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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, a series of nearly instantaneous vertical cross sections of power-plant plume concentrations obtained by both airborne and ground-based lidar systems for the EPRI Plume Model Validation and Development Project have been analyzed.
Abstract: A series of nearly instantaneous vertical cross sections of power-plant plume concentrations obtained by both airborne and ground-based lidar systems for the Electric Power Research Institute (EPRI) Plume Model Validation and Development Project have been analyzed. By statistically resampling the data, values of the ratio of the ensemble rms concentration fluctuation, σc, to the ensemble mean concentration, c, near the center of the plumes are found to vary from 0.2 to 4. More importantly, it is found that the normalized probability distribution function can be well represented as that resulting from a Gaussian distribution with any nonrealizable negative tail replaced by a delta function, representing intermittency at zero.
91 citations
TL;DR: In this paper, effects of parameter and philosophical choices are examined through all phases of sample calculations, and the results of choices made in stress transfer calculations, such as different slip models, fault rake, dip, and friction are tracked.
Abstract: [1] A sudden change in stress is seen to modify earthquake rates, but should it also revise earthquake probability? Data used to derive input parameters permit an array of forecasts; so how large a static stress change is required to cause a statistically significant earthquake probability change? To answer that question, effects of parameter and philosophical choices are examined through all phases of sample calculations. Drawing at random from distributions of recurrence-aperiodicity pairs identifies many that recreate long paleoseismic and historic earthquake catalogs. Probability density functions built from the recurrence-aperiodicity pairs give the range of possible earthquake forecasts under a point process renewal model. Consequences of choices made in stress transfer calculations, such as different slip models, fault rake, dip, and friction are tracked. For interactions among large faults, calculated peak stress changes may be localized, with most of the receiving fault area changed less than the mean. Thus, to avoid overstating probability change on segments, stress change values should be drawn from a distribution reflecting the spatial pattern rather than using the segment mean. Disparity resulting from interaction probability methodology is also examined. For a fault with a well-understood earthquake history, a minimum stress change to stressing rate ratio of 10:1 to 20:1 is required to significantly skew probabilities with >80–85% confidence. That ratio must be closer to 50:1 to exceed 90–95% confidence levels. Thus revision to earthquake probability is achievable when a perturbing event is very close to the fault in question or the tectonic stressing rate is low.
91 citations
TL;DR: In this article, the probability of a brittle crack formation in an elastic solid with fluctuating strength is considered, and a set of all possible crack trajectories reflecting the fluctuation of the strength field is introduced.
Abstract: Probability of a brittle crack formation in an elastic solid with fluctuating strength is considered. A set Omega of all possible crack trajectories reflecting the fluctuation of the strength field is introduced. The probability P(X) that crack penetration depth exceeds X is expressed as a functional integral over Omega of a conditional probability of the same event taking place along a particular path. Various techniques are considered to evaluate the integral. Under rather nonrestrictive assumptions, the integral is reduced to solving a diffusion-type equation. A new characteristic of fracture process, 'crack diffusion coefficient', is introduced. An illustrative example is then considered where the integration is reduced to solving an ordinary differential equation. The effect of the crack diffusion coefficient and of the magnitude of strength fluctuations on probability density of crack penetration depth is presented. Practical implications of the proposed model are discussed.
91 citations
Proceedings Article•
11 Apr 2019TL;DR: A method for probabilistic time series forecasting, which combines the modeling capacity of recurrent neural networks with the flexibility of a spline-based representation of the output distribution, and can flexibly adapt to different output distributions without manual intervention.
Abstract: In this paper, we propose a flexible method for probabilistic modeling with conditional quantile functions using monotonic regression splines. The shape of the spline is parameterized by a neural network whose parameters are learned by minimizing the continuous ranked probability score. Within this framework, we propose a method for probabilistic time series forecasting, which combines the modeling capacity of recurrent neural networks with the flexibility of a spline-based representation of the output distribution. Unlike methods based on parametric probability density functions and maximum likelihood estimation, the proposed method can flexibly adapt to different output distributions without manual intervention.
We empirically demonstrate the effectiveness of the approach
on synthetic and real-world data sets.
91 citations
TL;DR: In this article, a generalized probability density evolution equation (GPDEE) was derived to study the randomness propagation process in a physical system and a completely uncoupled partial differential equation was derived as well with respect to the evolutionary probability density function, which holds for any physical quantity of a probability dissipative system.
91 citations