Showing papers on "K-distribution published in 1975"

An introduction to probability and statistics

Abstract: Probability Random Variables and Their Probability Distributions Moments and Generating Functions Multiple Random Variables Some Special Distributions Limit Theorems Sample Moments and Their Distributions Parametric Point Estimation Neyman-Pearson Theory of Testing of Hypotheses Some Further Results on Hypotheses Testing Confidence Estimation The General Linear Hypothesis Nonparametric Statistical Inference.

On the probability distribution of line-of-sight fluctuations of optical signals

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.

Probability distributions in a round heated jet

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

Component Distributions for Fluctuating Radar Targets

Abstract: The paper describes a technique whereby with each physical model for fluctuating radar targets is associated a standard model and a mathematical model. All three models have radar cross section distributions and certain properties of component independence in common. A wide selection of mathematical models hence becomes available as a tool for analyzing physical target models. It is shown that the mathematical model can be represented by a quadratic form involving generalized Bessel and Gaussian components. The probability distribution of the quadratic form is derived and expressed in terms of confluent hypergeometric functions. The authors also derive the related pulse-train probability distributions for two pulse integration schemes using either scan-to-scan or pulse-to-pulse amplitude independence.

Special Functions and the Limit Properties of Probability Distributions. I

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.

Some characterizations of discrete distributions by properties of their moment distributions

Abstract: The moment distributions of a nonnegative random variable are defined and their applications in life length studies are indicated. Some properties of the moment distributions are employed to characterize the discrete distributions in the class of modified power series distributions introduced by the author (1974). In particular, characterisations of Poisson, binomial and negative binomial distributions are obtained.

On the dependence of X1 + X2 and X1/X2

Abstract: A well-known characterization of the family of gamma distributions is that if X1 and X2 are Independent positive random variables, then X1 + X2 and X1/X2 are independent if and only if X1 and X2 have gamma distributions with the same scale parameter. We describe the dependence of X1 + X2 and X1/X2 for certain classes of distributions, which include the common models used for positive random variables of the continuous type. A method for testing the hypothesis that a random sample comes from a gamma distribution is proposed.

On information-improvement

Abstract: Theil [1967] has introduced a quantity known as ‘Information-Improvement’ widely used in economic analysis. In this paper a mean-value representation of this measure for generalized probability distributions is given and some of its interesting properties are also studied. Finally the concept is extended to bivariate distributions.