Showing papers on "Symmetric probability distribution published in 1975"
145 citations
TL;DR: In this paper, some general problems concerning the probability distribution of an optical signal propagated over a line-of-sight path are discussed, and the basic physical models for the log-normal and Rice-Nakagami probability distributions are given.
Abstract: In this paper some general problems concerning the probability distribution of an optical signal propagated over a line-of-sight path are discussed. The basic physical models for the log-normal and Rice-Nakagami probability distributions are given, and various theoretical methods for finding the distribution are discussed, including application of the central-limit theorem, calculating moments, finding the characteristic functional, and trial and error. The not-well-known fact that the log-normal distribution is not uniquely determined by its moments is pointed out. A summary of the present theoretical and experimental work is given. In addition, some different methods of experimental analysis are suggested, including the use of hypothesis testing and goodness-of-fit tests. These methods should permit better presentation of information on probability distributions.
97 citations
55 citations
01 Jan 1975
TL;DR: In this paper, the absolute moments of probability distribution functions are derived using fractional calculus. But they are not used to obtain formulae for the absolute moment of probability distributions.
Abstract: Techniques of fractional calculus are used to obtain formulae for the absolute moments of probability distribution functions.
48 citations
TL;DR: In this article, a general stochastic model for the orientational motion of molecules in dense media is introduced, where the rotational motion is characterized by transition probabilities whose form can be chosen in accordance with the physical situation.
Abstract: We introduce a general stochastic model that encompasses all other commonly used stochastic models for the orientational motion of molecules in dense media. In this model the rotational motion is envisaged to proceed by an alternating sequence of collision and between collision events. These events are characterized by transition probabilities whose form can be chosen in accordance with the physical situation. The durations of the events are governed by probability density functions. These probability densities enable us to investigate the effects of finite durations of collisions and of time correlations between successive collisions. The effect of correlations between successive collisions is to produce nonexponential behavior in the time correlation functions of orientational variables. Indeed these time correlation functions can become negative and can have damped oscillatory behavior even in the complete absence of explicit inertial effects (free rotations). The finite duration of collisions insures ...
38 citations
TL;DR: In this paper, the marginal and joint probability density functions of the longitudinal and radial components of the velocity and temperature at three different radial positions of an axisymmetric heated turbulent air jet are presented.
Abstract: Measurements of the marginal and joint probability density functions of the longitudinal and radial components of the velocity, and temperature at three different radial positions of an axisymmetric heated turbulent air jet are presented The results are compared with normal distributions
36 citations
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TL;DR: An experiment is defined as a random variable which may take some posterior probability distributions according to a marginal probability and elementary properties of this definition with respect to information value theory are derived.
Abstract: An experiment is defined as a random variable which may take some posterior probability distributions according to a marginal probability. Elementary properties of this definition with respect to information value theory are derived as well as their practical implications.
21 citations
TL;DR: In this paper, an experiment is defined as a random variable which may take some posterior probability distributions according to a marginal probability, and elementary properties of this definition with respect to information value theory are derived as well as their practical implications.
Abstract: An experiment is defined as a random variable which may take some posterior probability distributions according to a marginal probability. Elementary properties of this definition with respect to information value theory are derived as well as their practical implications.
20 citations
TL;DR: The study of the limit properties of probability distributions is one of the classical problems in probability theory and the method of characteristic functions has become the principal approach and it has been developed to such an extent that the problem appears to have been almost closed as mentioned in this paper.
Abstract: The study of the limit properties of probability distributions is one of the classical problems in probability theory. The method of characteristic functions has become the principal approach and it has been developed to such an extent that the problem appears to have been almost closed.
18 citations
TL;DR: In this paper, it was shown that a class of spherically symmetric infinitely divisible distribution functions that contains the class of symmetric stable distribution functions is unimodal.
16 citations
Abstract: Link and Heath [1975] have analysed a random walk model for two-choice reaction time on the assumption that the two probability density functions (p.d.f.s) of the step-size, each p.d.f. corresponding to one stimulus, are mirror reflections of each other; and they have demonstrated the critical role played by the symmetry of the moment generating function (m.g.f.) of the step size in the determination of whether or not error and correct reaction times are equal. It is shown here that, given reflection symmetry, m.g.f. symmetry is necessary and sufficient for the random walk model to be equivalent to a sequential probability ratio test.
01 Jan 1975
TL;DR: In this article, lower confidence limits for the impact probability within a circle of fixed radius in the bivariate normal case with zero mean vector were derived for independent coordinates and known ratio of variances.
Abstract: : Lower confidence limits are derived for the impact probability within a circle of fixed radius in the bivariate normal case with zero mean vector. For independent coordinates and known ratio of variances, the lower confidence limit is a strongly consistent estimator of the impact probability and is uniformly most accurate (UMA). When the ratio of the variances is also unknown, the lower confidence limit is a strongly consistent estimator of the impact probability. Some discussion is provided when the correlation between the coordinates is unknown. A Table of the impact probability function is provided which can be employed for both point estimation and for obtaining lower confidence limits and the use of the table is demonstrated. A FORTRAN program for the computation of the impact probability is included. (Author)
TL;DR: In this article, a weighted Markov transition probability distribution of the number of transitions in a sequence of trials is derived, and the associated generating function is evaluated explicitly by contour integration and the desired probability distribution is extracted.
Abstract: There are numerous physical situations in which a sequence of changes of state occurs, in an apparently random manner. Examples range from the reigning party in a multiparty political system to the sequence of tissue types in a linear tissue sample of a disorganized tissue mass. The question arises whether the two successive states are really correlated. The subject considered in this paper is the following: given the number of occurrences of each event in a sequence of trials, what is the probability distribution of the number of transitions. A weighted Markov transition probability is found. The associated generating function is evaluated explicitly by contour integration, and the desired probability distribution is extracted. Its long-chain asymptotic value is also obtained. (RWR)
TL;DR: In this article, it was shown that the correlation lengths among physical quantities in space-time in an initial state are of short range under a finite order perturbation of an external field.
Abstract: The extensive property of the logarithm of probability distribution function on macro variables in the states far from thermal equilibrium is investigated with the aid of a cu~u lant-correlation function method. If the correlation lengths among physical quantities in space time in an initial state are of short range, then it is shown that the correlation lengths in space-time remain to be of short range· under a finite order perturbation of an external field. The extensive properties of the logarithms of the probability distribution funCtions of general types of macrovariable are found if the state observed can be reached by a finite order perturbation. At a critical point ( , line or domain) our analysis cannot be applied. The asymptotic evaluation of the probability distribution functions of macrovariables in non equilibrium state is thus shown. The applications are discussed. The logarithm of the proba bility distribution function of the time rate of change in the quantity conjugate -to the external field in a steady state leads· to the generalization of Onsage:r's po~ential. Some remarks on the variational principles are presented.
TL;DR: In this paper, the authors derived new theoretical expressions of probability density and cumulative distribution functions for the output response without any simplification of the problem and any approximation of analysis in the case when a general random signal with arbitrary probability distribution and correlation functions is passed through an arbitrary linear vibratory system with finite order.
TL;DR: The first-order term of the joint probability distribution of Eh1 + k,..., Ehm+ k, for h1, hm fixed and k variable, is derived for both space groups P{\bar 1} and P1.
Abstract: The first-order term of the joint probability distribution of Eh1 + k, . . . , Ehm + k, for h1, . . . , hm fixed and k variable, is derived for both space groups P{\bar 1} and P1. It appears that the first-order term affects the most probable values for the moduli of the structure factors, but that it has no influence on the most probable values for the phases.
TL;DR: In this paper, the authors examined the accuracy of several approximations which are checked against large sample Monte Carlo values and concluded that the accuracy was not significantly worse than the original Monte Carlo distribution.
Abstract: : The extreme spread, or greatest distance between all pairs of points on a target, is often used as a rapid measure of dispersion or precision of shot groups on a target. It is therefore desirable to know its statistical properties. Since the exact theoretical distribution has not yet been worked out, this report examines the accuracy of several approximations which are checked against large sample Monte Carlo values.
TL;DR: In this article, the Edgeworth expansion of a probability density function is used to refine an atom position so that it coincides with a position of maximum probability rather than the mean of the density function.
Abstract: A study of the Edgeworth expansion of a probability density function shows how an atom position may be refined so that it coincides with a position of maximum probability rather than the mean of the probability density function.
TL;DR: In this article, some criteria are given for type (B) of real probability distributions in terms of characteristic functions and of probability density functions, and a contribution to the asymptotic equivalence theory is made by the present author.
Abstract: Some criteria are given for type (B)
d
or uniform asymptotic equivalence of real probability distributions in terms of characteristic functions and of probability density functions. This work is a contribution to the asymptotic equivalence theory which has been developed by the present author [1], [2].