Probability density function

About: Probability density function is a research topic. Over the lifetime, 22321 publications have been published within this topic receiving 422885 citations. The topic is also known as: probability function & PDF.

Telegraphic processes with stochastic resetting.

Abstract: We investigate the effects of resetting mechanisms on random processes that follow the telegrapher's equation instead of the usual diffusion equation. We thus study the consequences of a finite speed of signal propagation, the landmark of telegraphic processes. Likewise diffusion processes where signal propagation is instantaneous, we show that in telegraphic processes, where signal propagation is not instantaneous, random resettings also stabilize the random walk around the resetting position and optimize the mean first-arrival time. We also obtain the exact evolution equations for the probability density of the combined process and study the limiting cases.

A simple and unifying physical interpretation of scalar fluctuation measurements from many turbulent shear flows

Abstract: It is shown that measurements of the statistical properties of the concentration distributions of dispersing scalars taken from many different turbulent shear flows have a great number of common features. In particular the same simple relationship between the mean concentration and the mean-square fluctuation is shown to hold in all the flows, and this relationship is derived theoretically from well-known results for the unreal case when there is no molecular diffusion by a natural hypothesis about the effects of molecular diffusion. Application of the hypothesis to the higher moments and shape parameters gives results that agree reasonably well with the data (given the unavoidable experimental errors). The hypothesis should be subjected to further experimental analysis, and could simplify the application of turbulence closures and similar models. Extensions of the ideas to the probability density function of the scalar concentration suggest that it becomes self-similar. A final conclusion is that more attention to experimental errors due to instrument smoothing is highly desirable.

Selecting Among Probability Distributions Used in Reliability

Abstract: A method is given for selecting the member of a collection of families of distributions that best fits a set of observations. This method requires a noncensored set of observations. The families considered include the exponential, gamma, Weibull, and lognormal. A selection statistic is proposed that is essentially the value of the density function of a scale transformation maximal invariant. Some properties of the selection procedures based on these statistics are stated, and results of a simulation study are reported. A set of time-to-failure data from a textile experiment is used as an example to illustrate the procedure, which is implemented by a computer program.

Non-Gaussian Simulation: Cumulative Distribution Function Map-Based Spectral Correction

Abstract: Methods for stochastic simulation of sample functions have increasingly addressed the preservation of both spectral and probabilistic contents to offer an accurate description of the dynamic behavior of system input for reliability analysis. This study presents an efficient, flexible and easily applied stochastic non-Gaussian simulation method capable of reliably converging to a target power spectral density function and marginal probability density function, or a close relative thereof. Several existing spectral representation-based non-Gaussian simulation algorithms are first summarized. The new algorithm is then presented and compared with these methods to demonstrate its efficacy. The advantages and limitations of the new method are highlighted and shown to complement those of the existing algorithms.