Showing papers on "Parametric statistics published in 1970"
TL;DR: In this article, a general multivariate normal distribution with a general parametric form of the mean vector and the variance-covariance matrix is proposed, where any parameter of the model may be fixed, free or constrained to be equal to other parameters.
Abstract: SUMMARY It is assumed that observations on a set of variables have a multivariate normal distribution with a general parametric form of the mean vector and the variance-covariance matrix. Any parameter of the model may be fixed, free or constrained to be equal to other parameters. The free and constrained parameters are estimated by maximum likelihood. A wide range of models is obtained from the general model by imposing various specifications on the parametric structure of the general model. Examples are given of areas and problems, especially in the behavioural sciences, where the method may be useful. 1. GENERAL METHODOLOGY 11. The general model We consider a data matrix X = {xOq} of N observations on p response variables and the following model. Rows of X are independently distributed, each having a multivariate normal distribution with the same variance-covariance matrix E of the form
1,115 citations
TL;DR: Using a combined distribution containing the component models as special cases, statistics are developed for testing for departures from one model in the direction of another and for testing the hypothesis that all models fit the data equally well.
Abstract: [Read before the ROYAL STATISTICAL SOCIETY at a meeting organized by the RESEARCH SECTION on Wednesday, May 13th, 1970, Professor J. DURBIN in the Chair] SUMMARY It is desired to determine which of several alternative models adequately describe the data. The properties of a combined distribution containing the component models as special cases are investigated. Using this distribution, statistics are developed for testing for departures from one model in the direction of another and for testing the hypothesis that all models fit the data equally well. The relationship with other procedures is investigated. Examples are given of the use of the method, especially when there are two component models belonging to separate parametric families.
259 citations
TL;DR: In this paper, a description of the parametric amplifier and frequency converter is presented without introducing the classical (i.e., parametric) approximation for the pumping field, and the time-dependent behavior of the mean number of photons in the amplified or frequency up-converted field is illustrated.
Abstract: A description of the parametric amplifier and frequency converter is presented without introducing the classical (i.e., parametric) approximation for the pumping field. Constants of the motion are found which reduce the solution of the Schr\"odinger equation to the diagonalization of a matrix. This diagonalization is accomplished numerically, and the eigenvalues and eigen-functions of a system with fixed energy are calculated. The time-dependent behavior of the mean number of photons in the amplified or frequency up-converted field is presented. The time evolution of the probability distributions is illustrated. The technique is extended to the problem of coherent spontaneous emission from a system of $N$ two-level atoms interacting with the radiation field where both the atomic system and the radiation field are quantized.
174 citations
TL;DR: In this article, two intrinsic criteria for runaway in fixed bed tubular reactors based on the occurrence of characteristic points in the temperature profile along the reactor were introduced, and their transposition in the partial pressure-temperature phase plane allows the derivation of some very simple formulae for the prediction of the critical values for the operating variables.
139 citations
TL;DR: The nonparametric representation of the curve, which is widely used since it lends itself to realization by ordinary DDA technique, is shown to be fully competitive.
Abstract: The process of converting a mathematically defined curve into unit steps along a fixed axis in digital technique is known as interpolation. The representation of the curve may be parametric or nonparametric. The parametric representation is widely used since it lends itself to realization by ordinary DDA technique. However, the nonparametric representation is shown to be fully competitive. In many cases, e.g., circle generation, it seems to be advantageous because it eliminates the risk of curve degradation.
103 citations
TL;DR: In this paper, the authors extended the Gourevitch and Galanter's large two sample test to a K-sample detection test and used the post hoc confidence interval procedure described in this paper to locate possible statistically significant sources of variance and differences.
Abstract: The basic models of signal detection theory involve the parametric measure,d′, generally interpreted as a detectability index. Given two observers, one might wish to know whether their detectability indices are equal or unequal. Gourevitch and Galanter (1967) proposed a large sample statistical test that could be used to test the hypothesis of equald′ values. In this paper, their large two sample test is extended to aK-sample detection test. If the null hypothesisd
1′=d
2′=...=d
K
′ is rejected, one can employ the post hoc confidence interval procedure described in this paper to locate possible statistically significant sources of variance and differences. In addition, it is shown how one can use the Gourevitch and Galanter statistics to testd′=0 for a single individual.
91 citations
01 May 1970
TL;DR: In this article, the authors consider some of the simpler nonparametric detection schemes and compare their asymptotic relative efficiencies to those of detectors which are optimal in the Neyman-Pearson sense.
Abstract: This paper considers some of the simpler nonparametric detection schemes and compares their asymptotic relative efficiencies to those of detectors which are optimal in the Neyman-Pearson sense. In the one-input case, the nonparametric sign and Wilcoxon detectors are compared to the linear detector which is optimal for the detection of a dc signal of unknown amplitude in Gaussian noise. For two-input systems the nonparametric polarity coincidence correlator is compared to the system which is optimal for the detection of a common random Gaussian component in two-input Gaussian noises. The nonparametric detectors are shown to offer advantages in simplicity of implementation and in insensitivity to changes in input statistics while performing moderately well compared to the parametric detectors. More impressive results can be obtained with more complicated detectors utilizing nonlinear rank statistics.
85 citations
TL;DR: In this paper, the authors studied three-wave parametric interactions in media exhibiting group-velocity dispersion and found the existence of steady-state pulse solutions in the parametric system, which are analogues of pi and two-pi pulses.
Abstract: Three-wave parametric interactions are studied in media exhibiting group-velocity dispersion. Under certain conditions these interactions may be described by the same equations that govern pulse propagation in a two-level resonant system. This analogy suggests the existence of steady-state pulse solutions in the three-wave parametric system. Such solutions are found, and are analogues of pi and two-pi pulses. The variety of solutions in the parametric system is greater than in the resonant case.
59 citations
44 citations
Book•
01 Jan 1970
39 citations
TL;DR: This paper describes the measurement and analysis of the quasi-static errors of a prototype hexapod milling machine at the National Institute of Standards and Technology (NIST).
Abstract: This paper describes the measurement and analysis of the quasi-static errors of a prototype hexapod milling machine at the National Institute of Standards and Technology (NIST). Emphasis is placed on a) the identification and definition of the parametric errors, b) the development of an analytical model to describe how these parametric errors affect errors in the position and orientation of the tool, c) identification of the most important parametric errors and their potential impact on performance, d) comparison of hexapod error characteristics to those of conventional machine tools, e) description of the techniques used to measure and estimate the hexapod errors, and f) application of the various concepts to model the geometrical and thermal errors of the NIST hexapod, including measurement results.
01 Feb 1970
TL;DR: The basic theoretical development of guaranteed cost control is given, and it is shown how it can be incorporated into an adaptive system.
Abstract: : Guaranteed cost control is a method of synthesizing a closed-loop system in which the controlled plant has large parameter uncertainty. This paper gives the basic theoretical development of guaranteed cost control, and shows how it can be incorporated into an adaptive system. The uncertainty in system parameters is reduced first by either on line measurement and evaluation prior knowledge on the parametric dependence of a certain easily measured situation parameter. Guaranteed cost control is then used to take up the residual uncertainty. (Author)
TL;DR: In this article, it was shown that exponential growth is not required to achieve useful parametric gain for the operation of continuously pumped optical parametric oscillators with very small gain coefficients, and an optimum phase relation between the three waves giving maximum gain was found.
Abstract: Solutions to the equations describing traveling‐wave parametric amplification are presented. These results extend previous work by including the effects of momentum mismatch and general initial conditions (nonzero pump, signal, and idler fields) on the gain expressions. In contrast to statements found in some earlier published results it is shown that exponential growth is not required to achieve useful parametric gain. This fact is particularly important in the operation of continuously pumped optical parametric oscillators which operate with very small gain coefficients. The equations for the parametric gain are presented in general as well as for a number of limiting cases, and an optimum phase relation between the three waves giving maximum gain is found.
TL;DR: It is found that the effects of dependence on ARE with respect to a parametric test can be offset to some extent by appropriately grouping sample values, and either the form of the dependence must be known or some learning scheme must be applied.
Abstract: This paper investigates the effects of dependence on rank tests, in particular on a class of recently defined nonparametric tests called "mixed" statistical tests. It is shown that the mixed test statistic is asymptotically normal for Gaussian processes with mild regularity properties justifying the use of asymptotic relative efficiency (ARE) as a figure of merit. Results are presented in terms of variations on three well-known statistics--the one-sample Wilcoxon, the two-sample Mann-Whitney, and the Kendall \tau . It is found that the effects of dependence on ARE with respect to a parametric test can be offset to some extent by appropriately grouping sample values. If, however, a constant false-alarm rate is to be attained, either the form of the dependence must be known or some learning scheme must be applied.
TL;DR: In this paper, a recent development in statisical theory known as parametric modeling is used to forecast wheat yields in the United States, Canada, Australia, and Argentina, using the data are used for identifying and estimating random components in the form of moving average and autoregressive processes.
Abstract: The purpose of this paper is to use a recent development in statisical theory known as parametric modeling to forecast wheat yields in the United States, Canada, Australia, and Argentina. The essence of this approach is that the data are used for identifying and estimating random components in the form of moving average and autoregressive processes. It does not identify and measure structural relationships as is attempted when forecasting with econometric models. Exponential smoothing is also used to forecast yields in the United States and Canada. The Thiel coefficient is then computed to determine the forecasting accuracy of parametric modeling compared with exponential smoothing.
Patent•
12 Jan 1970
TL;DR: In this article, the output of a parametric device is rectified and monitored by a sensing circuit which controls the frequency of the inverter to maintain the output voltage constant, and a sensing and control circuit is provided which permits the use of conventional transistors in the inverters by establishing a proper timing pattern for the triggering of these transistors into and out of conduction.
Abstract: A parametric regulator in which an inverter is positioned between the input source of power and a parametric device to provide the parametric device with a high frequency input. The output of the parametric device is rectified and monitored by a sensing circuit which controls the frequency of the inverter to maintain the output voltage constant. A sensing and control circuit is provided which permits the use of conventional transistors in the inverter by establishing a proper timing pattern for the triggering of these transistors into and out of conduction.
TL;DR: An analytical solution of the model equations which describe continuous direct thermal parametric pumping systems is presented and it is shown how it can be used quantitatively for comparing various open system configurations and operations.
TL;DR: In this article, the transient motion of non-linear dynamical systems with high frequency parametric excitation is studied with emphasis placed on determining estimates for the domains of attraction of the stable steady state motions.
Abstract: The transient motion of non-linear dynamical systems with high frequency parametric excitation is studied with emphasis placed on determining estimates for the domains of attraction of the stable steady state motions. It is shown that a natural Liapunov function exists for making these estimates. The results have asymptotic validity based on some recent mathematical results of Sethna and Moran. A detailed study is made of a spherical pendulum with high frequency support motion at an arbitrary angle to the vertical.
TL;DR: In this paper, the central potential introduced by Slatc~ is described as an analytical function of some par;imeters, which can be optinialired accordilig to several q~l~tlity critcrin.
Abstract: A summary of tlie ~>iiramctric ~,otcntial ~iietliod is prcscntcd : the central potential introduced by Slatc~. is c~l,rcsscd as an analytical function of some par;imeters, which can be optinialircd accordilig to several q~l~tlity critcrin. A spect~.oscopic criterion where the r. ni. s. deviation bct\veen rlicork and cwpeririien~ is ~iiinimali/ccl -uas applied to rare giises Nc I through R n 1. and ro tlic isoelectronic sequcncc Kc I lo V XIV. Once I-cla[ivislic corrcctions are introduced, as well as configu~.;ition mixing. I.. m . s. AE arc smallel' tlian 500 cm 1 , for coniputed spectra of c. a. 100.000 cm 1. As for I lie isoclcctronic scqilcncc. \vc \\ crc able to iiitcrcliange names ascribed to Icvels 2 p' 3 d 11'1 and :! 3 d 'Dl. A variational criterion mininialiration of ground statc first order cncrgy yields results very near those of Hi~rtrcc-S.ock. and is ~~scful as a starting point for perturbation studies.
TL;DR: In this paper, the authors present a mathematical model capable of determining the optimum amount of time that semiconductor devices, which have specified life characteristics, must be placed on burn-in to obtain maximum performance versus total cost.
Abstract: The object of this paper is to present a mathematical model capable of determining the optimum amount of time that semiconductor devices, which have specified life characteristics, must be placed on burn-in to obtain maximum performance versus total cost. To make the model operational and realistic, the traditional assumption of an exponential (more recently, Weibull) distribution of life is omitted in favor of the generalized gamma distribution (GGD). This is done because the GGD includes, as special cases, such distributions as the normal, Rayleigh, Maxwell, chi, chi2, Weibull, exponential, ordinary gamma, etc. The use of the greater representational capability of the GGD is justified in the results of the studies showing that (other things being equal) small changes in parametric values of life characteristics can cause vast differences in the optimum burn-in time and maximum system effectiveness. The physical performance sector of the model incorporates system effectiveness that includes such factors as availability, expected time to repair, mission reliability, system use coefficient, storage survival probability, and operational readiness. The costs considered are those due to burn-in operation, production, and sales. The model has been studied by use of computer runs from the standpoint of critical analysis and parametric sensitivity analysis.
DOI•
01 Jan 1970
TL;DR: A set of parametric studies, in the form of time and frequency dependent plots, is presented illustrating the influence of a number of parameters upon the response of the soil-foundations system.
Abstract: A direct time domain BEM formulation is used for the solution of a class of dynamic foundation-soil-foundation interaction problems. A set of parametric studies, in the form of time and frequency dependent plots, is presented illustrating the influence of a number of parameters upon the response of the soil-foundations system.
TL;DR: In this article, the authors define and demonstrate the occurrence of chaos in the iteration of mathematical formulae and show that such systems can be exposed by their dependence on the initial values of variables and parametric coefficients.
Abstract: The paper defines and demonstrates the occurrence of chaos in the iteration of mathematical formulae and shows that such systems can be exposed by their dependence on the initial values of variables and parametric coefficients. Filled Julia sets, although computationally intensive, give visual explanation of the fate of an iteration and indicate regions of crossover between stable and unstable operation. The paper then demonstrates that even the simplest process controllers may be subject to chaos in their component parts while still maintaining control of the primary outputs of the system. A variation on the Julia set is then described and offered as a possible “chaotic function analyzer” for such systems. The paper closes with some illustrations of phase plots in the stable and chaotic regions for a nonlinear plant that is examined by the proposed method.
TL;DR: In this paper, the behavior of the parametric backward wave oscillator above threshold when diffraction is taken into account is analyzed and compared to the plane wave case, the main results of diffraction are a more rapid pump depletion as the power is raised above threshold and a power dependent frequency shift.
DOI•
01 Jan 1970
TL;DR: In this paper, a scheme of classification of numerical models for the prediction of flow in tidal waters, including estuaries, was given by Hinwood and Wallis [11], who classified the models into an array according to the number of spatial dimensions, the level of physics represented and whether the model was eulerian or lagrangian.
Abstract: Parametric modelling of an estuary aims to produce cost effective and robust computer models for use by environmental managers. These requirements lead to a different approach to the developments of the last few decades which have emphasised detailed representation of the physics of the estuary. A scheme of classification of numerical models for the prediction of flow in tidal waters, including estuaries, was given by Hinwood and Wallis [11]. They classified the models into an array according to the number of spatial dimensions, the level of physics represented, and whether the model was eulerian or lagrangian. The spatial dimensions may be three, two (in plan or elevation), one (length) or zero (a single well-mixed box) dimensional. The levels of physics may be as follows: (i) Hydrodynamic uses momentum equations and hence can find velocities in new configurations. The energy equation may be used in one dimensional hydrodynamic models. (ii) Kinematic uses mass conservation equations and empirical data on velocity profiles and water levels to solve for velocities. (iii) Transport uses the convection-diffusion equation and data on velocities to solve for pollutant transport.