Search results for "probability density function"
showing 10 items of 183 documents
A flux retrieval error behavior with CERES/TRMM data
2003
With the aid of CERES/TRMM (Clouds and the Earth's Radiant Energy System/Tropical Rainfall Measuring Mission) data, sampling problems that may impact the construction of anisotropic models have been investigated. We show the influence of the sun-orbit geometry, which causes a lack of measurements in forward and backward scattering directions at large viewing zenith angles, and how cloud properties retrieval algorithms as obtained from the Visible Infrared Scanner (VIRS) also affect sampling. We have also focused our attention on the dependency of the cloud cover retrieval algorithm with respect to the viewing zenith angle (VZA), showing that the shape of the cloud cover probability density …
Path integral solution by fractional calculus
2008
In this paper, the Path Integral solution is developed in terms of complex moments. The method is applied to nonlinear systems excited by normal white noise. Crucial point of the proposed procedure is the representation of the probability density of a random variable in terms of complex moments, recently proposed by the first two authors. Advantage of this procedure is that complex moments do not exhibit hierarchy. Extension of the proposed method to the study of multi degree of freedom systems is also discussed.
A Wiener Path Integral Technique for Non-Stationary Response Determination of Nonlinear Oscillators with Fractional Derivative Elements
2014
In this paper a novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators with fractional derivative elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes. In this manner, the analytical Wi…
Annual runoff regional frequency analysis in Sicily
2009
Abstract This paper performs annual runoff frequency analysis in Sicily, Italy using the index runoff method. Homogeneous regions, not necessarily defined by geographical boundaries but sharing common features from a morphologic and climatic standpoint, have been identified. For each region a single probability distribution function can be fitted to the available annual runoff data scaled by the index runoff. Starting from an initial dataset of 105 hydrometric stations, 57 stations have been selected using heuristic criteria associated with the Hosking and Wallis’s discordancy measure. The Mantel tests have been then applied to find out the physical and morphological parameters best correla…
Quick and Slow Components of the Hydrologic Response at the Hillslope Scale
2016
It is widely recognized that the Hortonian mechanism of runoff generation occurs in arid and semi-arid regions, generally characterized by high rainfall intensity on soils exhibiting low infiltrabilities. Differently, in steeply sloping forested watersheds in humid climates, by infiltrating through a highly permeable upper soil horizon, water moves beneath the soil surface determining a slow response. However, in most real cases, for example when in arid regions mountain forested areas take place, both (quick and slow) runoff generation processes coexist and together contribute to the hydrologic hillslope response. In this paper, based on analytical solutions of the hydrologic response, ins…
Interval Length Analysis in Multi Layer Model
2009
In this paper we present an hypothesis test of randomness based on the probability density function of the symmetrized Kulback-Leibler distance estimated, via a Monte Carlo simulation, by the distributions of the interval lengths detected using the Multi-Layer Model (MLM). The $MLM$ is based on the generation of several sub-samples of an input signal; in particular a set of optimal cut-set thresholds are applied to the data to detect signal properties. In this sense MLM is a general pattern detection method and it can be considered a preprocessing tool for pattern discovery. At the present the test has been evaluated on simulated signals which respect a particular tiled microarray approach …
On the Statistical Properties of Phase Crossings and Random FM Noise in Double Rayleigh Fading Channels
2016
In this paper, we study the statistics of phase processes and random frequency modulation (FM) noise encountered in double Rayleigh fading channels. The Rayleigh processes making up the double Rayleigh channel are assumed to be independent but not necessarily identically distributed. The Doppler power spectral densities of these processes are supposed to be symmetric about the carrier frequency. Under these fading conditions, we derive first an expression for the joint probability density function (jpdf) of the phase process and its rate of change. Capitalizing on this jpdf formula, we then investigate the probability density function (pdf) and cumulative distribution function (cdf) of rand…
Statistical Properties of Double Hoyt Fading With Applications to the Performance Analysis of Wireless Communication Systems
2018
In this paper, we investigate the statistical properties of double Hoyt fading channels, where the overall received signal is determined by the product of two statistically independent but not necessarily identically distributed single Hoyt processes. Finite-range integral expressions are first derived for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades of the envelope fading process. A closed-form approximate solution is also deduced for the LCR by making use of the Laplace approximation theorem. Applying the derived PDF of the double Hoyt channel, we then provide analytical expressions for the average…
Probabilistic quantum clustering
2020
Abstract Quantum Clustering is a powerful method to detect clusters with complex shapes. However, it is very sensitive to a length parameter that controls the shape of the Gaussian kernel associated with a wave function, which is employed in the Schrodinger equation with the role of a density estimator. In addition, linking data points into clusters requires local estimates of covariance which requires further parameters. This paper proposes a Bayesian framework that provides an objective measure of goodness-of-fit to the data, to optimise the adjustable parameters. This also quantifies the probabilities of cluster membership, thus partitioning the data into a specific number of clusters, w…
Mapping properties of weakly singular periodic volume potentials in Roumieu classes
2020
The analysis of the dependence of integral operators on perturbations plays an important role in the study of inverse problems and of perturbed boundary value problems. In this paper, we focus on the mapping properties of the volume potentials with weakly singular periodic kernels. Our main result is to prove that the map which takes a density function and a periodic kernel to a (suitable restriction of the) volume potential is bilinear and continuous with values in a Roumieu class of analytic functions. This result extends to the periodic case of some previous results obtained by the authors for nonperiodic potentials, and it is motivated by the study of perturbation problems for the solut…