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# Topic: Laplace distribution

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 Laplace distribution - Wikipedia, the free encyclopedia The difference between two independent identically distributed exponential random variables is governed by a Laplace distribution, as is a Brownian motion evaluated at an exponentially distributed random time. The pdf of the Laplace distribution is also reminiscent of the normal distribution; however, whereas the normal distribution is expressed in terms of the squared difference from the mean μ, the Laplace density is expressed in terms of the absolute difference from the mean. The Laplace distribution is easy to integrate, if one distinguishes two symmetric cases, due to the use of the absolute value function. en.wikipedia.org /wiki/Laplace_distribution   (394 words)

 Laplace on probability and statistics   (Site not responding. Last check: 2007-11-06) Laplace's first memoir on recurrent series was "Recherches sur le calcul intégral aux différences infiniment petites, and aux différences finies" which was published in Mélanges de philosophie et de mathématiques de la Société royale de Turin, pour les années 1766-1769 (Miscellanea Taurensia IV), 273-345, 1771. Laplace realized that he could give a probabilistic justification to the method of least squares without assuming a normal distribution of errors through his central limit theorem. In this memoir, Laplace discusses the masses of Jupiter, Saturn and Uranus expressed as a fraction of the mass of the Sun using values obtained from Bouvard and also the length of the pendulum expressed in tenths of a second using the value of Mathieu. cerebro.xu.edu /math/Sources/Laplace   (3959 words)

 Probability distribution (via CobWeb/3.1 planetlab2.tamu.edu)   (Site not responding. Last check: 2007-11-06) A distribution is called discrete if its cumulative distribution function consists of a sequence of finite jumps, which means that it belongs to a discrete random variable X: a variable which can only attain values from a certain finite or countable set. The triangular distribution on [''a'', b], a special case of which is the distribution of the sum of two uniformly distributed random variables (the convolution of two uniform distributions). The Weibull distribution, of which the exponential distribution is a special case, is used to model the lifetime of technical devices. probability-distribution.iqnaut.net.cob-web.org:8888   (1311 words)

 Distribution Fitting To determine this underlying distribution, it is common to fit the observed distribution to a theoretical distribution by comparing the frequencies observed in the data to the expected frequencies of the theoretical distribution (i.e., a Chi-square goodness of fit test). The major distributions that have been proposed for modeling survival or failure times are the exponential (and linear exponential) distribution, the Weibull distribution of extreme events, and the Gompertz distribution. The logistic distribution is used to model binary responses (e.g., Gender) and is commonly used in logistic regression. www.statsoft.com /textbook/stdisfit.html   (1769 words)

 Business fluctuations: a new approach with heterogeneous interacting agents, scaling laws and financial fragility In a nutshell: the distribution is stable, or quasi-stable, because the dissipative force of the process (here, the Gibrat's law) produces a tendency to a growing dispersion, which is counteracted by a stabilizing force (i.e., the burden of debt commitments and the associated risk of bankruptcy). The change of firms' distribution (and the business cycle itself) has to be analyzed in terms of changes of the joint distribution of the population. As widely shown in the complexity literature, the emergence of such a distribution is deeply correlated with the hypothesis of interaction of heterogeneous agents that is at the root of the model. www.economicswebinstitute.org /essays/busflu.htm   (7786 words)

 Normal Distribution (via CobWeb/3.1 planetlab2.tamu.edu)   (Site not responding. Last check: 2007-11-06) The standard (or canonical) normal distribution is a special member of the normal family that has a mean of 0 and a standard deviation of 1. Exercise #2 requires you to compute probabilities and quantiles for the distribution of annual rainfall, assumed to be normally distributed, in a region. Exercise #3 requires you to compute probabilities and quantiles for the distribution of daily absences per 100 employees before and after a health improvement program, assumed to be normally distributed, at a large corporation. www.stat.wvu.edu.cob-web.org:8888 /SRS/Modules/Normal/normal.html   (833 words)

 Functions and CALL Routines : CDF The CDF function for the beta distribution returns the probability that an observation from a beta distribution, with shape parameters a and b, is less than or equal to x. The CDF function for the chi-squared distribution returns the probability that an observation from a chi-squared distribution, with df degrees of freedom and noncentrality parameter nc, is less than or equal to x. The CDF function for the F distribution returns the probability that an observation from an F distribution, with ndf numerator degrees of freedom, ddf denominator degrees of freedom, and noncentrality parameter nc, is less than or equal to x. www.okstate.edu /sas/v7/sashtml/books/langref/z0208980.htm   (1104 words)

 Publications Reliability and distribution of the ratio in a mixed distribution (with J. Woo and M. Pal), 2006, to be submitted. Efficient estimation of parameters of a uniform distribution in the presence of outliers (with U.J. Dixit and J. Woo). The jackknife quasi-ranges for a truncated arcsine distribution (with J. Woo). www.cs.bsu.edu /homepages/ali/wvita4.htm   (2966 words)

 Exponential The exponential distribution models the amount of time until an event occurs. Note that this is the continuous equivalent of the geometric distribution. Note that the exponential distribution is the same as the gamma distribution with parameters www.stanford.edu /~maureenh/quals/html/stats/node39.html   (90 words)

 Read This: Pierre-Simon Laplace, 1749-1827: A Life In Exact Science And Laplace by common repute is one of the commanding figures of the mathematics and science of that period. Clifford Truesdell writes, "Laplace is one of those mathematicians who won a great reputation in his own day and has held it ever since, safe within his forbidding eruption of formalism. On it Laplace constructs a 'curve of probability,' AZMB, along which every ordinate is proportional to the probability that the mean inclination is equal to the corresponding abscissa. www.maa.org /reviews/laplace.html   (1453 words)

 GNU Scientific Library -- Reference Manual - Random Number Distributions Distributions of random numbers can be obtained from any of the generators using the functions described in this section. More complicated distributions are created by the acceptance-rejection method, which compares the desired distribution against a distribution which is similar and known analytically. The Pascal distribution is simply a negative binomial distribution with an integer value of n. nereida.deioc.ull.es /html/gsl/gsl-ref_15.html   (2795 words)

 Francois Charlton on lossless audio compression On a specific set of residual, their ability to compress mostly depends on whether the actual distribution of residuals fits the implicit distributions these codes were designed to operate on. For the residuals to follow a gamma distribution, there should be more ‘large residuals” than normally, ie a number of “unnacounted for” stragglers, which is just what the predictor approach tries to avoid. This means that the empirical distribution of the residues will not be that close to a laplacian (there will be a few large outliers, not a lot of small probability values). www.firstpr.com.au /audiocomp/lossless/fc-lossless.html   (1467 words)

 LAD This type of regression is optimal when the disturbances have the Laplace distribution and is better than least squares (L2) regression for many other leptokurtic (fat-tailed) distributions such as Cauchy or Student's t. The likelihood function (@LOGL) and standard error estimates are computed as though the true distribution of the disturbances was Laplace; this is by analogy to least squares, where the likelihood function and conventional standard error estimates assume that the true distribution is normal (with a small sample correction to the standard errors). The alternative to these Laplace standard errors is to use the NBOOT= option to obtain bootstrap standard errors based on the empirical density. www.tspintl.com /products/tsphelp/lad.htm   (978 words)

 [Eeglablist] Ask a question again for Laplace distribution ~ Sech^2(X) distribution??? (via CobWeb/3.1 ...   (Site not responding. Last check: 2007-11-06) When I use the runica () for comparing the performance between the statistically independent sources with Laplace distribution and the statistically independent sources with the pdf: f(x)= 0.25*sech^2(0.5x), in which the default logistic algorithm is used, I don't understand why the blind separation performance of Laplace distributed data is always better than the latter. Checking their CDFs, the latter's CDF (i.e., 0.5*tanh(X)+0.5) is identical to the logistic kernel distribution (in runica (), So the latter should be better than the former (Laplace distributed data). We also tried 3 kinds of source signals (Gaussian, Laplace, Sech^()) together, the simulation results alwas show that Laplace case is better than others. sccn.ucsd.edu.cob-web.org:8888 /pipermail/eeglablist/2003/000048.html   (434 words)

 Distribution Fitting (via CobWeb/3.1 planetlab2.tamu.edu)   (Site not responding. Last check: 2007-11-06) These and other distributions are described in greater detail in the respective glossary topics. For predictive purposes it is often desirable to understand the shape of the underlying distribution of the population. The Pareto distribution can be used to model the length of wire between successive flaws. www.statsoft.com.cob-web.org:8888 /textbook/stdisfit.html   (1769 words)

 GNU Scientific Library -- Reference Manual - Random Number Distributions Samples from the distributions described in this chapter can be obtained using any of the random number generators in the library as an underlying source of randomness. In the simplest cases a non-uniform distribution can be obtained analytically from the uniform distribution of a random number generator by applying an appropriate transformation. For \alpha = 2 it is a Gaussian distribution with @c{$\sigma = \sqrt{2} c$} \sigma = \sqrt{2} c. www.math.umn.edu /systems_guide/gsl-1.3/gsl-ref_19.html   (2925 words)

 F-distribution - Wikipedia, the free encyclopedia In probability theory and statistics, the F-distribution is a continuous probability distribution. It is also known as Snedecor's F distribution or the Fisher-Snedecor distribution (after R.A. Fisher and George W. Snedecor). The F-distribution arises frequently as the null distribution of a test statistic, especially in likelihood-ratio tests, perhaps most notably in the analysis of variance; see F-test. en.wikipedia.org /wiki/F-distribution   (297 words)

 ProBT code samples The main goal of this program is to show how to construct a conditional anonymous kernel (i.e a conditional distribution defined by the user). The joint distribution contains the following variables: (i) n bathroom scales lectures, (ii) the “yesterday weight” and the “today's weights”. The lecture of the bathroom scales is supposed to be a random variable with a Laplace distribution centered at the real weight. www-laplace.imag.fr /bayesian-programming/showcode.php?pgrtype=SenFus   (294 words)

 Laplace Distribution The Laplace distribution is symmetrical and leptokurtic (a long word meaning more "peaky" than a normal distribution). Its kurtosis (dispersion of data around the mean) is higher than that of the normal, as shown in the table below. The Laplace distribution is also known as the double exponential distribution. www.brighton-webs.co.uk /distributions/laplace.asp   (88 words)

 SSRN-Modeling and Predicting Market Risk With Laplace-Gaussian Mixture Distributions by Markus Haas, Stefan Mittnik, ...   (Site not responding. Last check: 2007-11-06) While much of classical statistical analysis is based on Gaussian distributional assumptions, statistical modeling with the Laplace distribution has gained importance in many applied fields. This phenomenon is rooted in the fact that, like the Gaussian, the Laplace distribution has many attractive properties. They are also shown to be competitive with, or superior to, use of the hyperbolic distribution, which has gained some popularity in asset-return modeling and, in fact, also nests the Gaussian and Laplace. papers.ssrn.com /sol3/papers.cfm?abstract_id=701203   (343 words)

 [No title] The squared canonical correlation is an estimate of the common variance between two canonical variates, thus 1 minus this value is an estimate of the unexplained variance. In regression, this term refers to the diagonal elements of the hat matrix (X(X'X) A given diagonal element (h(ii)) represents the distance between X values for the ith observation and the means of all X values. The distribution of survival times is divided into a certain number of intervals. sunsite.univie.ac.at /textbooks/statistics/glosl.html   (2149 words)

 A history of mathematical statistics from 1750 to 1930-Hald Laplace's Sample Survey of the Population of France and the Distribution of the Ratio Estimator 283 On the distribution of the estimate of mean deviation obtained from samples from a normal population. Distribution of the ratio of the mean square successive difference to the variance. myriam.ulpgc.es /722468.htm   (10723 words)

 ADECDF , the asymmetric double exponential distribution reduces to the symmetric double exponential distribution. The asymmetric double exponential distribution is also known as the asymmetric Laplace distribution. "The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance", Birkhauser, 2001, pp. www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/adecdf.htm   (257 words)

 [No title] The graph at the right shows that the Laplace and Normal distributions with equal variances cross twice,.the Laplace distribution has higher kurtosis than the Normal. Not all symmetric distributions are ordered (see graph that shows that the Normal and Laplace are comparable but Laplace and t(6) are not). The graphs below show that: the Laplace distribution has more kurtosis than the Normal distribution the Laplace and the t(6) distributions are not really kurtosis comparable . www.etsu.edu /math/seier/Kurto100years.doc   (709 words)

 Octave Functions: L   (Site not responding. Last check: 2007-11-06) For each element of X, compute the cumulative distribution function (CDF) at X of the Laplace distribution. For each element of X, compute the quantile (the inverse of the CDF) at X of the Laplace distribution. Return an R by C matrix of random numbers from the Laplace distribution. octave.sourceforge.net /index/L.html   (1005 words)

 normal distribution ; Gaussian distribution ; Laplace-Gauss distribution ; Gauss distribution ; second law of Laplace distribution normale ; distribution gaussienne ; loi de Gauss ; distribution de Gauss ; distribution de Laplace-Gauss ; normalusis skirstinys ; Gauss skirstinys ; Laplace ir Gauss skirstinys ; Gauso skirstinys ; Laplaso ir Gauso skirstinys This Glossary may not be copied, reproduced or retained in any form whatsoever without the express permission of the ISI. isi.cbs.nl /glossary/term2311.htm   (189 words)

 LaPlace's and Poisson's Equations   (Site not responding. Last check: 2007-11-06) Expressing the LaPlacian in different coordinate systems to take advantage of the symmetry of a charge distribution helps in the solution for the electric potential V. For example, if the charge distribution has spherical symmetry, you use the LaPlacian in spherical polar coordinates. The use of Poisson's and Laplace's equations will be explored for a uniform sphere of charge. Since the zero of potential is arbitrary, it is reasonable to choose the zero of potential at infinity, the standard practice with localized charges. hyperphysics.phy-astr.gsu.edu /hbase/electric/laplace.html   (328 words)

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