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.

Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations

Abstract: Maximum-likelihood estimates of the parameters of stochastic differential equations are consistent and asymptotically efficient, but unfortunately difficult to obtain if a closed-form expression for the transitional probability density function of the process is not available. As a result, a large number of competing estimation procedures have been proposed. This article provides a critical evaluation of the various estimation techniques. Special attention is given to the ease of implementation and comparative performance of the procedures when estimating the parameters of the Cox–Ingersoll–Ross and Ornstein–Uhlenbeck equations respectively.

Monotonic continuous-time random walks with drift and stochastic reset events

Abstract: In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

Investigation of Reverberation Chamber Measurements Through High-Power Goodness-of-Fit Tests

Abstract: This paper aims to improve the analysis of distribution functions of a rectangular component of the electric field (ER) and the power received in an overmoded reverberation chamber. All data and analysis were achieved in the Institute of Electronics and Telecommunications of Rennes (IETR) mode-stirred chamber. For the power received on a large antenna, tests are consistent with the exponential probability density function assumption. However, high-power goodness-of-fit tests modify the determination of the lowest frequency from which the ideal underlying theoretical distributions can be associated with measurements. For the electric field in an overmoded regime, a Weibull distribution is proposed to model ER measurements, instead of the Rayleigh distribution hypothesis, which is rejected by statistical tests. Furthermore, Weibull distribution provides better agreement with standard deviation of samples. An additional experiment with a monopole-like antenna illustrates that the exponential distribution is rejected when the monopole is small with respect to the wavelength, but is accepted when the antenna length is roughly over lambda/4. Experimental results are provided by a large number of goodness-of-fit tests. The paper highlights that the use of adapted critical values is necessary for testing a distribution function whose parameters are estimated.

An Analytical Framework for Offshore Wind Farm Layout Optimization

Abstract: A method is developed for using the levelized cost of energy as the objective function for offshore wind farm layout optimization problems. The method converts the cost of energy into a function of turbine position only. To accomplish this, wind speed data are first characterized by direction sector. Continuous functions are then fitted to the Weibull parameters for each direction sector. The wind direction probability density function and the turbine power curve are also transformed into continuous functions. For each turbine in the farm, the continuous function that describes the Weibull scale parameter can be scaled to reflect wake losses from other turbines. The function may also be adjusted according to the variation in wind speed with fetch. The annual energy production of the farm is thus modeled as a function only of the turbine positions. When combined with wind farm cost estimates, the levelized cost of energy is still only a function of turbine position and can then be used as an objective func...