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Showing papers on "Parametric statistics published in 1976"


Journal ArticleDOI
TL;DR: A theoretical basis is established for utilizing a penalty-function method to estimate sensitivity information of a localsolution and its associated Lagrange multipliers of a large class of nonlinear programming problems with respect to a general parametric variation in the problem functions.
Abstract: In this paper we establish a theoretical basis for utilizing a penalty-function method to estimate sensitivity information (i.e., the partial derivatives) of a localsolution and its associated Lagrange multipliers of a large class of nonlinear programming problems with respect to a general parametric variation in the problem functions. The local solution is assumed to satisfy the second order sufficient conditions for a strict minimum. Although theoretically valid for higher order derivatives, the analysis concentrates on the estimation of the first order (first partial derivative) sensitivity information, which can be explicitly expressed in terms of the problem functions. For greater clarity, the results are given in terms of the mixed logarithmic-barrier quadratic-loss function. However, the approach is clearly applicable toany algorithm that generates a once differentiable "solution trajectory".

368 citations


Journal ArticleDOI
TL;DR: In this article, a method for summarizing the power of the parametric t tests and the nonparametric Spearman's rho test and Mann-Whitney's test against step and linear trends in a dimensionless trend number is presented.
Abstract: Classical statistical tests for trend, both parametric and nonparametric, assume independence of observations, a condition rarely encountered in time series obtained by using moderate to high sample frequencies. A method is developed for summarizing the power of the parametric t tests and the nonparametric Spearman's rho test and Mann-Whitney's test against step and linear trends in a dimensionless ‘trend number’ which is a function of trend magnitude, standard deviation of the time series, and sample size. For the case of dependent observations, use of an equivalent independent sample size rather than the actual sample size is shown to enable use of the same trend number developed for the independent case. An important related result is the existence of an upper limit on power (trend detectability) over a fixed time horizon, regardless of the number of samples taken, for a lag 1 Markov process.

287 citations



Journal ArticleDOI
TL;DR: In this article, a parametric linear programing (PLP) is used to identify the impulse response function of a linear hydrologic system from a relatively short input-output record.
Abstract: Experience indicates that in the identification of the impulse response function of a linear hydrologic system the results are extremely sensitive to minor errors in the input-output data. In particular, low-amplitude random errors in these data tend to cause severe oscillations in the response function, thereby making it often impossible to obtain a physically realizable solution by conventional methods. Artificial filtering of the input-output records may help, but since the extent of noise is seldom known a priori, one cannot be sure about the proper choice of a cutoff frequency. Such filtering also causes a loss of data at the end points of the record and is therefore undesirable when the number of data points is small. Filtering the response function itself is only effective in eliminating high-frequency oscillations, and it is far less effective when the frequency of the oscillations is relatively low. Clearly, the ultimate goal of identification is to determine a solution which optimizes the predictive capabilities of the linear model. To achieve this goal, it is not sufficient that an observed output be correctly reproduced from a given input; an equally important criterion of optimality is that the shape of the response function be physically plausible. It is shown that one way to obtain a stable and physically realizable response function from a relatively short input-output record is to use parametric linear programing. According to this approach, the problem is formulated as a multicriterion decision process under uncertainty in a manner analogous to that previously described by one of the authors in connection with the inverse problem of groundwater hydrology. Parametric programing serves as a means of generating a continuous set of alternative solutions to the identification problem together with a bicriterion function representing these alternatives. The shape of this bicriterion curve is then used as a guide by the hydrologist in selecting a particular solution when he is relying on his own value judgment. If none of the alternative solutions appears to be physically plausible at this stage, the hydrologist has a further option of imposing modality constraints to eliminate undesirable low-frequency oscillations from the response function. The method is illustrated by two examples, and the results are compared with those obtained by another approach developed previously by one of the authors.

64 citations


Journal ArticleDOI
TL;DR: In this paper, an extended interior penalty function formulation is proposed for determining the transition between the interior and extended parts of a planar orthogonal frame subjected to ground motion, and a rational method is proposed to find the most important parts of the parameter interval.
Abstract: The extended interior penalty function formulation is implemented. A rational method for determining the transition between the interior and extended parts is set forth. The formulation includes a straightforward method for avoiding design points with some negative components, which are physically meaningless in structural analysis. The technique, when extended to problems involving parametric constraints, can facilitate closed form integration of the penalty terms over the most important parts of the parameter interval. The method lends itself well to the use of approximation concepts, such as design variable linking, constraint deletion and Taylor series expansions of response quantities in terms of design variables. Examples demonstrating the algorithm, in the context of planar orthogonal frames subjected to ground motion, are included.

58 citations


Journal ArticleDOI
TL;DR: The spectral bandwidth and acceptance angles are determined by expanding the wave vector mismatch in a Taylor series and retaining terms through second order even when the first order term vanishes.
Abstract: A systematic evaluation of the spectral bandwidth and two acceptance angles of parametric generation processes is presented. The spectral bandwidth and acceptance angles are determined by expanding the wave vector mismatch in a Taylor series and retaining terms through second order. This allows a determination of these parameters even when the first order term vanishes. Conditions where the first order term vanishes are presented and compared with similar cases where the first order term does not vanish.

55 citations


Journal ArticleDOI
TL;DR: In this paper, the first-order Taylor series expansions of the dynamic response functions with respect to the design variables were used for the unconstrained minimization of the exterior penalty function.
Abstract: Dynamic response quantities, treated parametrically in time, are included in the problem for the first time. The method is made efficient by the use of the following approximation concepts: (1)Design variable linking; (2)time parametric constraint deletion; and (3)use of the first-order Taylor series expansions of the dynamic response functions with respect to the design variables. It is found that the feasible design space in an optimum structural design problem in the dynamic response regime is usually disjoint. The Davidon-Fletcher-Powell algorithm is used for the unconstrained minimizations. To successfully implement the exterior penalty function with approximate constraints, dummy boundaries and a new concept of move limits are introduced. It is found that the sinusoidal contributions in the relation between design variables and dynamic response functions can cause infeasible minima of the exterior penalty function.

55 citations


Journal ArticleDOI
TL;DR: In this paper, a new class of optimal design problems that incorporate environmental uncertainty is formulated and related to worst-case design, minimax objective design, and game theory and a numerical solution technique is developed and applied to a weapon allocation problem, a structural design problem with an infinite family of load conditions, and a vibration isolator problem with a band of excitation frequencies.
Abstract: A new class of optimal design problems that incorporates environmental uncertainty is formulated and related to worst-case design, minimax objective design, and game theory. A numerical solution technique is developed and applied to a weapon allocation problem, a structural design problem with an infinite family of load conditions, and a vibration isolator design problem with a band of excitation frequencies.

31 citations


Journal ArticleDOI
Paul Switzer1
TL;DR: In this article, a treatment-effect function t is defined and distribution-free confidence bounds for the function t both in the case where t has specified parametric forms and the case when t is not parameterized.
Abstract: In the usual two-sample problem one is estimating the constant additive effect of a treatment or the additive constant by which two random variables differ. However, if the treatment-effect may depend on the response level, then a more general approach to twosample problems seems appropriate. We define a treatment-effect function t and characterize distribution-free confidence bounds for the function t both in the case where t has specified parametric forms and in the case where t is not parameterized.

30 citations




Journal ArticleDOI
TL;DR: The power of parametric ANCOVA was compared with the power of three nonparametric techniques both when the parametric assumption of equal slopes was violated and when all parametric assumptions were met as discussed by the authors.
Abstract: The power of parametric ANCOVA was compared with the power of three nonparametric ANCOVA techniques both when the parametric assumption of equal slopes was violated and when all parametric assumptions were met. The data situations involved two groups with one covariate and one criterion, normal distributions, equal group sizes, and varying slope combinations. Parametric ANCOVA maintained larger empirical power for nearly all of the data situations. Both parametric and nonparametric techniques appeared not to be robust when violation of the parametric assumption of equal slopes was coupled with unequal group sizes and distributions were normal.

Journal ArticleDOI
TL;DR: In this article, the authors studied the statistical properties of parametric processes (parametric amplification, frequency conversion, splitting of frequency, etc.) described by the trilinear Hamiltonian and of the second harmonic generation including the lossy mechanism and rotating terms.
Abstract: We study the statistical properties of parametric processes (parametric amplification, frequency conversion, splitting of frequency, etc.) described by the trilinear Hamiltonian and of the second harmonic generation including the lossy mechanism and rotating terms. In a short-time approximation some conservation laws are derived and the existence of the Glauber-Sudarshan weighting function is discussed. It is shown in the second harmonic generation case that good coherence of the incident radiation is lost proportionally to the intensity in interaction while the second harmonic radiation has tendency to be coherent. The effects of the spontaneous emission of the medium and of the physical vacuum are also discussed. In this approximation the statistics is generally described by the superposition of coherent and chaotic fields with correlated components.



Journal ArticleDOI
TL;DR: This paper presents general algorithms for solving redundancy optimization problem for non series-parallel networks using closed form expressions for star-delta and delta-star conversions and the exact system reliability expression (objective function) is written down in a straightforward manner.
Abstract: This paper presents general algorithms for solving redundancy optimization problem for non series-parallel networks. Using closed form expressions for star-delta and delta-star conversions, the exact system reliability expression (objective function) is written down in a straightforward manner. The Box method has been employed to get the optimal continuous solution. The integer solution is obtained by a modified Box method and Branch and bound technique. The scheme is illustrated with an example. The parametric method is used throughout

Journal ArticleDOI
TL;DR: Two algorithms for the solution of a parametric optimal design problem are developed and applied to example problems from diverse fields, such as finite allocation problems, optimal design of dynamical systems, and Chebyshev approximation.
Abstract: Two algorithms for the solution of a parametric optimal design problem are developed and applied to example problems from diverse fields, such as finite allocation problems, optimal design of dynamical systems, and Chebyshev approximation. Sensitivity analysis gives rise to a first-order feedback law, which contains a compensating term for any error in the nominal solution, as well as sensitivity of the solution with respect to design parameters. The compensating term, when used alone, leads to a new second-order method of maximization for a linearly-constrained nonlinear programming problem.

Book ChapterDOI
01 Jan 1976
TL;DR: This chapter provides an overview of the parameter identification field and highlights its applications to a variety of respiratory system problems, and reviews the basic structure of a parametric identification problem.
Abstract: Publisher Summary This chapter provides an overview of the parameter identification field and highlights its applications to a variety of respiratory system problems. It focuses on an area of system science that can be expected to have increasing importance in the study of biological systems. Estimation of state variables from noisy data, determination of optimum inputs for parameter identification, and criteria for identifiability of given model structures are among the topics that are likely to influence the development of mathematical models of biological systems in the near future. The chapter reviews the basic structure of a parametric identification problem. Both parametric and nonparametric methods have been applied extensively to the identification of a variety of complex engineering systems. The identification techniques designed for systems where input and output signals can be clearly isolated may not work at all in the biological situation. The very nature of the living organism, particularly in higher animals, leads to such a complex of interconnections of subsystems that isolation of a portion of the system may destroy its natural function and, thus, lead to identification of a purely hypothetical process. On the other hand, in the cases when input and output can be isolated, often by exceedingly clever surgical procedures, and the system in question is approximately linear, frequency response methods have been applied with considerable success.

01 Jan 1976
TL;DR: This thesis attempts to evaluate and understand the relative merits of a number of alternative design choices at that level of speech recognition, and develops a methodology for such comparative evaluation.
Abstract: : This thesis studies speech recognition at the parametric level. It attempts to evaluate and understand the relative merits of a number of alternative design choices at that level. In particular, it involves an investigation of segmentation and labeling techniques, and the use of parametric representations for the acoustic signal. Every speech recognition system employs some parametric representation and some initial signal to symbol transformation. The author shows the performance currently available for these initial processes, and asserts that such performance is comparable to human performance. After presenting the relative merits of some typical parametric representations, we develop a methodology for such comparative evaluation. Simple, parameter- independent schemes for segmenting, labeling, and training are also developed. The role of pattern classification techniques is clarified, as it relates to the initial signal to symbol transformation. Four parametric representations were chosen for study: a set of amplitudes and zero-crossing measurements from 5 octave filters; a set of energy measurements from a 1/3 octave filter bank; a smoothed, short-time spectrum computed from the LPC filter and the LPC coefficients themselves. Note that the first two involve the use of analog devices. Each method yields a set of measurements at uniform, short intervals--a pattern. Distance functions, chosen from pattern classification theory, are then applied to the parameter patterns as measures of acoustic similarity.

Journal ArticleDOI
TL;DR: In this paper, a rigorous mathematical analysis shows that parametric pumps can separate, concentrate, and recover in pure form all components of a multi-solute mixture and that the obtained separation cannot be predicted by existing linear models.
Abstract: A rigorous mathematical analysis shows that parametric pumps can separate, concentrate, and recover in pure form all components of a multi-solute mixture. The obtained separation cannot be predicted by existing linear models. Criteria for determining steady periodic separations of binary mixtures are discussed in detail for batch and continuous systems.

Journal ArticleDOI
TL;DR: In this paper, the results of a theoretical and experimental investigation of three-photon parametric amplification and generation of ultrashort light pulses in KDP and α-HIO3 crystals were given.
Abstract: The results are given of a theoretical and experimental investigation of three-photon parametric amplification and generation of ultrashort light pulses in KDP and α-HIO3 crystals. It is shown that parametric amplifiers can be used in spectroscopy to determine the shape and duration of ultrashort weak optical signals. Commissioning of a continuously tunable optical parametric oscillator with a high pulse repetition frequency (up to 25 Hz) is reported.

Journal ArticleDOI
TL;DR: In this article, a particular class of linear parametric stochastic systems is considered and the moment stability problem is analyzed: it is shown that the stability conditions do not depend on the noise bandwidth.
Abstract: In this paper a particular class of linear parametric stochastic systems is considered. For this class the moment stability problem is analysed: it is shown that the stability conditions do not depend on the noise bandwidth. An equivalent Ito equation is derived. Explicit criteria for the stability of the moments, for pth mean stability and for almost sure stability are obtained.


Journal ArticleDOI
TL;DR: Refinery relief-header network design can be optimized by a new discrete optimization technique which requires no rounding of decision variables, no initial guesses for the solution, and no artificial termination criteria; it produces parametric solutions when the optimum is attained.
Abstract: Refinery relief-header network design can be optimized by a new discrete optimization technique which requires no rounding of decision variables, no initial guesses for the solution, and no artificial termination criteria; it produces parametric solutions when the optimum is attained. The method is also faster and more compact than the alternative continuous optimization methods.

Journal ArticleDOI
TL;DR: In this article, the authors present a comparison of different approaches to the problem of soil-structure interaction with an elastic half-space or continuum solution, showing that both the finite element and lumped parameter approaches should yield similar results if they are appropriately used to solve the same problems.

Journal ArticleDOI
TL;DR: An automated method is presented in which the effects of overlap of left and right sided chambers or vessels are minimized by the automatic elimination of regions which have two distinct peak concentration times, one preceding the pulmonary phase of the study, and the other one following it.
Abstract: An automated method is presented in which regions of interest are selected on the basis of peak concentration times and in which the effects of overlap of left and right sided chambers or vessels are minimized by the automatic elimination of regions which have two distinct peak concentration times, one preceding the pulmonary phase of the study, and the other one following it. As part of the permanent record a set of parametric images is produced in which the progression of the bolus is represented in a pseudo gray scale with later times represented by darker shades. One of the parametric images documents the choice of the regions of interest, from each of which a time-activity curve is automatically generated. Besides providing the basis for these curves, the parametric images often help to clarify the nature of complex cardiac anomalies. Additional significant advantages of the method are minimal operator interaction and bias, and speed of analysis and presentation.


Journal ArticleDOI
TL;DR: In this paper, an experimental investigation of parametric processes which govern the structure of the angular distribution of the intensity of the second Stokes and two anti-Stokes components of the stimulated Raman scattering in liquid nitrogen is presented.
Abstract: The results are given of an experimental investigation of parametric processes which govern the structure of the angular distribution of the intensity of the second Stokes and two anti-Stokes components of the stimulated Raman scattering in liquid nitrogen. The investigation was made using a collimated pump beam with a large transverse cross section. The angular structure of the first Stokes component included a highly directional peak against the background of diffuse radiation. These conditions made it possible to observe simultaneously for the first time three types of parametric generation at the second Stokes frequency. The observed angular spectra of the Raman components were explained on the basis of the theory of parametric interactions between plane waves. The reliable interpretation of the angular spectra and the high experimental precision made it possible to correct and extend the long-wavelength edge of the dispersion curve of liquid nitrogen at T = 77 °K.

Journal ArticleDOI
TL;DR: In this article, an analytical solution using the Fokker-Planck-Kolmogorov equation was obtained for the problem of response of a non-linearly damped oscillator to combined periodic parametric and random external excitation.
Abstract: An analytical solution, using the Fokker-Planck-Kolmogorov equation, is obtained for the problem of response of a non-linearly damped oscillator to combined periodic parametric and random external excitation. The solution yields first-order probability densities of amplitude and phase. These expressions are employed to distinguish between oscillations excited by external and parametric periodic forces in the presence of additional broadband random external excitation. Through decoupling of fast and slow motions an approximate expression is obtained for expected value of time to phase “switch”.

Journal ArticleDOI
TL;DR: In this paper, the non-linear response of thin elastic plates under parametric excitation is investigated and a new analytical method is proposed, which gives the possibility to obtain all the characteristic features of the phenomenon considered, which are known from experiments.
Abstract: In this paper the non-linear response of thin elastic plates under parametric excitation is investigated. A new analytical method is proposed. It gives the possibility to obtain all the characteristic features of the phenomenon considered, which are known from experiments—the existing of beats, their dependence on the excitation parameter, the influence of the initial conditions, the typical character of the vibrations in the different regions. Analog computer studies are carried out, and they show clearly the influence of different parameters on the output of the problem considered.