Showing papers in "Metrika in 2005"

Estimation of P[Y < X] for generalized exponential distribution

Abstract: This paper deals with the estimation of P[Y < X] when X and Y are two independent generalized exponential distributions with different shape parameters but having the same scale parameters. The maximum likelihood estimator and its asymptotic distribution is obtained. The asymptotic distribution is used to construct an asymptotic confidence interval of P[Y < X]. Assuming that the common scale parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are obtained. Different confidence intervals are proposed. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of a simulated data set has also been presented for illustrative purposes.

Recent and classical tests for exponentiality: a partial review with comparisons

Abstract: A wide selection of classical and recent tests for exponentiality are discussed and compared. The classical procedures include the statistics of Kolmogorov-Smirnov and Cramer-von Mises, a statistic based on spacings, and a method involving the score function. Among the most recent approaches emphasized are methods based on the empirical Laplace transform and the empirical characteristic function, a method based on entropy as well as tests of the Kolmogorov-Smirnov and Cramer-von Mises type that utilize a characterization of exponentiality via the mean residual life function. We also propose a new goodness-of-fit test utilizing a novel characterization of the exponential distribution through its characteristic function. The finite-sample performance of the tests is investigated in an extensive simulation study.

A method to obtain new copulas from a given one

Abstract: Given a strictly increasing continuous function φ from [0, 1] to [0, 1] and its pseudo-inverse φ[−1], conditions that φ must satisfy for C φ (x1, . . . ,xn)=φ[−1](C(φ(x1), . . . ,φ(xn))) to be a copula for any copula C are studied. Some basic properties of the copulas obtained in this way are analyzed and several examples of generator functions φ that can be used to construct copulas C φ are presented. In this manner, a method to obtain from a given copula C a variety of new copulas is provided. This method generalizes that used to construct Archimedean copulas in which the original copula C is the product copula, and it is related with mixtures

On some applications of Hadamard matrices

Abstract: Modern communications systems are heavily reliant on statistical techniques to recover information in the presence of noise and interference. One of the mathematical structures used to achieve this goal is Hadamard matrices. They are used in many different ways and some examples are given. This paper concentrates on code division multiple access systems where Hadamard matrices are used for user separation. Two older techniques from design and analysis of experiments which rely on similar processes are also included. We give a short bibliography (from the thousands produced by a google search) of applications of Hadamard matrices appearing since the paper of Hedayat and Wallis in 1978 and some applications in telecommunications.

Bayesian Life Test Planning for the Weibull Distribution with Given Shape Parameter

Abstract: This paper describes Bayesian methods for life test planning with Type II censored data from a Weibull distribution, when the Weibull shape parameter is given. We use conjugate prior distributions and criteria based on estimating a quantile of interest of the lifetime distribution. One criterion is based on a precision factor for a credibility interval for a distribution quantile and the other is based on the length of the credibility interval. We provide simple closed form expressions for the relationship between the needed number of failures and the precision criteria. Examples are used to illustrate the results.

A catalogue of three-level regular fractional factorial designs

Abstract: A common problem that experimenters face is the choice of fractional factorial designs. Minimum aberration designs are commonly used in practice. There are situations in which other designs meet practical needs better. A catalogue of designs would help experimenters choose the best design. Based on coding theory, new methods are proposed to classify and rank fractional factorial designs efficiently. We have completely enumerated all 27 and 81-run designs, 243-run designs of resolution IV or higher, and 729-run designs of resolution V or higher. A collection of useful fractional factorial designs with 27, 81, 243 and 729 runs is given. This extends the work of Ch93, who gave a collection of fractional factorial designs with 16, 27, 32 and 64 runs.

A two-stage stratified Warner’s randomized response model using optimal allocation

Abstract: This paper applies Kim and Warde’s (2004) stratified Warner’s randomized response model to Mangat and Singh’s (1990) two-stage randomized response model. The proposed stratified randomized response model has an optimal allocation and a large gain in precision. Hence, the estimator based on the proposed method is more efficient than Kim and Warde’s (2004) and Mangat and Singh’s (1990) estimators under the conditions presented in both the case of completely truthful reporting and that of not completely truthful reporting by the respondents.

A Simple Derivation of Moments of the Exponentiated Weibull Distribution

Abstract: The Exponentiated Weibull family is an extension of the Weibull family obtained by adding an additional shape parameter. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates which are quite common in reliability and biological studies. As with any other distribution, many of its interesting characteristics and features can be studied through moments. Presently, moments of this distribution are available only under certain restrictions. In this paper, a general derivation of moments without any restriction whatsoever is proposed. A compact expression for moments is presented.

Multiple aspect testing for case-control designs

Abstract: When testing for the equality of two distributions in a case-control design with treatment effects presumed to act possibly on more than one aspect, different tests may be properly considered for testing for different features of a null hypothesis, leading to the multiple aspect testing issue. Two different aspects are therefore of interest: the location-aspect, based on the comparison of location indexes, and the distributional-aspect, based on the comparison of the empirical distribution functions. A simulation study shows that the combined testing procedure exhibits a good robust overall performance, and an application in biomedical research is also presented.

Tests for location-scale families based on the empirical characteristic function

Abstract: A class of procedures is presented for using random samples to test the fit of location-scale families—distributions F(·;θ1,θ2) such that Z=(X−θ1)/θ2 has distribution Open image in new window Working with empirically standardized data, Open image in new window the test statistic is a measure of Open image in new window distance between the empirical characteristic function, Open image in new windowOpen image in new window and the c.f. of Z under the null hypothesis, ϕ0(t). The closed-form test statistic is derived by integrating over Open image in new window the product of a weight function times Open image in new window Using as weight function for each location-scale family the squared modulus of ϕ0 itself presents a unified test procedure. Included as special cases are well-known tests for normal and Cauchy laws. Small-sample powers are compared with those of Anderson-Darling tests for each of seven univariate location-scale families.

Monitoring the cross-covariances of a multivariate time series

Abstract: In this paper sequential procedures are proposed for jointly monitoring all elements of the covariance matrix at lag 0 of a multivariate time series. All control charts are based on exponential smoothing. As a measure of the distance between the target values and the actual values the Mahalanobis distance is used. It is distinguished between residual control schemes and modified control schemes. Several properties of these charts are proved assuming the target process to be a stationary Gaussian process. Within an extensive Monte Carlo study all procedures are compared with each other. As a measure of the performance of a control chart the average run length is used. An empirical example about Eastern European stock markets illustrates how the autocovariance and the cross-covariance structure of financial assets can be monitored by these methods.

Optimality and efficiency of circular neighbor balanced designs for correlated observations

Abstract: The purpose of this paper is to apply the Kunert and Martin’s (2000b) method for finding optimal designs into the case of dependence. Using this method we study optimality of circular neighbor balanced designs at distances 1 and 2 under the one-dimensional interference model with errors correlated according to a circular autoregressive process. We determine the efficiency of binary designs for specified values of correlation coefficient, for which these designs are not optimal.

The median of the poisson distribution

Abstract: The purpose of this paper is twofold: first, to provide a closed form expression for the median of the Poisson distribution and, second, to improve the known estimates of the difference between the median and the mean of the Poisson distribution. We use elementary techniques based on the monotonicity of certain sequences involving tail probabilities of the Poisson distribution and the Central Limit Theorem

Randomized response technique for two sensitive characteristics at the same time

Abstract: In this paper we present a randomized response technique which can be used to estimate the proportion of individuals having two sensitive characteristics at the same time. The information obtained from this procedure can be used for weighting (post-stratification) purposes.

Projection properties of certain three level orthogonal arrays

Abstract: Two orthogonal arrays based on 3 symbols are said to be isomorphic or combinatorially equivalent if one can be obtained from the other by a sequence of row permutations, column permutations and permutations of symbols in each column. Orthogonal arrays are used as screening designs to identify active main effects, after which the properties of the subdesign for estimating these effects and possibly their interactions become important. Such a subdesign is known as a ``projection design''. In this paper we have identified all the inequivalent projection designs of an OA(27,13,3,2), an OA(18,7,3,2) and an OA(36,13,3,2) into k=3,4 and 5 factors. It is shown that the generalized wordlength pattern criterion proposed by Ma and Fang [23] can distinguish between most, but not all, inequivalent classes. We propose an extension of the Es2 criterion (which is commonly used for measuring efficiency of 2-level designs) to distinguish further between the non-isomorphic classes and to measure the efficiency of the designs in these classes. Some concepts on generalized resolution are also discussed.

Recurrence relations for moment and conditional moment generating functions of generalized order statistics

Abstract: In this paper, we obtain recurrence relations for moment and conditional moment generating functions of generalized order statistics (gos) based on random samples drawn from a population whose distribution is a member of a doubly truncated class of distributions denoted by . Members of the class are characterized in Section (2) based on recurrence relations for moment generating functions (moments) of gos. In Section (3), we shall characterize members of the class based on recurrence relations for conditional moment generating functions (conditional moments) of gos. These results are specialized to the left, right and non-truncated cases. Ordinary order statistics and ordinary record values are also obtained as special cases of the gos. Characterizations of some members of class such as the Weibull, compound Weibull, Pareto, power function (beta is a special case), Gompertz and compound Gompertz distributions are given as illustrative examples.

Process capability assessment for index C pk based on bayesian approach

Abstract: Process capability indices have been proposed in the manufacturing industry to provide numerical measures on process reproduction capability, which are effective tools for quality assurance and guidance for process improvement. In process capability analysis, the usual practice for testing capability indices from sample data are based on traditional distribution frequency approach. Bayesian statistical techniques are an alternative to the frequency approach. Shiau, Chiang and Hung (1999) applied Bayesian method to index C pm and the index C pk but under the restriction that the process mean μ equals to the midpoint of the two specification limits, m. We note that this restriction is a rather impractical assumption for most factory applications, since in this case C pk will reduce to C p . In this paper, we consider testing the most popular capability index C pk for general situation – no restriction on the process mean based on Bayesian approach. The results obtained are more general and practical for real applications. We derive the posterior probability, p, for which the process under investigation is capable and propose accordingly a Bayesian procedure for capability testing. To make this Bayesian procedure practical for in-plant applications, we tabulate the minimum values of Ĉ pk for which the posterior probability p reaches desirable confidence levels with various pre-specified capability levels.

Construction of Block Designs Admitting an Abelian Automorphism Group

Abstract: Construction of block designs admitting an action of a presumed automorphism group consists of two basic steps: 1.construction of orbit structures for the given automorphism group, 2. construction of block designs for the orbit structures obtained in 1. For an abelian group G, the second step, called indexing, often lasts too long, because there are too many possibilities to be enumerated with today's computer facilities. To make such a construction possible we use a principal series of the group G to obtain a refinement of the orbit structures.

Analysis of a change-point regression problem in quality control by partial sums processes and Kolmogorov type tests

Abstract: In practice, it is an important problem (especially in quality control) to secure that a known regression function occurs during a certain period in time. In the present paper, we consider the change-point problem that under the null hypothesis this known regression function occurs. As alternative, we consider a certain non-parametric class of functions that is of particular interest in quality control. We analyze this test problem by using partial sums of the data. Asymptotically, we get Brownian motion and Brownian motion with trend (≠0) under the hypothesis and under the alternative, respectively. We prove that tests based on partial sums have a larger power when the partial sums are taken from the time reversed data. This can be quantitatively determined in an asymptotic way by some new results on Kolmogorov type tests for Brownian motion with trend. We illustrate our results by a certain model that is interesting in quality control and by an example with real data.

Choice of optimal initial designs in sequential experiments

Abstract: Combined-optimal designs (Li and Lin, 2003) are obviously the best choices for the initial designs if we partition the experiment into two parts with equal size to obtain some information about the process, especially for the case not considering the blocking factor. In this paper, the definition of combined-optimal design is extended to the case when blocking factor is significant, and this new class of designs is called blocked combined-optimal designs. Some general results are obtained which relate 2k−pIII initial designs with their complementary designs when Open image in new window, where n=2k−p. By applying these results, we are able to characterize 2k−pIII combined-optimal designs or blocked combined-optimal designs in terms of their complementary designs. It is also proved that both 2k−pIII combined-optimal and blocked combined-optimal designs are not minimum aberration designs when Open image in new window and n−1−k > 2. And some combined-optimal and blocked combined-optimal designs with 16 and 32 runs are constructed for illustration.

Verständnis und Organisation des Controlling in kleinen und mittleren Unternehmen

Abstract: Wahrend sich Veroffentlichungen zur betriebswortschaftlichen Teildisziplin Controlling anfangs vornehmlich auf die institutionelle Verankerung und die Gestaltung von Controllinginstrumenten fur Grosunternehmen beschrankten, geriet in den vergangenen 15 Jahren auch das Controlling in mittelstandischen Unternehmen starker in den Fokus Unterschiede lassen sich dabei vor allem aufgrund spezifischer Anforderungen kleiner und mittlerer Unternehmen (KMU) hinsichtlich ihrer begrenzten Ressourcenausstattung sowie ihrer fuhrungsspezifischen Besonderheiten vermuten, doch besteht Bedarf an neueren empirischen Erkenntnissen hierzu Vor dem Hintergrund dieses Mangels liefert der vorliegende Beitrag neue Befunde aus einer empirischen Befragung zum vorherrschenden Controllingverstandnis sowie zur Ausgestaltung der Controllingorganisation bei KMU

The maximal {-1,1}-determinant of order 15

Abstract: We demonstrate the D-optimality of the 15×15 −1,1-matrix discovered independently by Smith and Cohn. This matrix has determinant 25515×214 and is unique up to Hadamard equivalence. In addition, we confirm the previously established values of the maximal determinant for all other odd orders up to 21, excluding 19, and we improve the upper bounds on the maximal determinant in orders 29, 33, and 37.

Asymptotic seat bias formulas

Abstract: Apportionment methods are used to round the vote proportions of parties in a proportional representation system to integer numbers of seats in the parliament. Seat biases quantify by how much on average a particular apportionment method favors larger (or smaller) parties. In this paper, we prove a previous conjecture on asymptotic seat biases of stationary divisor methods and the quota method of greatest remainders, as the size of the parliament tends to infinity.

On exact D-optimal designs with 2 two-level factors and n autocorrelated observations

Abstract: In this paper we consider the exact D-optimal designs for estimation of the unknown parameters in the two factors, each at only two-level, main effects model with autocorrelated errors. The vector of the n random errors in the observed responses is assumed to follow a first-order autoregressive model (AR(1)). The exact D-optimal designs seek the optimal combinations of the design levels as well as the optimal run orders, so that the determinant of the information matrix of BLUE’s for the unknown parameters is maximized. Bora-Senta and Moyssiadis (1999) gave some conjectures about the exact D-optimal designs based on their experience of several exhaustive searches. In this paper their conjectures are partially proved to be true.

On the two-sided power distribution

Abstract: This paper concerns a two-parameter two-sided power distribution introduced by van Dorp and Kotz on the interval [0,1]. We introduce a reformulated two-sided power distribution (with the same number of parameters) and provide evidence to prove that it is more flexible than the one suggested by van Dorp and Kotz. We derive various properties of the new distribution as well as provide several hitherto unknown properties of the distribution due to van Dorp and Kotz. We also discuss estimation by the method of moments and the method of maximum likelihood.

Revenue Management Konzepte zur Entscheidungsunterstützung bei der Annahme von Kundenaufträgen

Abstract: Die Herstellung von kundenindividuellen Produkten fuhrt zu einem heterogen zusammengesetzten Produktionsprogramm, das in eine unregelmasige Kapazitatsauslastung mundet. Mit der Entscheidung uber die Annahme von Kundenauftragen wird diese Kapazitatsauslastung determiniert, wodurch dieser Prozess einer fundierten Entscheidungsunterstutzung bedarf. In der Dienstleistungsproduktion werden Revenue Management Konzepte bei der Auftragsannahme erfolgreich in der Praxis eingesetzt. Dieser Beitrag legt die grundlegenden Konzepte dar und untersucht die Anwendbarkeit dieser bei kundenindividueller Produktion am Beispiel der Eisen und Stahl erzeugenden Industrie.

Reconstruction of previous failure times and records

Abstract: For the sequences of independent identically distributed random variables with continuous distributions, we provide the optimal upper bounds for the increments of order and record statistics under condition that the values of future order statistics and records are known. The bounds are expressed in terms of quantiles and absolute moments centered about the quantiles of the parent distribution. We also describe the distributions which approach the bounds with arbitrary desired accuracy.

A new bivariate distribution in natural exponential family

Abstract: We propose a new bivariate distribution following a GLM form i.e., natural exponential family given the constantly correlated covariance matrix. The proposed distribution can represent an independent bivariate gamma distribution as a special case. In order to derive the distribution we utilize an integrating factor method to satisfy the integrability condition of the quasi-score function. The derived distribution becomes a mixture of discrete and absolute continuous distributions. The proposal of our new bivariate distribution will make it possible to develop some bivariate generalized linear models. Further the discrete correlated bivariate distribution will also arise from an independent bivariate Poisson mass function by compounding our proposed distribution (Iwasaki and Tsubaki, 2002).

Optimal criteria and equivalence for nonregular fractional factorial designs

Abstract: By considering the so-called algebraic orthogonality among experimental runs, this paper introduces a new criterion, minimum inner-product moment (MIPM), for general asymmetrical designs, and shows that MIPM is equivalent to the minimum moment aberration (MMA) criterion for the natural weights. Furthermore, the relationship between the generalized minimum aberration (GMA) and some model-dependent efficiency criteria is investigated by using the complex contrasts. Thus, two new justifications of GMA criterion is given from the points of view of orthogonality among experimental runs and design efficiency. They are generalizations of the related results of Butler (2003) and Cheng, Deng, and Tang (2002) for two-level factorial designs.