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.

Time-Dependent Mechanism Reliability Analysis With Envelope Functions and First-Order Approximation

Abstract: This work develops an envelope approach to time-dependent mechanism reliability defined in a period of time where a certain motion output is required. Since the envelope function of the motion error is not explicitly related to time, the time-dependent problem can be converted into a time-independent problem. The envelope function is approximated by piecewise hyperplanes. To find the expansion points for the hyperplanes, the approach linearizes the motion error at the means of random dimension variables, and this approximation is accurate because the tolerances of the dimension variables are small. The expansion points are found with the maximum probability density at the failure threshold. The time-dependent mechanism reliability is then estimated by a multivariable normal distribution at the expansion points. As an example, analytical equations are derived for a four-bar function generating mechanism. The numerical example shows the significant accuracy improvement.

Fast Global Kernel Density Mode Seeking: Applications to Localization and Tracking

Abstract: Tracking objects in video using the mean shift (MS) technique has been the subject of considerable attention. In this work, we aim to remedy one of its shortcomings. MS, like other gradient ascent optimization methods, is designed to find local modes. In many situations, however, we seek the global mode of a density function. The standard MS tracker assumes that the initialization point falls within the basin of attraction of the desired mode. When tracking objects in video this assumption may not hold, particularly when the target's displacement between successive frames is large. In this case, the local and global modes do not correspond and the tracker is likely to fail. A novel multibandwidth MS procedure is proposed which converges to the global mode of the density function, regardless of the initialization point. We term the procedure annealed MS, as it shares similarities with the annealed importance sampling procedure. The bandwidth of the procedure plays the same role as the temperature in conventional annealing. We observe that an over-smoothed density function with a sufficiently large bandwidth is unimodal. Using a continuation principle, the influence of the global peak in the density function is introduced gradually. In this way, the global maximum is more reliably located. Since it is imperative that the computational complexity is minimal for real-time applications, such as visual tracking, we also propose an accelerated version of the algorithm. This significantly decreases the number of iterations required to achieve convergence. We show on various data sets that the proposed algorithm offers considerable promise in reliably and rapidly finding the true object location when initialized from a distant point

Outage Probability in Arbitrarily-Shaped Finite Wireless Networks

Abstract: This paper analyzes the outage performance in finite wireless networks. Unlike most prior works, which either assumed a specific network shape or considered a special location of the reference receiver, we propose two general frameworks for analytically computing the outage probability at any arbitrary location of an arbitrarily-shaped finite wireless network: (i) a moment generating function-based framework which is based on the numerical inversion of the Laplace transform of a cumulative distribution and (ii) a reference link power gain-based framework which exploits the distribution of the fading power gain between the reference transmitter and receiver. The outage probability is spatially averaged over both the fading distribution and the possible locations of the interferers. The boundary effects are accurately accounted for using the probability distribution function of the distance of a random node from the reference receiver. For the case of the node locations modeled by a Binomial point process and Nakagami-m fading channel, we demonstrate the use of the proposed frameworks to evaluate the outage probability at any location inside either a disk or polygon region. The analysis illustrates the location-dependent performance in finite wireless networks and highlights the importance of accurately modeling the boundary effects.

Seismic Fragility Functions via Nonlinear Response History Analysis

Abstract: The estimation of building fragility, ie, the probability function of seismic demand exceeding a certain limit state capacity given the seismic intensity, is a common process inherent in

Deriving Exact Predictions From the Cascade Model

Abstract: McClelland's (1979) cascade model is investigated, and it is shown that the model does not have a well-defined reaction time (RT) distribution function because it always predicts a nonzero probability that a response never occurs. By conditioning on the event that a response does occur, RT density and distribution functions are derived, thus allowing most RT statistics to be computed directly and eliminating the need for computer simulations. Using these results, an investigation of the model revealed that (a) it predicts mean RT additivity in most cases of pure insertion or selective influence; (b) it predicts only a very small increase in standard deviations as mean RT increases; and (c) it does not mimic the distribution of discrete-stage models that have a serial stage with an exponentially distributed duration. Recently, McClelland (1979) proposed a continuous-time linear systems model of simple cognitive processes based on sequential banks of parallel integrators. This model, referred t o by McClelland as the cascade model, exhibits some potentially very interesting properties. For example, McClelland argues that under certain conditions it mimics some of the reaction time (RT) additivities characteristic o f serial discrete-stage models. Unfortunately, however, rigorous empirical testing of the model is precluded because McClelland (1979) offers no method for computing any of the RT statistics it predicts. The format of this note is as follows: I will show that the model always predicts a nonzero probability that a response never occurs, which means, for example, that it always predicts infinite mean RTs. One way to circumvent this problem is to look only at trials on which a reponse does occur. By doing this it is possible to derive an RT probability density function predicted by the cascade model. From it, virtually any desired RT statistic can be accurately computed. Some of these (e.g., means and variances) will be examined, with particular regard to how well they correspond t o known empirical results. For example, it turns out