The study of ionospheric scintillation belongs to the class of problems dealing with wave diffraction and propagation through a random medium, and its complete theoretical solution is presently not available. Approximate solutions or models, such as the 'thin phase diffraction screen model' and the 'Rytov solution for weak scintillation', have been proposed and do apply under restrictive condit...

Motivated by interest in probability density functions (pdf’s) with nonexponential tails in queueing and related areas, we introduce and investigate two classes of beta mixtures of exponential pdf’s. These classes include distributions introduced by Boxma and Cohen (1997) and Gaver and Jacobs (1998) to study queues with long-tail service-time distributions. When the standard beta pdf is used as...

While second and higher order correlations of the light distribution have received extensive study, the lowest order probability distribution function (PDF) — the probability that a unit volume of space will emit a given amount of light — has received very little attention. We estimate this function with the aid of hydrodynamic simulations of the ΛCDM model, finding it significantly different f...

Meals are clusters of feedbunk visit (BV) events that are differentiated from the next meal by a nonfeeding interval that is longer compared with the nonfeeding intervals within a meal. The longest nonfeeding interval considered to be part of a meal is defined as the meal criterion. The objective of this study was to determine which combination of 2 probability density functions [(PDF): Gaussia...

-In this paper, the critical clearing time, tcc in power system transient stability analysis is modeled as a random variable due to the randomness nature of power system load. A linear approximation approach that mainly involves the sensitivity calculation of the derivative of tcc to system load is developed to obtain the probability density function (pdf) of tcc based on the pdf of system load...

We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. For the PDFs of velocity and...

Reactive flow simulations using large-eddy simulations (LES) require modelling of sub-filter fluctuations. Although conserved scalars like mixture fraction can be represented using a beta-function, the reactive scalar probability density function (PDF) does not follow an universal shape. A one-point one-time joint composition PDF transport equation can be used to describe the evolution of the s...

Rejection sampling is a well-known method to generate random samples from arbitrary target probability distributions. It demands the design of a suitable proposal probability density function (pdf) from which candidate samples can be drawn. These samples are either accepted or rejected depending on a test involving the ratio of the target and proposal densities. The adaptive rejection sampling ...

In this paper we investigate the performance of probability estimation methods for reliability analysis. The probability estimation methods typically construct the probability density function (PDF) of a system response using estimated statistical moments, and then perform reliability analysis based on the approximate PDF. In recent years, a number of probability estimation methods have been pr...

A technique is presented in order to evaluate the probability of failure in analytical form instead of approximation methods like FORM/SORM and no series expansion is involved in this expression. This technique is based on the Finite Element Method to obtain the expression of the response of stochastic systems, and the transformation of random variables to obtain the probability density functio...