Topic
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.
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TL;DR: In this article, a mathematical and statistical study which shows the flexibility and limitations of the log Pearson type 3 distribution is carried out, and the results indicate the various forms of density function and relationships that exist between distribution parameters and moments, coefficient of variation, and coefficient of skewness.
Abstract: A mathematical and statistical study which shows the flexibility and limitations of the log Pearson type 3 distribution is carried out. The results obtained indicate the various forms of density function and relationships that exist between distribution parameters and moments, coefficient of variation, and coefficient of skewness. The method of fitting proposed by the Hydrology Committee of the Water Resources Council is compared with a new method which instead of using moments of the logarithmic values retains the moments of the original data. In the case of events with a large return period the results obtained by the two methods may deviate appreciably, and because in the proposed method the same weight is given to each of the observed values, it will result in a better fit of the data.
144 citations
TL;DR: The adaptive importance sampling approach is further developed by incorporating a nonparametric multimodal probability density function model called the Gaussian mixture as the importance sampling density, which is used to fit the complex shape of the absolute best sampling density functions including those with multiple important regions.
143 citations
TL;DR: In this paper, spherically invariant random processes (SIRPs) are used as stationary models for speech signals in telephone channels and a comprehensive mathematical treatment is achieved by means of Meijer's G -functions.
143 citations
Journal Article•
TL;DR: In this article, a random walk model is proposed for space fractional diffusion, where the fundamental solutions of these generalized diffusion equations are shown to provide certain probability density functions, in space or time, which are related to the relevant class of stable distributions.
Abstract: FRACTIONAL calculus allows one to generalize the linear (one-dimensional) diffusion equation by replacing either the first time-derivative or the second space-derivative by a derivative of a fractional order. The fundamental solutions of these generalized diffusion equations are shown to provide certain probability density functions, in space or time, which are related to the relevant class of stable distributions. For the space fractional diffusion, a random-walk model is also proposed.
143 citations
TL;DR: In this article, an analytical method and specific results are presented for random vibrations of systems with lumped parameters and classical impacts whereby finite relations between impact/rebound velocities are imposed at the impact instants that are not known in advance but rather governed by the equations of motion.
Abstract: Analytical methods and specific results are presented for random vibrations of systems with lumped parameters and “classical” impacts whereby finite relations between impact/rebound velocities are imposed at the impact instants that are not known in advance but rather governed by the equations of motion. Emphasis is placed on the procedures using special piecewise-linear transformation of state variables that exclude the velocity jumps at impacts or makes them small if impact losses are present. In the former case, exact analyses for stationary probability densities of the response to white-noise excitation are possible, whereas the stochastic averaging method is applied in the latter case. Furthermore, the special case of an isochronous system permits a more profound response analysis, such as predicting the spectral density of the response or subharmonic response to narrow-band excitation. The method of direct energy balance is also illustrated, based on direct application of the stochastic differential equation calculus between impacts. Certain two-degree-of-freedom impacting systems are considered, with application to moored systems, as used in ocean engineering.
143 citations