Showing papers on "Parametric statistics published in 1978"

On the Likelihood of a Time Series Model

Abstract: The conventional approach to parametric model fitting of time series is realized through the comparison of various competing models by some ad hoc criterion. Since each of the models is usually specified by the parameters determined by the information from the data, the extension of the classical concept of likelihood to this situation is not obvious. By asking the log likelihood of a model to be an unbiased estimate of the expected log likelihood of the model, a reasonable definition of the likelihood is obtained and this allows us to develop a systematic approach to parametric time series modelling. Practical utility of this approach is demonstrated by numerical examples.

The behaviour of axially and laterally loaded single piles embedded in nonhomogeneous soils

Abstract: An approximate elastic analysis is made of the working load responses of single piles embedded in a soil of linearly increasing modulus with depth. The formulation employs, within a boundary element algorithm, the fundamental solution for point loads acting at the interface of a two-layer elastic half-space. This analysis is of comparable generality and computational efficiency to earlier elastic solutions of the corresponding homogeneous problem and has distinct advantages in practical applications over the simpler homogeneous soil model, namely, improved predictions of the response due to lateral loads and the rationalization of the selection of soil moduli. These advantages are highlighted in the comparisons made between reported observations on the behaviour of single piles from model and full scale field tests and those predicted by the theory. Comprehensive plots of the results of a parametric study are presented in non-dimensional form. Une analyse elastique approximative est faite a partir des rep...

Parametric processes in magnetically confined CTR plasmas

Abstract: The theory and present experimental status of parametric instabilities in CTR oriented magnetized plasmas is reviewed. Both linearized theory and the most recent non-linear theory are summarized in a compact form. The regimes of upper hybrid frequency, lower hybrid frequency, ion cyclotron frequency, Alfven wave, and TTMP are covered. In each case the important parametric processes are discussed, including some work on the coupling to drift waves. Then recent experimental results which indicate the importance of parametric phenomena are presented.

A Class of Parametric Tests for Heteroscedasticity in Linear Econometric Models

Abstract: A class of parametric tests for heteroscedasticity in linear models is discussed. For models with nonstochastic regressors, new exact tests within this class are suggested which utilize existing tables of the distribution of the von Neumann ratio and of the Durbin-Watson bounding ratios. "Bound tests" for heteroscedasticity in least squares regression are proposed. A rigorous treatment of tests within this class for heteroscedasticity in the errors of structural relations in dynamic simultaneous equations models is provided.

Estimation Problems with Data from a Mixture

Abstract: The problem of estimating density functions using data from different distributions, and a mixture of them, is considered. Maximum likelihood and Bayesian parametric techniques are summarized and various approaches using distribution‐free kernel methods are expounded. A comparative study is made using the halibut data of Hosmer (1973) and the problem of incomplete data is briefly discussed.

Parametric Instabilities in Elastic Structures under Stochastic Loading

Abstract: The dynamic stability of nongyroscopic, elastic structures under parametric random loading of small intensity is investigated. Conditions for stability in the second norm of the dynamic response are obtained and shown to depend only on those values of the excitation spectral density near twice the natural frequencies and the combination frequencies of the structure. As an application, the flexural-torsional stability of a simply supported thin elastic beam subjected to stochastically fluctuating end couples is studied.

Mode-locked optical parametric oscillator apparatus

Abstract: Improved mode-locked optical parametric oscillator apparatus comprises a mode-locked pump laser having a cavity with a predetermined effective length l p and a parametric oscillator having a nonlinear crystal, such as lithium niobate (LiNbO 3 ), and singly resonant mirrors spaced apart by an effective distance l o which is substantially less than l p , i.e., l p ≈nl o where n≈5-50. The interaction of the mode-locked pump output with the nonlinear crystal produces parametric outputs at signal (f s ) and idler (f i ) frequencies, the parametric oscillator mirrors being singly resonant at one of those two frequencies. The parametric oscillator may be disposed either externally of or within the pump cavity and the pump laser optionally may be Q-switched. The parametric oscillator apparatus of this invention greatly increases the stability of the mode-locked output under normal operating conditions and enables relatively wide tuning of the apparatus without adjustment of the pump or oscillator cavity lengths.

Simple models for positive-valued and discrete-valued time series with ARMA correlation structure

Abstract: : Three models for positive-valued and discrete-valued stationary time series are discussed. All have the property that for a range of specified marginal distributions the time series have the same correlation structure as the usual linear, autoregressive-moving average (ARMA) model. The models differ in the range of marginal distributions which can be accommodated and in the simplicity and flexibility of each model. Specifically the EARMA-type processes can be extended from the exponential distribution to a rather narrow range of continuous distributions; the DARMA-type processes can be defined usefully for any discrete marginal distribution and are simple and flexible. Finally the marginally controlled semiMarkov generated process can be defined for any continuous or discrete positive-valued distribution and is therefore very flexible. However, the model suffers from some complexity and parametric obscurity. (Author)

Quantum statistics of parametric amplification

Abstract: Quantum statistical properties of the parametric amplification and generation are investigated. The losses are included and the pump field is treated classically. It is shown that the normal counting generating function decomposes into the product of two functions which are the generating functions for the superposition of coherent and chaotic field and that the outputting field exhibits the anticorrelation effect when the phase of incident fields fulfil a certain condition.

Graphical circuit analysis of two C-core type parametric power converter

Abstract: A new graphical method for analyzing the operation of two C-Core type parametric power converter is presented in this paper. The analytical results agree well with the experimental ones. The graphical method presented here is useful for designing the converter with excellent characteristics and for analyzing other power converters operating on the principle of parametric excitation.

Tuning characteristics of parametric interactions in a three‐dimensional LiNbO3 optical waveguide

Abstract: Tuning characteristics of parametric interactions in a three‐dimensional LiNbO3 optical waveguide fabricated by a Ti in‐diffusion process are revealed by experimenting on both second harmonic and sum frequency generation. The experimental results agree well with the theoretical results, where Sellmeier’s equation and Marcatili’s approximation are used to evaluate the tuning characteristics of parametric interactions. The waveguide parameters are decided by the experimental phase‐matching temperature difference between the generated second harmonic fundamental and higher‐order modes.

Parametric excitation of coupled plasma waves

Abstract: A general approach to analyze the parametric decay processes of plasma waves is presented. The approach is based on the modal Hamiltonians of the decay waves and is valid for all wave types. In the limiting cases of B0=0 and of longitudinal waves, results of previous investigations are recovered. Comparisons with experiments are favorable.

Nonparametric Statistics: Use and Nonuse:

Abstract: This paper clarifies the distinctions among parametric, non-parametric, and distribution free statistical tests. The principal circumstances prompting the use of nonparametric procedures, both rank...

The application of dynamic relaxation to the design of modular space structures

Abstract: This thesis is concerned with the development and assessment of computer techniques for the formfinding and sizing of large modular building space structures suitable for urban development. The contents of the Chapters are summarised as follows: 1: An introduction to conceptual and computer aided design of large building space structures. 2: A review of topological computer design methods. 3: A comparison of a dynamic relaxation method, for the formfinding of modularly constrained structures subject to a dominant design loading case, with linear programming and fully stressed design methods. This comparison shows that the dynamic relaxation method is efficient and particularly suitable for interactive use. 4: A parametric study of the effects of the iteration parameters on the stability and rate of convergence is presented. No general rules appear to be possible regarding the effects of these parameters on stability. It is noted, however, that the number of structure modifications before the solution becomes apparent is independent of the parameters. The dynamic relaxation formfinding procedure is generalised to cater for different stress constraints in tension and compression members and, for the problem considered, derives a lighter form than the fully stressed design technique. The optimum form of the D.R. solution is verified by the linear programming technique. 5: An intuitive dynamic relaxation method for the sizing of structures of fixed topology subject to multiple loading cases ,and stress constraints is presented. The method also caters for maximum member area sizes and deflection constraints by the use of parallel elastic and elasto-plastic analyses. Solutions derived using this method are compared with solutions derived using the non-linear program algorithm. They are shown to be of similar weight and to require similar solution times. 6: Two dynamic relaxation methods are presented for the formfinding and sizing of multiply loaded space structures. The first or parallel method is suitable for deriving and sizing forms of optimum or near optimum weight by deleting members which are small in area size and reducing in size. The second or series method is particularly suitable for interactive use and consists of testing the efficiency of each member with respect to each loading case. The final topology is then sized considering all loading cases simultaneously. These methods are both applied to a bridging ground structure subject to multiple loads and compared with solutions derived using linear, nonlinear programming and topological design methods. The parallel dynamic relaxation method is then extended to cater for cable members allowing for on-off non-linearities and prestress effects. The bridging structure is subsequently redesigned using internal cable members and adjusting the prestress level to ensure that the bridge deck does not deflect vertically under the action of the primary loading case. 7: A summary of conclusions.

Parametric oscillatory motion in electromechanical devices

Abstract: An analysis is presented which explains the mechanism of parametric motion in electromechanical devices The implications of the mechanism, in the unstable operation of a wide range of electrical machines, are indicated; for example, in stepper motors where, under certain combinations of system parameters and operating conditions, oscillations superimposed on the synchronous rotary motion are observed The simplest possible device in which parametric oscillations occur, the magnetically-maintained pendulum, is considered in detail and the conditions necessary for maintenance of motion are given Expressions are derived for (a) the boundary frequency above which the damping torque is negative, and (b) the frequency at which peak negative damping occurs

Three‐field electroacoustic parametric interactions in piezoelectric crystals

Abstract: We derive the coupled mode equations governing the Thompson–Quate experiment, that is, the parametric interaction of two counterpropagating bulk acoustic waves and a spatially uniform electric field oscillating at the second harmonic of the acoustic frequency. The derivation applies to propagation of any acoustic mode type in any direction in any piezoelectric or pyroelectric crystal. A new result of the derivation is a general but explicit expression for the material interaction coefficient that governs the strength of the process. We also find that the equations differ from the generic equations assumed by Thompson and Quate by the replacement of a phase velocity with the component of the group velocity normal to the crystal surface. As an aid to this derivation we also derive the coupled mode equations governing the parametric interaction of three acoustic waves. This derivation applies to the propagation of any mode types in any directions (consistent with being close to or at phase matching) in any d...

Reflooding phase of the LOCA in PWRs. Part I: core heat transfer and fluid flow

Abstract: The article is a general description of core behavior during the reflooding phase of the LOCA. A succession of heat-transfer and two-phase flow regimes moves along the rod bundle during reflooding of the core. Parametric ranges and other features of transient reflooding experiments that have been conducted with rod bundles and in simple single-channel geometries are tabulated. Experimental findings and parametric trends are summarized and explained. Core heat-transfer and hydrodynamics analysis methods incorporated in emergency core-cooling system evaluation models used for licensing purposes are reviewed, and the work on more advanced models that attempt to estimate core heat-transfer coefficients on the basis of calculated local flow conditions is noted.

Parametric studies in industrial distillation: Part III. Design methods and their evaluation

Abstract: Distillation networks are described as sets of composition nodes which are used to estimate material and energy balances. Comparisons with equivalent, equilibrium stage models indicate that these simplified design methods consistently result in small, but acceptable, overdesign, even when applied to complex, thermally coupled tower configurations.

Percentile Regression: A Parametric Approach

Abstract: For situations in which no assumptions are explicitly made about error distributions, other model assumptions may imply constraints on the form of the residual distribution This is true of regression models which assume that percentiles are functions of the regressor variable Hogg (1975) used a procedure based on signs of residuals to fit linear percentile models Advantages of making (and testing!) explicit parametric assumptions in this context are illustrated using a linear model for scale and location with normal errors This is applied to the data on professors' salaries discussed by Hogg