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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01 Jan 1998
TL;DR: The solution method uses the concept of a p-Ievel efficient point (pLEP) intoduced by the first author (1990) and works in such a way that first all pLEP's are enumerated, then a cutting plane method does the rest of the job.
Abstract: The most important static stochastic programming models, that can be formulated in connection with a linear programming problem, where some of the right-hand side values are random variables, are: the simple recourse model, the probabilistic constrained model and the combination of the two. In this paper we present algorithmic solution to the second and third models under the assumption that the random variables have a discrete joint distribution. The solution method uses the concept of a p-level efficient point (pLEP) intoduced by the first author (1990) and works in such a way that first all pLEP’s are enumerated, then a cutting plane method does the rest of the job.
82 citations
TL;DR: The approximation is based on a generalization of the well known moment matching approximation (MMA) for the sum of lognormal RVs, and it allows quite simple handling of the power sum of interfering signals even in rather complicated scenarios.
Abstract: Moving from the need for a simple and versatile method for outage computation in various contexts of interest in wireless communications, in this paper we propose a lognormal approximation for the linear combination of a set of lognormal random variables (RV) with one-sided random weights. The approximation is based on a generalization of the well known moment matching approximation (MMA) for the sum of lognormal RVs, and it allows quite simple handling of the power sum of interfering signals even in rather complicated scenarios. Specifically, composite multiplicative channel models with unequal parameters can be handled, and generic (unequal) correlation patterns for some channel components can be handled with reference to any pair of signals. At this stage of the computation, only moments of the random weights are required. The probability density function of the random weight for the useful signal component may be required in computing outage probability, and numerical methods may be only required to solve a single integral at this second stage. The suitability of the approximation is examined by evaluating outage performance for various values of system parameters in some contexts of interest, namely spread spectrum systems and typical reuse-based systems with composite Rayleigh-lognormal and Nakagami-lognormal channels.
82 citations
TL;DR: In this paper, the influence of the tail weight of the error distribution is addressed in the setting of choosing threshold and truncation parameters, and different approaches to correction for stochastic design are suggested.
Abstract: SUMMARY Concise asymptotic theory is developed for non-linear wavelet estimators of regression means, in the context of general error distributions, general designs, general normalizations in the case of stochastic design, and non-structural assumptions about the mean. The influence of the tail weight of the error distribution is addressed in the setting of choosing threshold and truncation parameters. Mainly, the tail weight is described in an extremely simple way, by a moment condition; previous work on this topic has generally imposed the much more stringent assumption that the error distribution be normal. Different approaches to correction for stochastic design are suggested. These include conventional kernel estimation of the design density, in which case the interaction between the smoothing parameters of the non-linear wavelet estimator and the linear kernel method is described.
82 citations
TL;DR: Two numerical integration methods for inverting the characteristic function of a general quadratic form in normal random variables are presented in this paper, which make use of paths of integration that pass through, or near to, a suitable saddle-point.
Abstract: The problem of calculating the distribution function of a general quadratic form in normal random variables is examined. Two numerical integration methods for inverting the characteristic function are presented. Both make use of paths of integration that pass through, or near to, a suitable saddle-point. It is assumed that a computer is available for the calculation of functions of complex variables and for the performance of various matrix computations. Approximations for special cases are stated and examples are given.
82 citations
TL;DR: In this article, an easily computable predictive density is considered, which coincides with the posterior predictive density with a non-informative prior, for standard situations achievements are comparable with classical inference.
Abstract: An easily computable predictive density is considered. Although involving a plain maximum likelihood technique, it coincides with the posterior predictive density with a noninformative prior. For standard situations achievements are comparable with classical inference.
82 citations