Analytical moments of skewed Gaussian distribution functions

1973 ◽  
Vol 45 (8) ◽  
pp. 1541-1543 ◽  
Author(s):  
P. F. Rusch ◽  
J. P. Lelieur
Keyword(s):  
Gaussian Distribution ◽  
Distribution Functions ◽  
Analytical Moments

scholarly journals WAVE-CURRENT INTERACTION OVER SEABEDS WITH DIFFERENT ROUGHNESS: A STATISTICAL ANALYSIS

2017 ◽  
pp. 16
Author(s):  
Carla Faraci ◽  
Pietro Scandura ◽  
Enrico Foti
Keyword(s):  
Gaussian Distribution ◽  
Current Velocity ◽  
Mass Conservation ◽  
Distribution Functions ◽  
Wave Velocities ◽  
Velocity Statistics ◽  
Steady Current ◽  
Wave Effects ◽  
Current Interaction ◽  
Rippled Bed

Wave-current flow over seabeds covered with different roughness has been studied in order to deepen the knowledge on the statistical properties of the near-bed velocity. The results of three different experimental campaigns performed in the presence of a sandy bed, a gravel bed and a rippled bed, carried out superimposing a steady current onto an orthogonal wave, have been analysed. The statistics of the current velocity, including the wave effects on the steady current have been investigated. It has been observed that in the absence of waves, the fluctuations of the near-bed velocities closely follow a Gaussian distribution. When waves are also present, in order to obtain consistent near-bed velocity statistics, it is necessary to decouple the velocity events in the current direction by taking into account the sign of the wave velocities. In the latter case, the nature of the distribution functions is influenced by the mass conservation principle. A Gaussian distribution well describes the turbulent fluctuations obtained by removing the phase averaged velocity from the current velocity.

Comparative Study of Probability Distribution Functions of Wind Power Variation

2014 ◽  
Vol 953-954 ◽  
pp. 414-418
Author(s):  
An Jue Dai ◽  
Qian Wang ◽  
Yan Nan Zhou
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Wind Power ◽  
Gaussian Distribution ◽  
Gaussian Mixture ◽  
Second Order ◽  
Distribution Functions ◽  
Normal Distribution Function ◽  
One Dimensional ◽  
Power Variation

This work focuses on the probability distribution function of wind power variation. After analyzing the characters of the power fluctuation data, normal distribution function, t location-scale distribution function and mixed second-order one-dimensional Gaussian distribution function are chosen to describe the wind power variation. Then K-S test(Kolmogorov-Smirnov) test and Pearson product-moment correlation coefficient are used to evaluate the fitting effect of the three distribution functions respectively, which indicates that the mixed second-order one-dimensional Gaussian distribution is the most appropriate one. At last, the factors affecting the parameters of Gaussian mixture distribution and to what degree they can achieve are investigated.

Bimodal distribution of the solar wind using data from ACE spacecraft.

2020 ◽  
Author(s):  
Carlos Larrodera ◽  
Consuelo Cid
Keyword(s):  
Solar Wind ◽  
Gaussian Distribution ◽  
Bimodal Distribution ◽  
Distribution Functions ◽  
Solar Cycles ◽  
Proton Temperature ◽  
Gaussian Distribution Function ◽  
Transient Events ◽  
Solar Wind Parameters ◽  
Using Data

<p>The main goal of this work is to separate the behavior of the two types of quiet solar wind at 1 AU: fast and slow.<br>Our approach is a bi-Gaussian distribution function, formed by the addition of two Gaussian distribution functions, where each one represents one type of wind. We check our approach by fitting the bi-Gaussian to data from ACE spacecraft. We use level 2 data measured during solar cycles 23 and 24 of different solar wind parameters, including proton speed, proton temperature, density and magnetic field. Our results show that the approach is fine and only transient events departs from the proposed function. Moreover, we can show bi modal behavior of the solar wind at 1 AU, not only for the proton speed, but also for the other analyzed parameters. We also check the solar cycle dependence of the different fitting parameters.</p>

scholarly journals Analysis of Cohesive Microsized Particle Packing Structure Using History-Dependent Contact Models

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Raihan Tayeb ◽  
Xin Dou ◽  
Yijin Mao ◽  
Yuwen Zhang
Keyword(s):  
Particle Size ◽  
Coordination Number ◽  
Gaussian Distribution ◽  
Packing Density ◽  
Mean Value ◽  
Distribution Functions ◽  
Particle Packing ◽  
Size Distributions ◽  
Packing Structure ◽  
Contact Models

Granular packing structures of cohesive microsized particles with different sizes and size distributions, including monosized, uniform, and Gaussian distribution, are investigated by using two different history dependent contact models with discrete element method (DEM). The simulation is carried out in the framework of liggghts, which is a DEM simulation package extended based on branch of granular package of widely used open-source code LAMMPS. Contact force caused by translation and rotation, frictional and damping forces due to collision with other particles or container boundaries, cohesive force, van der Waals force, and gravity is considered. The radial distribution functions (RDFs), force distributions, porosities, and coordination numbers under cohesive and noncohesive conditions are reported. The results indicate that particle size and size distributions have great influences on the packing density for particle packing under cohesive effect: particles with Gaussian distribution have the lowest packing density, followed by the particles with uniform distribution; the particles with monosized distribution have the highest packing density. It is also found that cohesive effect to the system does not significantly affect the coordination number that mainly depends on the particle size and size distribution. Although the magnitude of net force distribution is different, the results for porosity, coordination number, and mean value of magnitude of net force do not vary significantly between the two contact models.

scholarly journals On the time of the maximum of Brownian motion with drift

2003 ◽  
Vol 16 (3) ◽  
pp. 201-207 ◽  
Author(s):  
Emannuel Buffet
Keyword(s):  
Brownian Motion ◽  
Gaussian Distribution ◽  
Integral Identity ◽  
Distribution Functions ◽  
Brownian Motion With Drift ◽  
Elementary Methods

The distribution of the time at which Brownian motion with drift attains its maximum on a given interval is obtained by elementary methods. The proof depends on a remarkable integral identity involving Gaussian distribution functions.

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