Discrete Distribution Functions for Log-Normal Moments

2020 ◽  
pp. 1-21
Author(s):  
Catherine M. Bonan-Hamada ◽  
William B. Jones ◽  
W. J. Thron ◽  
Arne Magnus
Keyword(s):  
Discrete Distribution ◽  
Distribution Functions ◽  
Log Normal

The diffusive strip method for scalar mixing in two dimensions

2010 ◽  
Vol 662 ◽  
pp. 134-172 ◽  
Author(s):  
P. MEUNIER ◽  
E. VILLERMAUX
Keyword(s):  
Diffusion Problem ◽  
Two Dimensions ◽  
Distribution Functions ◽  
Radius Of Curvature ◽  
Scalar Mixing ◽  
Mixing Properties ◽  
Convection Diffusion ◽  
Concentration Probability ◽  
Log Normal ◽  
Large Peclet Number

We introduce a new numerical method for the study of scalar mixing in two-dimensional advection fields. The position of an advected material strip is computed kinematically, and the associated convection–diffusion problem is solved using the computed local stretching rate along the strip, assuming that the diffusing strip thickness is smaller than its local radius of curvature. This widely legitimate assumption reduces the numerical problem to the computation of a single variable along the strip, thus making the method extremely fast and applicable to any large Péclet number. The method is then used to document the mixing properties of a chaotic sine flow, for which we relate the global quantities (spectra, concentration probability distribution functions (PDFs), increments) to the distributed stretching of the strip convoluted by the flow, possibly overlapping with itself. The numerical results indicate that the PDF of the strip elongation is log normal, a signature of random multiplicative processes. This property leads to exact analytical predictions for the spectrum of the field and for the PDF of the scalar concentration of a solitary strip. The present simulations offer a unique way of discovering the interaction rule for building complex mixtures which are made of a random superposition of overlapping strips leading to concentration PDFs stable by self-convolution.

Statistical Inferences of Lift-Off Velocity Distribution Function Form for Saltating Particles

2010 ◽  
Vol 108-111 ◽  
pp. 783-788
Author(s):  
Jian Jun Wu ◽  
Li Hong He
Keyword(s):  
Distribution Function ◽  
Weibull Distribution ◽  
Velocity Distribution ◽  
Goodness Of Fit ◽  
Velocity Distribution Function ◽  
Forward Direction ◽  
Distribution Functions ◽  
Velocity Distribution Functions ◽  
Lift Off ◽  
Log Normal

The lift-off velocity distribution of saltating particles, which have been proposed to characterize the dislodgement state of saltating particles, is one of the key issues in the theoretical study of windblown sand transportation. But there were various statistical relations in the early researches. In this paper, the Kolmogorov-Smirnov test for goodness-of-fit is adopted to make an inference of the most probable form of lift-off velocity distribution functions for saltating particles on the basis of the experimental data. The statistical results show that the distribution function of vertical lift-off velocities conforms better to Weibull distribution function than to the normal, log-normal, gamma and exponential ones; while, the distribution function of the absolute values of horizontal lift-off velocities is best described by log-normal distribution in forward direction and Weibull distribution in backward direction, respectively. Finally, two more examples prove to support the above conclusions.

scholarly journals Using Probability Distribution Functions to Correlate Breakthrough Curves of Water and air Contaminants

2021 ◽  
Author(s):  
Khim Hoong Chu
Keyword(s):  
Breakthrough Curve ◽  
Inflection Point ◽  
Initial Period ◽  
Normal Function ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Good Representation ◽  
Air Contaminants ◽  
Inflection Points ◽  
Log Normal

Abstract This paper reports the use of five probability cumulative distribution functions (normal, log-normal, logistic, Gompertz, and Weibull) to correlate published breakthrough data of water and air contaminants (ciprofloxacin, ammonium, hydrogen chloride, and hydrogen sulfide). Because the shape of the ciprofloxacin breakthrough curve is fairly symmetric, it is well correlated by all five functions (R2 > 0.99). They also provide a good representation of the overall shape of the ammonium breakthrough curve (R2 > 0.99). However, none can describe the leakage of ammonium during the initial period of column operation. The log-normal and Weibull functions give an excellent representation of the tailing HCl data while the normal, logistic, and Gompertz functions are quite poor. This difference in performance can be explained by the different characteristics of their inflection points. The log-normal and Weibull functions have a floating inflection point, which gives them flexibility in tracing the shape of the tailing data. The invariant inflection points of the normal, logistic, and Gompertz curves restrict their data fitting ability. Only the log-normal function can provide a reasonable fit to the H2S data with strong tailing. It is shown that the invariant inflection point of a probability function can be converted to a floating one. A version of the Gompertz function so modified provides a good quantitative correlation of the tailing data of H2S (R2 = 0.99).

scholarly journals Stochastic Bioimpedance-Based Channel Model of the Human Body for Galvanic Coupling

2021 ◽  
Vol 12 (1) ◽  
pp. 117-124
Author(s):  
Aaron Roopnarine ◽  
Sean A. Rocke
Keyword(s):  
Human Body ◽  
Channel Model ◽  
Random Variable ◽  
Distribution Functions ◽  
Galvanic Coupling ◽  
Body Segments ◽  
Generalized Pareto ◽  
Body Parameter ◽  
Log Normal ◽  
Body Parameters

Abstract Human body communication (HBC) uses the human body as the channel to transfer data. Extensive work has been done to characterize the human body channel for different HBC techniques and scenarios. However, statistical channel bioimpedance characterisation of human body channels, particularly under dynamic conditions, remains relatively understudied. This paper develops a stochastic fading bioimpedance model for the human body channel using Monte Carlo simulations. Differential body segments were modelled as 2-port networks using ABCD parameters which are functions of bioimpedance based body parameters modelled as random variables. The channel was then modelled as the cascade of these random 2-port networks for different combinations of probability distribution functions (PDFs) assumed for the bioimpedance-based body parameters. The resultant distribution of the cascaded body segments varied for the different assumed bioimpedance based body parameter distributions and differential body segment sizes. However, considering the distribution names that demonstrated a best fit (in the top 3 PDF rankings) with highest frequency under the varying conditions, this paper recommends the distribution names: Generalized Pareto for phase distributions and Log-normal for magnitude distributions for each element in the overall cascaded random variable ABCD matrix.

scholarly journals On convergence and compactness in variation with shift of discrete probability laws

2021 ◽  
Vol 8 (3) ◽  
pp. 385-393
Author(s):  
Ivan A. Alexeev ◽  
◽  
Alexey A. Khartov ◽  
Keyword(s):  
Real Line ◽  
Discrete Distribution ◽  
Distribution Functions ◽  
Divisible Distribution ◽  
Characteristic Functions ◽  
Infinitely Divisible Distribution ◽  
Infinitely Divisible ◽  
The Real ◽  
Convergence In Variation ◽  
Compactness Theorems

We consider a class of discrete distribution functions, whose characteristic functions are separated from zero, i. e. their absolute values are greater than positive constant on the real line. The class is rather wide, because it contains discrete infinitely divisible distribution functions, functions of lattice distributions, whose characteristic functions have no zeroes on the real line, and also distribution functions with a jump greater than 1/2. Recently the authors showed that characteristic functions of elements of this class admit the Lévy-Khinchine type representations with non-monotonic spectral function. Thus our class is included in the set of so called quasi-infinitely divisible distribution functions. Using these representation the authors also obtained limit and compactness theorems with convergence in variation for the sequences from this class. This note is devoted to similar results concerning convergence and compactness but with weakened convergence in variation. Replacing of type of convergence notably expands applicability of the results.

scholarly journals A Comparative Study on the Double Prior for Reliability Kumaraswamy Distribution with Numerical Solution

2020 ◽  
Vol 17 (1) ◽  
pp. 0159
Author(s):  
Abraheem Et al.
Keyword(s):  
Numerical Solution ◽  
Shape Parameter ◽  
Expansion Method ◽  
Reliability Function ◽  
Distribution Functions ◽  
Kumaraswamy Distribution ◽  
Bayes Methods ◽  
Probability Distribution Functions ◽  
Symmetric Loss ◽  
Log Normal

This work, deals with Kumaraswamy distribution. Kumaraswamy (1976, 1978) showed well known probability distribution functions such as the normal, beta and log-normal but in (1980) Kumaraswamy developed a more general probability density function for double bounded random processes, which is known as Kumaraswamy’s distribution. Classical maximum likelihood and Bayes methods estimator are used to estimate the unknown shape parameter (b). Reliability function are obtained using symmetric loss functions by using three types of informative priors two single priors and one double prior. In addition, a comparison is made for the performance of these estimators with respect to the numerical solution which are found using expansion method. The results showed that the reliability estimator under Rn and R3 is the best.

scholarly journals A nonparametric approach toward upper bounds to transit time distribution functions

2017 ◽  
Author(s):  
Earl Bardsley
Keyword(s):  
Distribution Function ◽  
Transit Time ◽  
Time Distribution ◽  
Discrete Distribution ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Linear Measure ◽  
Time Varying ◽  
Transit Time Distribution ◽  
The Individual

Abstract. A nonparametric method is proposed as a possible approach to obtaining upper bounds to distribution functions of time-varying transit times for catchment environmental tracers. A discretization is employed for the tracer throughput process, with tracer input represented as a sequence of K discrete pulses over a given time period. Each input pulse is associated with a different and unknown upper-bounded nonparametric discrete transit time distribution. The model transit time distribution function is therefore a K-component finite mixture of different and unknown discrete distribution functions, weighted by the relative magnitudes of the respective tracer pulses. Upper bounds to this distribution function can be obtained by linear programming to achieve a sequence of K discrete optimised transit time distributions which yield the maximum possible value of tracer fraction less than a given age, subject to a constraint of matching the catchment tracer output time series to some specified linear measure of accuracy. The individual optimised distributions do not estimate actual transit time distributions and the optimisation procedure is not hydrological modelling. This is actually a strength of the methodology in that the true transit time distributions are permitted to be created as a consequence of any time-varying nonlinear catchment process with complete or partial mixing. However, a negative aspect is that the extreme flexibility of K different nonparametric distributions is likely to give transit time distribution functions upper bounds near 1, unless sufficient constraints can be imposed on the form of the individual optimised distributions. There is a possibility, however, that optimising just a single nonparametric L-shaped discrete distribution could yield useful distribution function upper bounds for time-varying situations.

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