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.

A modified model for the fading signal at a mobile radio channel

Abstract: A generalization of an existing model for the fading signal at a mobile radio antenna has been made. The generalization lies in letting the scattering waves not necessarily be traveling horizontally. The effects of this generalization are investigated concerning probability density function (pdf), correlational properties, and power spectra of the phase and envelope. The pdf is not affected, but the power spectrum of the envelope is significantly affected. This generalized spectrum is smoother than the original and always finite, which the latter is not. Thus it is assumed that the generalized model is more consistent with measured spectra, especially in urban environments.

flexsurv: A Platform for Parametric Survival Modeling in R

Abstract: flexsurv is an R package for fully-parametric modeling of survival data. Any parametric time-to-event distribution may be fitted if the user supplies a probability density or hazard function, and ideally also their cumulative versions. Standard survival distributions are built in, including the three and four-parameter generalized gamma and F distributions. Any parameter of any distribution can be modeled as a linear or log-linear function of covariates. The package also includes the spline model of Royston and Parmar (2002), in which both baseline survival and covariate effects can be arbitrarily flexible parametric functions of time. The main model-fitting function, flexsurvreg, uses the familiar syntax of survreg from the standard survival package (Therneau 2016). Censoring or left-truncation are specified in 'Surv' objects. The models are fitted by maximizing the full log-likelihood, and estimates and confidence intervals for any function of the model parameters can be printed or plotted. flexsurv also provides functions for fitting and predicting from fully-parametric multi-state models, and connects with the mstate package (de Wreede, Fiocco, and Putter 2011). This article explains the methods and design principles of the package, giving several worked examples of its use.

Neural Spline Flows

Abstract: A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the parameterization of an easily invertible elementwise transformation, whose choice determines the flexibility of these models. Building upon recent work, we propose a fully-differentiable module based on monotonic rational-quadratic splines, which enhances the flexibility of both coupling and autoregressive transforms while retaining analytic invertibility. We demonstrate that neural spline flows improve density estimation, variational inference, and generative modeling of images.

Characterisation of radar clutter as a spherically invariant random process

Abstract: A statistical characterisation of clutter as a complex random process is needed in the design of optimum detection schemes. The paper considers modelling complex clutter as a spherically invariant random process (SIRP), namely assuming that its PDFs can be expressed as non-negative definite quadratic forms, a generalisation of a Gaussian process. Relevant properties of SIRPs are summarised, and shown to comply with basic requirements such as circular symmetry of the joint PDF of the in-quadrature components or, equivalently, the uniformity of the phase distribution. A constraint of admissibility must be imposed on the envelope distribution, but most commonly used envelope distributions, including Weibull, contaminated Rayleigh and K-distribution are shown to be admissible. Although a general SIRP is not ergodic, a characterisation of the clutter process as an SIRP scanned in the ensemble is finally proposed, which restores ergodicity. The interpretation of this model in the light of already proposed composite scattering models is also discussed.