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: Results show that LIF and the new method proposed in this research are very efficient when dealing with nonlinear performance function, small probability, complicated limit state and engineering problems with high dimension.
268 citations
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TL;DR: The Gamma function as discussed by the authors is a generalized factorial function that can be used to estimate the probability distribution of a probability distribution, and it has been used in many applications, e.g., as part of probability distributions.
Abstract: In what follows, we introduce the classical Gamma function in Sect. 2.1. It is essentially understood to be a generalized factorial. However, there are many further applications, e.g., as part of probability distributions (see, e.g., Evans et al. 2000). The main properties of the Gamma function are explained in this chapter (for a more detailed discussion the reader is referred to, e.g., Artin (1964), Lebedev (1973), Muller (1998), Nielsen (1906), and Whittaker and Watson (1948) and the references therein).
267 citations
TL;DR: In this article, a new approach, TDMAinv, was proposed to represent the inverted GF-PDF as a piecewise linear function, where the convergence of the inversion is robust and independent of the initial guess.
266 citations
TL;DR: A Bayesian probabilistic inferential framework, which provides a natural means for incorporating both errors and prior information about the source, is presented and the inverse source determination method is validated against real data sets acquired in a highly disturbed flow field in an urban environment.
266 citations
TL;DR: In this article, a stochastic parameterization scheme for deep convection is described, suitable for use in both climate and NWP models, and theoretical arguments and results of cloud-resolving models are discussed in order to motivate the form of the scheme.
Abstract: A stochastic parameterization scheme for deep convection is described, suitable for use in both climate and NWP models. Theoretical arguments and the results of cloud-resolving models are discussed in order to motivate the form of the scheme. In the deterministic limit, it tends to a spectrum of entraining/detraining plumes and is similar to other current parameterizations. The stochastic variability describes the local fluctuations about a large-scale equilibrium state. Plumes are drawn at random from a probability distribution function (PDF) that defines the chance of finding a plume of given cloud-base mass flux within each model grid box. The normalization of the PDF is given by the ensemble-mean mass flux, and this is computed with a CAPE closure method. The characteristics of each plume produced are determined using an adaptation of the plume model from the Kain–Fritsch parameterization. Initial tests in the single-column version of the Unified Model verify that the scheme is effective in producing the desired distributions of convective variability without adversely affecting the mean state.
266 citations