Showing papers on "Symmetric probability distribution published in 1976"

Asymptotic Linearity of Wilcoxon Signed-Rank Statistics

Abstract: As a "robust" alternative to the least squares estimates for a regression parameter, Koul (1969) proposed new estimates based on signed-rank statistics. To find out their asymptotic distribution Koul proved that under quite general assumptions, the signed-rank statistics of Wilcoxon type are asymptotically linear in the sense that they are uniformly approximable by linear forms in the regression parameter. More general results have been obtained by Van Eeden (1972) in a paper which is an analog to Jureckova's paper (1969) dealing with linear rank statistics. In 1972 the author proved that the statistic used to define the Hodges-Lehmann estimate for a location parameter is asymptotically linear in a stronger sense, the result being to Koul's theorem what the central limit theorem is to the weak law of large numbers. For the general linear regression model with one parameter the signed-rank statistics are proved to be linear in a strong sense, that is, the differences between the statistics and the linear forms mentioned above, properly normalized, converge weakly to linear processes. Results in this direction for linear rank statistics have been obtained by Jureckova (1973). As an application of the theorems presented here, one can construct new estimates for the squared $L_2$-norm of the underlying density, and this in much the same way as in Antille (1974). It is also possible to get more information about the asymptotic behavior of the linearized versions, proposed by Kraft and Van Eeden (1972).

Approximation and probability

Abstract: If the stochastic nature of input and desired output are known and if a set of admissible operators is given, one may choose an admissible operator which is efficient or nearly efficient for the approximation of desired output in terms of input; and such an operator may be strongly efficient or nearly so. The object being approximated may be a map.

The probability of information loss at the edges of bubble propagation margins

Abstract: A study has been made of the probability of error as a function of bias field near the edges of the propagation margin on the minor loops of an experimental magnetic bubble circuit using a computer controlled test apparatus. At the high bias edge of the margin, failure is dominated by the number of times the rotating field is turned off and on. Application of a constant in-plane field in any direction did not improve margins on this circuit. The probability of failure per bubble per operation can be described by a normal probability distribution in contrast to the exponential distribution others have used. This implies that margins decrease more slowly than linearly with the logarithm of the number of operations. At the low bias edge of the margin the transition from reliable operation is sharper, does not depend on the number of times the rotating field is turned off, and is consistent with a flat margin edge as the number of operations increases.

The joint probability density function of the occupation time of a three-state problem

Abstract: The joint probability density function of the occupation time of a three-state stochastic process with constant transition matrix: a,, # 0, i X j, i, j = 1,2, 3 but a,, = 0, i = 1,2, 3 is studied. STOCHASTIC PROCESS; OCCUPATION TIME; PROBABILITY DENSITY FUNCTION; RANDOM WALK

The collapse of the wave function

Abstract: Probability distributions are seen to be observer dependent. The probability function ψ†ψ can be put into an observer-dependent form. This eliminates the acausal behavior of the collapse of the wave function.

Admissible Translates for Probability Distributions

Abstract: A real number $t$ is an admissible translate of a probability $\varphi$ if $\varphi (A) = 0$ implies that $\varphi_t(A) \equiv \varphi (A - t) = 0$. Conditions are given on its set of admissible translates which ensure that $\varphi$ has a density. The theorems also describe the set where the density is positive and contain as a corollary the result that if $\varphi$ is not absolutely continuous, then the set of admissible translates has an empty interior.

On the problem of one-dimensional disordered chain

Abstract: Some properties of a one-dimensional disordered homogeneous chain were studied in this paper. Using standard techniques of probability theory, expressions for the frequency distribution function (2) and the localization length (6) were derived. Having considered only pair correlations between atoms, both these expressions contained only one unknown function — the joint probability distribution of the massm n and the ratiot n ± = −kun±1/u n which could be found as a solution of the integral equation (5). Our approach to the problem was applied on the ideal lattice and the lattice with low concentration of impurities. In these cases the solutions of the integral equation (5) reduced to the functional form (7) were found analytically. Using these solutions, old well-known results for ϱ(ω2) and the local vibration of impurities were derived by this method.

The rate distortion theory and probability models

Abstract: The Rate Distortion Theory is a branch of the Information Theory applicable to the case when the entropy of the source exceeds the capacity of the Channel. A rate distortion function R(D) is defined between the input and output alphabets X, Y of a channel. It can be shown that it is possible to design a communication system which achieves a fidelity D when the capacity of the channel C is greater than R(D). In this paper, the formulation of the Rate Distortion Theory is used for the problem of derived probability models. The variables X, Y and the Channel are given new interpretations, and the result is an ability to pick a derived probability model for Y when X is of a known probability structure. The fidelity criterion assumes the rle of an error function in this terminology. Two specific cases are discussed.

Measurements of the stochastic nature of atmospheric spectral amplitudes

Abstract: The stochastic nature of the power spectral amplitudes of the neutral atmospheric boundary layer is examined Probability density distributions and probability distributions of longitudinal and lateral power spectra amplitudes are computed from neutral atmospheric boundary layers The statistical distributions are computed for frequencies of 0006, 001, 003, 006, 01, and 05 Hz at each of the elevations of 18, 30, 60, 90, 120, and 150 m When the probability density distributions are properly nondimensionalized, the data tend to collapse to a universal curve An empirical curve fit to the universal nondimensionalized probability density distribution is also given Probability distributions of individual frequency power spectral amplitudes are also presented for all elevations and frequencies An interesting observation from the data is that greater than 10 percent of the time the power spectral amplitude at a given frequency will genrally be more than three times the temporal mean value computed by standard Fourier techniques The standard power spectral density curves are also included in the report