Showing papers on "K-distribution published in 1973"

Consistency of an estimate of tree-dependent probability distributions (Corresp.)

Abstract: We demonstrate in this correspondence that the procedure introduced by Chow and Liu for estimating tree-dependent probability distributions is consistent.

Some interesting properties of lagrangian distributions

Abstract: Several discrete Lagrangian probability distributions have been generated by Consul and Shanton (1972) by using the Lagrange expansion in y of a probability generating function f(x) under the transformation x = y g(x) where g(x) is another pgf. By using probabilistic arguments the authors show that the transformation x = y g(x) occurs naturally in the distribution of the number of customers served during a busy period which implies that at least one particular family of these Lagraagian distributions must play a basic role in queueing theory. It has also been proved that under one set of conditions all discrete Lagrangian distributions approach to the normal density function while under another set of conditions they approach the inverse Gaussiam density function.

Techniques for Efficient Monte Carlo Simulation. Volume 2. Random Number Generation for Selected Probability Distributions

Abstract: : Algorithms for efficient generation of random numbers from various probability distributions are presented, in both a flowchart form and as a sample FORTRAN subroutine. Twenty-two different distributions, including all commonly encountered discrete and continuous functions, the Weibull, Johnson, and Pearson families of empirical distributions, and histogram distributions, are covered. The general techniques to apply in deriving a random number selection scheme for an arbitrary distribution are discussed. A machine- independent subroutine for generating uniform random numbers is also described.

Extended and multivariate Tukey lambda distributions

Abstract: SUMMARY The symmetrical Tukey lambda distributions are obtained by simple transformations of a uniformly distributed variable. Systems of multivariate distributions can be formed by applying these transformations to sets of variables having a joint Dirichlet distribution. Since no more than one of such a set of variables can have a uniform distribution, though all have beta distributions, we are led to study distributions of transforms of variables having standard beta distributions. These distributions are termed extended Tukey lambda distributions. Properties of these distributions are studied. Properties of the multivariate distributions are also described and a numerical illustration is presented.

Correlated Clutter and Resultant Properties of Binary Signals

Abstract: A simple Markov process model of binary, digitized radar clutter returns is assumed. Probability distributions for the number of hits in n observations are developed for small n with a binary parameter describing the process derived for Rayleigh distributed clutter. Tables of distributions are included, along with an example to show the effects of correlation on the false-alarm probabilities of a sliding-window detector.

Some uses of lagrange’s formula in the distribution theory with reference to queuing problems

Abstract: LAGRANGE's formula has been used to derive certain expression which occur frequently in the theory of queues. The method is perhaps the simplest one to prove that these expressions are probability distributions. In particular the generalized forms of POISSON and negative binomail distributions are obtained. Expressions for certain summaation series have also been derived. The use of the formula enables us to relax some conditions on the parameters of these distributions.

On the Effective Single Trial Probability of Success

Abstract: Define the cumulative probability Pn of occurence of some event as the probability that it occurs at least once in n trials. If the single trial probabilities are not fixed, but are drawn from a distribution of their own, or are dependent on some other nonfixed variable, then it would be convenient to have an ?effective single trial probability (esp)? for use in the simple Bernoulli model which would give the same cumulative probability of occurence as actually observed. We show here that the esp can be interpreted as a kind of average, and that its value is given by 1 minus the geometric mean of 1-d(p), where d(p) is the probability density function of the single trial probabilities, the p's. We further define this geometric mean for both discrete and continuous distributions and evaluate the esp for several cases. These results are compared with earlier ones which suggest that the esp is given by the (arithmetic) average or expectation of the single trial probabilities, and we determine under what conditions this simpler result can be used.