistic based on the extremal process is much more efficient and robust than the statistic based on the record values.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 60G70, 62F03.Strong Consistency of the Conditional Least Squares Estimator for a Nonstationary Process. Example of the Garch Model
http://hdl.handle.net/10525/2230
Title: Strong Consistency of the Conditional Least Squares Estimator for a Nonstationary Process. Example of the Garch Model<br/><br/>Authors: Jacob, Christine<br/><br/>Abstract: We consider the Conditional Least Squares Estimator (CLSE) of a unknown parameter θ0 ∈ Rp of the conditional expectation of a real stochastic process {Yn} having finite first two conditional moments E(Yn|Fn-1)< ∞, E(Yn2 | F n-1)< ∞ at each time n, where E(Yn|Fn-1) is Lipschitz and may be nonlinear in θ0 and {Fn} is an increasing sequence of σ-algebra. We generalize to this class of processes the necessary and sufficient condition got for the strong consistency of the CLSE of θ0 in the particular linear deterministic (or linear stochastic if p = 1) model E(Yn|Fn-1) = θT0Wn. We illustrate this theoretical result with examples, mainly a nonstationary GARCH (1,1) model.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary: 62M10, 62J02, 62F12, 62M05, 62P05, 62P10; secondary: 60G46, 60F15.Queue Length Simulations in a Finite Single-line Queueing System with Repeated Calls
http://hdl.handle.net/10525/2228
Title: Queue Length Simulations in a Finite Single-line Queueing System with Repeated Calls<br/><br/>Authors: Ilieva Dragieva, Velika<br/><br/>Abstract: Simulated results about the queue length and the server state in a finite single server queuing system with repeated calls are presented. Formulas for the basic probability characteristics of the corresponding distributions are obtained in previous papers of the author. The numerical values computed according to these formulas are compared with the simulated results. Empirical mean values of the idle period are obtained as well.<br/><br/>Description: 2000 Mathematics Subject Classification: 60K25.On Y-Linked Genes and Bisexual Branching Processes
http://hdl.handle.net/10525/2227
Title: On Y-Linked Genes and Bisexual Branching Processes<br/><br/>Authors: Gonzalez, M.; Gutierrez, C.; Mota, M.<br/><br/>Abstract: In this paper we survey the results concerning the extinction problem for a two-allele Y-linked gene in a two-sex monogamic population, with a preference of females for males carrying one of the two alleles of the gene. First we give the mathematical definition of the Y-linked bisexual branching process to model this situation and study some of its relevant properties. Then, we research the extinction of the population and also the survival of each genotype depending on the behaviour of the other genotype. Finally, we simulate the evolution of the population and conjecture its long term behaviour, for some critical situations.<br/><br/>Description: 2000 Mathematics Subject Classification: 60J80.On a Second Order Condition for Max-Semistable Laws
http://hdl.handle.net/10525/2226
Title: On a Second Order Condition for Max-Semistable Laws<br/><br/>Authors: Canto e Castro, LuIsa; da Graca Temido, Maria<br/><br/>Abstract: In statistics of extremes the great importance of the Normal approximation of intermediate order statistics is well known when the parent distribution function is in a max-stable domain of attraction and verifies the first and the second order extreme value conditions. The generalization of these conditions to max-semistable contexts is the object of this paper, aiming to be a basis of future developments in statistical inference under max-semistability.<br/><br/>Description: 2000 Mathematics Subject Classification: 62G32, 62G20.Tail Inference for a Law in a Max-Semistable Domain of Attraction
http://hdl.handle.net/10525/2225
Title: Tail Inference for a Law in a Max-Semistable Domain of Attraction<br/><br/>Authors: Canto e Castro, Luisa; Dias, Sandra; da Graca Temido, Maria<br/><br/>Abstract: The class of max-semistable distributions appeared in the literature of extremes, in a work of Pancheva (1992), as the limit distribution of samples with size growing geometrically with ratio r > 1. In Canto e Castro et al. (2002) it is proved that any max-semistable distribution function has a logperiodic component and can be characterized by the period therein, by a tail index parameter and by a real function y representing a repetitive pattern. Statistical inference in the max-semistable setup can be performed through convenient sequences of generalized Pickands' statistics, depending on a tuning parameter s. More precisely, in order to obtain estimators for the period and for the tail index, we can use the fact that the mentioned sequences converge in probability only when s = r (or any of its integer powers), having an oscillatory behavior otherwise. This work presents a procedure to estimate the function y as well as high quantiles. The suggested methodologies are applied to real data consisting in seismic moments of major earthquakes in the Pacific Region.<br/><br/>Description: 2000 Mathematics Subject Classification: 62G32, 62G05.