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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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Journal ArticleDOI
TL;DR: This paper characterize situations where the fast rate is valid, and also gives rates for a variety of cases where they are slower, and a modification of the usual variable window width estimator is proposed, which does have the earlier claimed rates of convergence.
Abstract: Variable window width kernel density estimators, with the width varying proportionally to the square root of the density, have been thought to have superior asymptotic properties. The rate of convergence has been claimed to be as good as those typical for higher-order kernels, which makes the variable width estimators more attractive because no adjustment is needed to handle the negativity usually entailed by the latter. However, in a recent paper, Terrell and Scott show that these results can fail in important cases. In this paper, we characterize situations where the fast rate is valid, and also give rates for a variety of cases where they are slower. In addition, a modification of the usual variable window width estimator is proposed, which does have the earlier claimed rates of convergence.

97 citations

Journal ArticleDOI
TL;DR: In this article, the random response of highway bridges under the passage of vehicles is studied and the Poisson process is used to represent the vehicular traffic and the bridge is idealized as a linear system.
Abstract: The random response of highway bridges under the passage of vehicles is studied. The Poisson process is used to represent the vehicular traffic and the bridge is idealized as a linear system. The probability density function and expected rate of threshold crossings of the bridge response are obtained.

96 citations

Journal ArticleDOI
TL;DR: By using the analytical expressions of the capacity, it is observed that the optimal power and rate adaptation provides better capacity than the optimal rate adaptation with constant power from low to moderate signal-to-noise ratio values over dissimilar Rician fading channels.
Abstract: In this letter, we derive the probability density function (PDF) and cumulative distribution function (CDF) of the minimum of two non-central Chi-square random variables with two degrees of freedom in terms of power series. With the help of the derived PDF and CDF, we obtain the exact ergodic capacity of the following adaptive protocols in a {decode-and-forward} (DF) cooperative system over dissimilar {Rician} fading channels: (i) constant power with optimal rate adaptation; (ii) optimal simultaneous power and rate adaptation; (iii) channel inversion with fixed rate. By using the analytical expressions of the capacity, it is observed that the optimal power and rate adaptation provides better capacity than the optimal rate adaptation with constant power from low to moderate signal-to-noise ratio values over dissimilar Rician fading channels. Despite low complexity, the channel inversion based adaptive transmission is shown to suffer from significant loss in capacity as compared to the other adaptive transmission based techniques over DF Rician channels.

96 citations

Journal ArticleDOI
TL;DR: The derivation and analysis of mesoscopic (continuous-time random walk) equations for both jump and velocity models with stochastic resetting shows that stationary states emerge for any shape of the waiting-time and jump length distributions.
Abstract: It is known that introducing a stochastic resetting in a random-walk process can lead to the emergence of a stationary state. Here we study this point from a general perspective through the derivation and analysis of mesoscopic (continuous-time random walk) equations for both jump and velocity models with stochastic resetting. In the case of jump models it is shown that stationary states emerge for any shape of the waiting-time and jump length distributions. The existence of such state entails the saturation of the mean square displacement to an universal value that depends on the second moment of the jump distribution and the resetting probability. The transient dynamics towards the stationary state depends on how the waiting time probability density function decays with time. If the moments of the jump distribution are finite then the tail of the stationary distributions is universally exponential, but for Levy flights these tails decay as a power law whose exponent coincides with that from the jump distribution. For velocity models we observe that the stationary state emerges only if the distribution of flight durations has finite moments of lower order; otherwise, as occurs for Levy walks, the stationary state does not exist, and the mean square displacement grows ballistically or superdiffusively, depending on the specific shape of the distribution of movement durations.

96 citations

Journal ArticleDOI
TL;DR: The escape from a metastable state over a fluctuating barrier of a physical system is experimentally investigated and resonant activation, namely a minimum of the average escape time as a function of the correlation rate, is observed.
Abstract: We experimentally investigate the escape from a metastable state over a fluctuating barrier of a physical system. The system is switching between two states under electronic control of a dichotomous noise. We measure the escape time and its probability density function as a function of the correlation rate of the dichotomous noise in a frequency interval spanning more than four frequency decades. We observe resonant activation, namely a minimum of the average escape time as a function of the correlation rate. We detect two regimes in the study of the shape of the escape time probability distribution: (i) a regime of exponential and (ii) a regime of nonexponential probability distribution.

96 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023382
2022906
2021906
20201,047
20191,117
20181,083