Showing papers on "Parametric statistics published in 1975"
TL;DR: In this paper, two widely used methods, one replacing the unknown parameter by an efficient estimate and so termed estimative and the other using a mixture of the possible density functions and commonly termed predictive, are compared.
Abstract: SUMMARY Fitting a parametric model or estimating a parametric density function plays an important role in a number of statistical applications. Two widely-used methods, one replacing the unknown parameter by an efficient estimate and so termed estimative and the other using a mixture of the possible density functions and commonly termed predictive, are compared. On a general criterion of closeness of fit based on a discriminating information measure the predictive method is shown to be preferable. Explicit measures of the relative closeness of predictive and estimative fits are obtained for gamma and multinormal models.
259 citations
TL;DR: In this article, the theory of parametric amplification by a series of unbiased Josephson junctions is presented, and various regimes of operation are explored, including a very small pump power and a large bandwidth.
Abstract: The theory of parametric amplification by a series of unbiased Josephson junctions is presented. The various regimes of operation are explored. This device is in many ways different from the usual varactor parametric amplifier. In particular, a very small pump power is required and a large bandwidth is obtained. Comparison with experimental data is made.
84 citations
TL;DR: For the class of parametric linear programs with continuous dependence of coefficients on parameters, the following theorem is proven: for any parameter vectort ≥ 0 in the domain of definition of the maximum, if the set of optimal solutions is bounded, then the maximum is upper semicontinuous att ≥ 0 as mentioned in this paper.
Abstract: For the widest class of parametric linear programs with continuous dependence of coefficients on parameters, the following theorem is proven: for any parameter vectort
0 in the domain of definition of the maximum, if the set of optimal solutions is bounded, then the maximum is upper semicontinuous att
0. If the same proviso is met also in the dual program, then the maximum must be continuous att
0.
42 citations
TL;DR: It is shown that a parametric constraint may be replaced by an equivalent "minimum value" constraint which is more efficient computationally for optimization problems.
Abstract: Many optimum structural-design problems involve constraints which have to be satisfied for an entire range of certain parameters. For example, in a structure under dynamic loads the stress constraint has to be satisfied for a given range of time. The properties of parametric constraints are investigated in the present paper. It is shown that a parametric constraint may be replaced by an equivalent "minimum value" constraint which is more efficient computationally for optimization problems. The efficiency of the minimum value constraint is due to the minimal amount of computation needed to update it as the structure is changed in the optimization process. The results obtained for the general case of parametric constraints are applied to the problem of optimal structural design under flutter constraints. It is shown that a recently developed continuous flutter constraint is a parametric constraint and may be replaced by the equivalent minimum value constraint. An example problem is solved using the continuous flutter constraint. It is shown that the design obtained for this problem could not be obtained by using a more conventional flutter constraint.
40 citations
Dissertation•
01 Jan 1975
32 citations
01 Jan 1975
TL;DR: The von Mises-Fisher distribution is the most important distribution in directional data analysis as discussed by the authors, and the sampling distributions of the sample resultant length, the sample mean direction and the component lengths are derived for the multi-sample case.
Abstract: The von Mises-Fisher distribution is the most important distribution in directional data analysis. We derive the sampling distributions of the sample resultant length, the sample mean direction and the component lengths. For the multi-sample case, the conditional distribution of the individual sample resultant lengths given the combined sample resultant length is derived. These results depend heavily on the corresponding distributions for the isotropic random walk on hypersphere. Using these results we investigate some optimum properties of various important tests. Most of these tests were formulated intuitively by Watson and Williams (1956). Mardia (1972) in his book concentrated on the optimum properties of the circular and spherical cases, and this paper extends and unifies some of the parametric work.
32 citations
TL;DR: In this paper, it was shown that the efficiency of the parametric transmitting array may be improved over that obtained where two equal amplitude-frequency components are employed in the primary wave through suitable periodic shaping of the envelope of the PWR, through which improvements in the output at the difference between 2.1 and 6.0 dB are possible in principle.
Abstract: It is shown that the efficiency of the parametric transmitting array may be improved over that obtained where two equal amplitude‐frequency components are employed in the primary wave. Through suitable periodic shaping of the envelope of the primary wave, available improvements in the output at the ’’difference’’ frequency of between 2.1 and 6.0 dB are possible in principle. The degree of available improvement depends upon whether the transmitter is peak power or average power limited and whether finite‐amplitude attenuation of the primary wave is significant. It is proposed that the on–off modulation of a single‐frequency carrier provides a simple, practical method through which near optimum efficiencies may be obtained under most circumstances. A bandwidth greater than the ’’difference’’ frequency is required at the transducer in order to achieve this improvement.Subject Classification: 25.35; 30.75.
31 citations
TL;DR: In this article, explicit parametric relations are derived between the parameters of a continuous time stationary stochastic process governed by a second-order linear differential equation and its uniformly sampled discrete representation.
Abstract: SUMMARY Explicit parametric relations are derived between the parameters of a continuous time stationary stochastic process governed by a second-order linear differential equation and its uniformly sampled discrete representation. These relations are used to analyze and resolve the multiplicity of the parameters of the continuous process estimated from sampled data, leading to alias-free estimates of spectra. A limiting case of the sampled process, including integrated random walk, is pointed out. The estimation procedure is illustrated by data obtained from a mechanical system.
30 citations
28 citations
TL;DR: In this article, a general treatment is proposed in which transport limitations are also considered, and it is shown that the critical inlet partial pressure is strongly dependent on the transport processes, based on the analysis presented, four regimes of fixed-bed reactor operation are postulated and conditions are stated to identify the regime in which a given system would operate.
26 citations
TL;DR: In this article, the onset of parametric instability and the steady-state parametric response of a beam with variable cross-section resting on an elastic foundation were studied both theoretically and experimentally.
TL;DR: Several nonparametric and parametric statistics for testing the equality of scale parameters are compared with respect to their power and stability of error rates as mentioned in this paper, and the results show that the c-sample analogs of the sum of squared ranks test and the Kruskal-Wallis test are very robust and powerful.
Abstract: Several nonparametric and parametric statistics for testing the equality of scale parameters are compared with respect to their power and stability of error rates. When the populations have mass confined to the positive axis, the c-sample analog of the sum of squared ranks test and the Kruskal-Wallis test are found to be very robust and powerful. When the populations are symmetrical, the c-sample analogs of the two-sample Mood and two-sample Ansari-Bradley tests are robust for small samples, and are more powerful than Box's test. Tables of exac probabilities and corresponding critical values of the nonparametric statistics are given for testing the equality of scales for small samples.
TL;DR: In this paper, it is shown that soliton formation and the resulting plasma heating are nothing more than the description in configuration space of well-known parametric processes and quasi−linear theory.
Abstract: It is shown that soliton formation and the resulting plasma heating are nothing more than the description in configuration space of well‐known parametric processes and quasi−linear theory
TL;DR: In this article, a simpler solution to the combined burn-in and replacement problems is given. But this solution is not suitable for the case of a U shaped failure rate, which makes parametric estimation of reliability difficult.
Abstract: Bum-in and replacement policies have been used to reduce the cost of maintaining a system function. Existing solutions to the burn-in and the combined burn-in, replacement problems are typically difficult to apply. A simpler solution to this problem is given. The only distributional property required is the reliability function. Thus either parametric or nonparametric estimates of reliability can be used in the solution. The nonparametric solution is appealing in the case of a combined burn-in and replacement policy because the U shaped failure rate makes parametric estimation of reliability difficult.
TL;DR: In this article, an alternative method is suggested for reducing aggregation bias which uses regression estimates of farm resonrce availabilities as functions of farm size, incorporated in a parametric run of the LP problem in which size is parameterized.
Abstract: Because methods of eliminating aggregation bias are impracticable, an alternative method is suggested for reducing aggregation bias which uses regression estimates of farm resonrce availabilities as functions of farm size. The estimates are incorporated in a parametric run of the LP problem in which size is parameterized. The method is applied to a case study problem, and the results compared with other methods of demarcating representative farms.
01 Jan 1975
TL;DR: Two approaches to an identification problem in hydrology are presented, based upon concepts from modern control and estimation theory, and offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.
Abstract: Two approaches to an identification problem in hydrology are presented, based upon concepts from modern control and estimation theory. The first approach treats the identification of unknown parameters in a hydrologic system subject to noisy inputs as an adaptive linear stochastic control problem; the second approach alters the model equation to account for the random part in the inputs, and then uses a nonlinear estimation scheme to estimate the unknown parameters. Both approaches use state-space concepts. The identification schemes are sequential and adaptive and can handle either time-invariant or time-dependent parameters. They are used to identify parameters in the Prasad model of rainfall-runoff. The results obtained are encouraging and confirm the results from two previous studies; the first using numerical integration of the model equation along with a trial-and-error procedure, and the second using a quasi-linearization technique. The proposed approaches offer a systematic way of analyzing the rainfall-runoff process when the input data are imbedded in noise.
TL;DR: In this paper, a procedure for the synthesis of controllers which discriminate the trajectories according to their insensitivity to various parameters is proposed, and it is shown that such controllers are consistent with completely arbitrary pole assignment.
TL;DR: While the results presented were developed for finding a minimum cost solar electric energy power plant, the method employed has been found to have general applicability.
TL;DR: In this paper, the autocorrelation of first-order autoregression and firstorder moving averages is used to test for randomness in multivariate normality with a single parameter, and the asymptotic efficiencies of these tests are compared with tests based on the firstorder sample serial correlation.
Abstract: SUMMARY Testing for randomness is studied for an alternative model of multivariate normality with the autocorrelation specified by a single parameter. First-order autoregression and first-order moving averages are special cases of this model. The likelihood derivative method is used to obtain tests. The asymptotic efficiencies are derived of these tests compared with tests based on the first-order sample serial correlation.
01 Jan 1975
Dissertation•
01 Jan 1975
TL;DR: In this paper, the temporal growth rates for side-scattering of light by modes near the upper and lower hybrid frequencies in a turbulent, inhomogeneous plasma were calculated.
Abstract: Abstract The temporal growth rates are calculated for side-scat-tering of light by modes near the upper and lower hybrid frequencies in a turbulent, inhomogeneous plasma.
24 Sep 1975
TL;DR: In this paper, the relative merits of a single driver supplying both primary frequencies to the projector as opposed to the 'checkerboard' technique are discussed, and the distortion in both the parametric source and in receiving systems used in measurements is considered with suggestions on how these problems can be minimized.
Abstract: : A brief non-mathematical explanation of the difference frequency generation and beamforming process is followed by a step-by-step design procedure using the Mellen-Moffett parametric source model. The relative merits of projector feed with a single driver supplying both primary frequencies to the projector as opposed to the 'checkerboard' technique are discussed. Distortion in both the parametric source and in receiving systems used in measurements is considered with suggestions on how these problems can be minimized. Applications of the parametric array to communications, echo ranging, and sub-bottom profiling are mentioned, and salient performances from tests of practical sources are listed. Finally, brief discussions of the results obtained from a cavitating, parametric source and from a parametric receiving array are given.
TL;DR: In this paper, an efficient and accurate computational form for β which minimizes using the Moore-Penrose g-inverse is given, no rank conditions are imposed on R or X, the results are applied (i) to estimate the parameters in linear model which are subject to linear equality constraints and (ii) to obtain the generalized inverse of X″X which yields a solution of the normal equations subject to nonestimable constraints on the parameters.
Abstract: An efficient and accurate computational form for β which minimizes using the Moore-Penrose g-inverse is given, No rank conditions are imposed on R or X, The results are applied (i) to estimate the parameters in linear model which are subject to linear equality constraints and (ii) to obtain the generalized inverse of X″X which yields a solution of the normal equations subject to non-estimable constraints on the parameters.
TL;DR: It is suggested that parametric energy conversion may be the uniform basis of energy conversion in biological structures and that the path of bioenergetic evolution might have essentially followed the line marked by the characteristic properties of this flexible mechanism.
TL;DR: In this article, a procedure for statistical correction of numerical prediction equations at the end of each predictive time step is described and tested with a one-dimensional prediction model, which is a modified Burgers equation that allows the formation of shocks, analogous to atmospheric fronts, and which contains a space and velocity-dependent source of energy to maintain the flow against dissipation.
Abstract: A procedure for statistical correction of numerical prediction equations at the end of each predictive time step is described and tested with a one-dimensional prediction model. The model equation is a modified Burgers equation that allows the formation of shocks, analogous to atmospheric fronts, and which contains a space and velocity-dependent source of energy to maintain the flow against dissipation. The detailed flow is calculated from a fine-grid numerical integration. Coarse-grid values, for testing a coarse-grid prediction scheme, are obtained by space-time averages. Since the coarse-grid prediction equation cannot represent the sub-grid-scale motions, statistical corrections are added in the form of parametric terms as a pragmatic substitute for the missing sub-grid-scale effects. Tests with different versions of the model show that substantial improvement over the straight- forward coarse-grid prediction can he obtained when the coefficients of appropriate parametric terms are determined...
04 Dec 1975
TL;DR: In this paper, the first-order changes in a Kuhn-Tucker triple and second-order change in the optimal value function of a class of general parametric nonlinear programming problems, with respect to a perturbation of the problem parameters, are investigated.
Abstract: : Pursuing a number of theoretical results recently obtained by Fiacco, this paper continues the development of a basis for calculating first-order changes in a Kuhn-Tucker triple and second-order changes in the optimal value function of a class of general parametric nonlinear programming problems, with respect to a perturbation of the problem parameters. Exploiting problem structure, specific formulas are derived for calculating the first partial derivatives of a Kuhn-Tucker triple. Approximations to these quantities are obtained in parallel throughout, by way of an associated logarithmic-quadratic penalty function. Applications are indicated.
01 Jan 1975
TL;DR: In this article, a method to construct non-elimination type sequential procedures to select a subset containing all the superior populations is described. But this method is not applicable to the problem of choosing normal populations for the superior population with smaller variance.
Abstract: Publisher Summary This chapter discusses some parametric and nonparametric sequential subset selection procedures. In sequential selection and ranking procedures, the best population is selected by using the indifference zone approach. Multiple decision procedures can be defined that select a subset of a fixed or random size. The chapter describes a method to construct nonelimination type sequential procedures to select a subset containing all the superior populations. These procedures are formed by choosing a statistic based on the observations from any two of the populations and performing a sequential probability ratio test (SPRT) based on this statistic. The selection procedure is applied to the problem of choosing normal populations for the superior populations with smaller variance. An appropriate population is removed from a set of contending populations, if the associated SPRTs terminate. This is continued until the elimination is stopped.