Simulation of the Variability in Next-Generation Microelectronic Capacitors with Polycrystalline Dielectrics

2001 ◽  
Vol 688 ◽  
Author(s):  
Jesse L. Cousins ◽  
David E. Kotecki
Keyword(s):  
Monte Carlo ◽  
Standard Deviation ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Probability Density ◽  
Area Distribution ◽  
The Mean ◽  
Polycrystalline Microstructure ◽  
Probability Density Function Pdf ◽  
Lognormal Probability

AbstractMonte Carlo simulations of capacitors with polycrystalline (Bax, Sr1−x)TiO3 (BST) dielectrics were performed. The variation in capacitors due to the polycrystalline microstructure of the dielectric was investigated, as well as the effects of varying the distribution of crystal sizes. When a lognormal probability density function (pdf) was used to approximate the crystal area pdf and the average number of crystals per capacitor was near 100, it was found that the minimum capacitance value was nearly independent of the standard deviation of crystal area distribution. Both the mean and maximum capacitance values were found to increase as the width of the standard deviation increased.

scholarly journals Moments of Distance from a Vertex to a Uniformly Distributed Random Point within Arbitrary Triangles

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Hongjun Li ◽  
Xing Qiu
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Standard Deviation ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Cumulative Distribution Function ◽  
Random Point ◽  
Cumulative Distribution ◽  
Computational Technique ◽  
Probability Density Function Pdf

We study the cumulative distribution function (CDF), probability density function (PDF), and moments of distance between a given vertex and a uniformly distributed random point within a triangle in this work. Based on a computational technique that helps us provide unified formulae of the CDF and PDF for this random distance then we compute its moments of arbitrary orders, based on which the variance and standard deviation can be easily derived. We conduct Monte Carlo simulations under various conditions to check the validity of our theoretical derivations. Our method can be adapted to study the random distances sampled from arbitrary polygons by decomposing them into triangles.

scholarly journals A fractional generalization of the dirichlet distribution and related distributions

2021 ◽  
Vol 24 (1) ◽  
pp. 112-136
Author(s):  
Elvira Di Nardo ◽  
Federico Polito ◽  
Enrico Scalas
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Probability Density ◽  
Dirichlet Distribution ◽  
One Dimensional ◽  
Reasonable Approximation ◽  
Generalized Dirichlet Distribution ◽  
The One ◽  
Generalized Dirichlet

Abstract This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the n partitions of the interval [0, Wn ] are independent and identically distributed random variables following the generalized Mittag-Leffler distribution. The expected value and variance of the one-dimensional marginal are derived as well as the form of its probability density function. A related generalized Dirichlet distribution is studied that provides a reasonable approximation for some values of the parameters. The relation between this distribution and other generalizations of the Dirichlet distribution is discussed. Monte Carlo simulations of the one-dimensional marginals for both distributions are presented.

Improved MCMC Method for Parameter Estimation Based on Marginal Probability Density Function

2011 ◽  
Author(s):  
Dawn An ◽  
Joo-Ho Choi
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Uncertain Parameters ◽  
Marginal Probability ◽  
Mcmc Method ◽  
Proposal Distribution ◽  
Engineering Problems ◽  
Probability Density Function Pdf

In many engineering problems, sampling is often used to estimate and quantify the probability distribution of uncertain parameters during the course of Bayesian framework, which is to draw proper samples that follow the probabilistic feature of the parameters. Among numerous approaches, Markov Chain Monte Carlo (MCMC) has gained the most popularity due to its efficiency and wide applicability. The MCMC, however, does not work well in the case of increased parameters and/or high correlations due to the difficulty of finding proper proposal distribution. In this paper, a method employing marginal probability density function (PDF) as a proposal distribution is proposed to overcome these problems. Several engineering problems which are formulated by Bayesian approach are addressed to demonstrate the effectiveness of proposed method.

Proposition of a New Conformity Criterion for the Assessment of the Concrete Compressive Strength

2017 ◽  
Vol 259 ◽  
pp. 106-110
Author(s):  
Elżbieta Szczygielska ◽  
Viktar V. Tur
Keyword(s):  
Monte Carlo Simulation ◽  
Compressive Strength ◽  
Monte Carlo ◽  
Standard Deviation ◽  
Probability Density Function ◽  
Concrete Strength ◽  
Test Results ◽  
Concrete Compressive Strength ◽  
Strength Assessment ◽  
Probability Density Function Pdf

A new conformity criterion for concrete strength assessment that could be used at the initial production stage, is proposed. As an innovative conformity criterion was evaluated based on Order Statistics Theory, it is independent from the type probability density function (PDF) in population, estimation of the standard deviation, shape of the specimen and the level of autocorrelation of the test results. Proposed criterion was evaluated and positively verified both AOQL-concept using Monte Carlo simulation and the test results obtained under real production.

scholarly journals The Probability Distribution of Sea Surface Wind Speeds. Part I: Theory and SeaWinds Observations

2006 ◽  
Vol 19 (4) ◽  
pp. 497-520 ◽  
Author(s):  
Adam Hugh Monahan
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Density Function ◽  
Surface Wind ◽  
Sea Surface ◽  
Wind Speeds ◽  
Sea Surface Wind ◽  
The Mean

Abstract The probability distribution of sea surface wind speeds, w, is considered. Daily SeaWinds scatterometer observations are used for the characterization of the moments of sea surface winds on a global scale. These observations confirm the results of earlier studies, which found that the two-parameter Weibull distribution provides a good (but not perfect) approximation to the probability density function of w. In particular, the observed and Weibull probability distributions share the feature that the skewness of w is a concave upward function of the ratio of the mean of w to its standard deviation. The skewness of w is positive where the ratio is relatively small (such as over the extratropical Northern Hemisphere), the skewness is close to zero where the ratio is intermediate (such as the Southern Ocean), and the skewness is negative where the ratio is relatively large (such as the equatorward flank of the subtropical highs). An analytic expression for the probability density function of w, derived from a simple stochastic model of the atmospheric boundary layer, is shown to be in good qualitative agreement with the observed relationships between the moments of w. Empirical expressions for the probability distribution of w in terms of the mean and standard deviation of the vector wind are derived using Gram–Charlier expansions of the joint distribution of the sea surface wind vector components. The significance of these distributions for improvements to calculations of averaged air–sea fluxes in diagnostic and modeling studies is discussed.

Estimation of the Radionuclide Transport by Applying the Mean, the Standard Deviation and the Skewness of Permeability

1996 ◽  
Vol 465 ◽  
Author(s):  
Y. Niibori ◽  
O. Tochiyama ◽  
T. Chida
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Lognormal Distribution ◽  
Heterogeneous Media ◽  
Arithmetic Mean ◽  
Bernoulli Trials ◽  
The Mean ◽  
Independent Parameters

ABSTRACTA new method for estimating the mass transport by using the stochastic values (the arithmetic mean, the standard deviation and the skewness) of permeability is presented. Generally, detail of permeability distribution cannot be obtained except for moments of the distribution. Also, measurement results of permeability for the rock matrix including cracks or fast flowpaths do not always follow the log-normal distribution frequently applied. In such a situation, we must evaluate the characteristic permeabilities for the whole or some regions of the disposal site including the accessible environment.The authors have investigated the characteristic permeability on the basis of some probability density functions of permeability, applying the Monte Carlo method and FEM. It was found that its value does not depend on type of probability density function of permeability, but on the arithmetic mean, the standard deviation and the skewness of permeability [1].This paper describes the use of the stochastic values of permeability for estimating the rate of radioactivity release to the accessible environment, applying the advection-dispersion model to two-dimensional, heterogeneous media. When a discrete probability density function (referred to as ‘the Bernoulli trials’) and the lognormal distribution have common values for the arithmetic mean, the standard deviation and the skewness of permeability, the calculated transport rates (described as the pseudo impulse responses) show good agreements for Peclet number around 10 and the dimensionless standard deviation around 1. Further, it is found that the transport rates apparently depends not only on the arithmetic mean and the standard deviation, but also on the skewness of permeability. When the value of skewness dose not follow the lognormal distribution which has only two independent parameters (the mean and the standard deviation), we can replicate the three moments estimated from an observed distribution of permeability, by using the Bernoulli trials having three independent parameters.

On the Uncertainty of the EN12354-1: Estimate of the Flanking Sound Reduction Index Due to the Uncertainty of the Input Data

2009 ◽  
Vol 16 (3) ◽  
pp. 199-231 ◽  
Author(s):  
Jeffrey Mahn ◽  
John Pearse
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Input Data ◽  
Vibration Reduction ◽  
Uncertainty In Measurement ◽  
Sound Reduction ◽  
Expression Of Uncertainty ◽  
Lognormal Probability ◽  
Reduction Index

Equations to calculate the uncertainty of the EN12354-1 estimate of the flanking sound reduction index due to the uncertainty of the input data are derived using the method of the ISO Guide to the Expression of Uncertainty in Measurement (GUM). The uncertainty equations have been validated using Monte Carlo simulations. It is shown that the magnitude of the uncertainty depends on the uncertainty of the resonant sound reduction indices of the elements, the uncertainty of the vibration reduction index and the uncertainty of the equivalent absorption lengths and areas of the elements. However, equations could not be derived to calculate the uncertainty of the EN12354 estimate of the apparent sound reduction index which has a lognormal probability density function and is therefore outside of the scope of the method of GUM. Monte Carlo simulations must be used to calculate the uncertainty of the apparent sound reduction index. It is recommended that guidance for calculating and declaring the uncertainty is included in future versions of EN12354, ISO10848 and ISO15712.

scholarly journals The Distribution of Path Losses for Uniformly Distributed Nodes in a Circle

2008 ◽  
Vol 2008 ◽  
pp. 1-4 ◽  
Author(s):  
Zubin Bharucha ◽  
Harald Haas
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Path Loss ◽  
System Level ◽  
Random Component ◽  
Simulated Network ◽  
Log Normal ◽  
Probability Density Function Pdf ◽  
System Level Simulations

When simulating a wireless network, users/nodes are usually assumed to be distributed uniformly in space. Path losses between nodes in a simulated network are generally calculated by determining the distance between every pair of nodes and applying a suitable path loss model as a function of this distance (power of distance with an environment-specific path loss exponent) and adding a random component to represent the log-normal shadowing. A network with nodes consists of path loss values. In order to generate statistically significant results for system-level simulations, Monte Carlo simulations must be performed where the nodes are randomly distributed at the start of every run. This is a time-consuming operation which need not be carried out if the distribution of path losses between the nodes is known. The probability density function (pdf) of the path loss between the centre of a circle and a node distributed uniformly within a the circle is derived in this work.

scholarly journals The normal-tangent-G class of probabilistic distributions: properties and real data modellin

2020 ◽  
pp. 827-838
Author(s):  
Fábio Silveira ◽  
Frank Gomes-Silva ◽  
Cícero Brito ◽  
Moacyr Cunha-Filho ◽  
Jader Jale ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Probability Distributions ◽  
Series Representation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Special Cases ◽  
Probability Density Function Pdf

This paper introduces a novel class of probability distributions called normal-tangent-G, whose submodels are parsi- monious and bring no additional parameters besides the baseline’s. We demonstrate that these submodels are iden- tifiable as long as the baseline is. We present some properties of the class, including the series representation of its probability density function (pdf) and two special cases. Monte Carlo simulations are carried out to study the behav- ior of the maximum likelihood estimates (MLEs) of the parameters for a particular submodel. We also perform an application of it to a real dataset to exemplify the modelling benefits of the class.

scholarly journals Concomitant of Order Statistics from New Bivariate Gompertz Distribution

2020 ◽  
Vol 18 (2) ◽  
pp. 2-20
Author(s):  
Sumit Kumar ◽  
M. J. S. Khan ◽  
Surinder Kumar
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Order Statistics ◽  
Density Function ◽  
Generating Function ◽  
Moment Generating Function ◽  
Exact Expression ◽  
Gompertz Distribution ◽  
The Mean ◽  
Probability Density Function Pdf

For the new bivariate Gompertz distribution, the expression for probability density function (pdf) of rth order statistics and pdf of concomitant arising from rth order statistics are derived. The properties of concomitant arising from the corresponding order statistics are used to derive these results. The exact expression for moment generating function (mgf) of concomitant of order rth statistics is derived. Also, the mean of concomitant arising from rth order statistics is computed using the mgf of concomitant of rth order statistics, and the exact expression for joint density of concomitant of two non-adjacent order statistics are derived.

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