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Topic: Gumbel distribution


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In the News (Wed 24 Apr 19)

  
  Fisher-Tippett distribution - Wikipedia, the free encyclopedia
In probability theory and statistics the Gumbel distribution is used to find the minimum (or the maximum) of a number of samples of various distributions.
The Gumbel distribution, and similar distributions, are used in extreme value theory.
In particular, the Gumbel distribution is a special case of the Fisher-Tippett distribution, also known as the log-Weibull distribution.
en.wikipedia.org /wiki/Fisher-Tippett_distribution   (240 words)

  
 math lessons - Probability distribution
A probability distribution is a special case of the more general notion of a probability measure, which is a function that assigns probabilities satisfying the Kolmogorov axioms to the measurable sets of a measurable space.
The rectangular distribution is a uniform distribution on [-1/2,1/2].
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).
www.mathdaily.com /lessons/Probability_distribution   (1254 words)

  
 1.3.6.6.16. Extreme Value Type I Distribution
The following is the plot of the Gumbel inverse survival function for the minimum case.
The formula for the inverse survival function of the Gumbel distribution (maximum) is
The following is the plot of the Gumbel inverse survival function for the maximum case.
www.itl.nist.gov /div898/handbook/eda/section3/eda366g.htm   (611 words)

  
 Technical indicator based on the distribution of Gumbel maximums
In the calculus of the volume of flow for the dimension and design of the overflow channel in big water dams the use of Gumbel distribution is frequent.
Gumbel's distribution is a exponential generalized gamma distribution.
By applying Gumbel's distribution to quotation temporal series of any title it is easy to build an indicator, whose main virtue is the measure of unstability in zones of maximums.
www.aernsoft.com /eng/ayuda/gumbel.htm   (460 words)

  
 Articles - Probability distribution   (Site not responding. Last check: 2007-10-19)
The Kumaraswamy distribution is as versatile as the Beta distribution but has simple closed forms for both the cdf and the pdf.
The F-distribution, which is the distribution of the ratio of two (normalized) chi-square distributed random variables, used in the analysis of variance.
The Ewens's sampling formula is a probability distribution on the set of all partitions of an integer n, arising in population genetics.
www.anfolk.com /articles/Probability_distribution   (999 words)

  
 Distribution Form Frame   (Site not responding. Last check: 2007-10-19)
The exponential distribution, also known as the waiting-time distribution, describes the amount of time or distance between the occurrence of random events (such as the time between major earthquakes or the time between no hitters pitched in major league baseball).
The distribution is used in the analysis of variance and is a function of the ratio of two independent random variables each of which has a chi-square distribution and is divided by its number of degrees of freedom.
The Gumbel distribution, a special case of the Fisher-Tippett Distribution, is particularly convenient for extreme value distribution purposes, and it may be used as an alternative to the normal distribution in the case of skewed empirical data.
ic.net /~jnbohr/java/CdfDemoArgs.html   (1657 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.
More complicated distributions are created by the acceptance-rejection method, which compares the desired distribution against a distribution which is similar and known analytically.
www.dulug.duke.edu /~mstenner/free-docs/gsl-ref-1.0/gsl-ref_267.html   (136 words)

  
 HESS - Abstract   (Site not responding. Last check: 2007-10-19)
Abstract: The widely-used hydrological procedures for calculating events with T-year return periods from data that follow a Gumbel distribution assume that the data sequence from which the Gumbel distribution is fitted remains stationary in time.
The paper describes an alternative model in which the Gumbel distribution has a (possibly) time-variant mean, the time-trend in mean value being determined, for the present purpose, by a single parameter β estimated by Maximum Likelihood (ML).
Simulated samples from a standard Gumbel distribution were given superimposed linear trends of different magnitudes, and the power of each of three trend-testing procedures (Maximum Likelihood, Linear Regression, and the non-parametric Mann-Kendall test) were compared.
www.copernicus.org /EGU/hess/6/1/17.htm?FrameEngine=false   (232 words)

  
 CAS- Scandinavian Actuarial Journal   (Site not responding. Last check: 2007-10-19)
Wüthrich's paper is concerned with the distribution of the maximum of n identically distributed observations in the case where the observations are not independent.
The celebrated Fisher-Tippett Extreme Value Theorem that says that if the (suitably normalized) distribution of maximums of independent, identically distributed variables converges to a non-degenerate limit distribution F then F must be one of the three extreme value distributions (EVDs): a Weibull, a Frechet or a Gumbel.
The author extends this result to the case where the underlying distributions are continuous and have a dependence relationship specified by an Archimedian copula.
www.casact.org /research/summaries/SAJ2004-3.htm   (491 words)

  
 The Distribution of Fitness Effects Among Beneficial Mutations -- Orr 163 (4): 1519 -- Genetics
Three cases are shown: those in which the distributions of absolute allelic fitnesses were (a) exponential with mean = 1, (b) gamma with shape parameter of 2 and scale parameter of 2 (mean = 1), and (c) half-normal with mean = 1.
The distribution of beneficial effects is exponential (straight line on a semilog plot) and essentially identical despite different starting wild-type fitness ranks (i = 2, 10, and 25).
The distribution of fitness effects among beneficial mutations when sampling from the mixture distributions of allelic fitnesses shown in Fig 3 (computer simulations; semilog plot).
www.genetics.org /cgi/content/full/163/4/1519   (3981 words)

  
 Gumbel Distribution
The Gumbel distribution is a special case of the Generalized Extreme Value distribution.
An attractive feature of the Gumbel distribution is that the parameter equations provide an estimate of the mode.
As a form of comparison, the Pareto and Cauchy distributions are classed as having thick/heavy tails and the Beta distribution is bounded by its maximum and minimum values.
www.brighton-webs.co.uk /distributions/gumbel.asp   (268 words)

  
 Extreme values
Extreme values are often assumed to follow the Gumbel distribution (extreme-value distribution or Fisher-Tippett type 1 distribution).
for the Gumbel distribution is shown in Fig.
Both normal and exponential distribution lie in the domain of the attraction of the Gumbel function (the latter lies closest).
web.gfi.uib.no /~nilsg/kurs/notes/node45.html   (382 words)

  
 Heat Exchanger IRIS Wall Thickness And Gumbel Smallest Distribution
A plot of the Y-axis of the Gumbel distribution is the same as for a Weibull distribution.
The Weibull plot is well known for representing the “weakest link” (not to be confused with the tag line for a current television program where contestants are informed they are “the weakest link” because of their inferior performance).
The conditions described in BS 5760 seems appropriate for the condition of a heat exchanger where the tubes are functionally in series as any tube failure causes the heat exchanger system to fail and the data for wall thickness represents the minimum value in each tube.
www.barringer1.com /mar01prb.htm   (1504 words)

  
 GNU Scientific Library -- Reference Manual - Random Number Distributions   (Site not responding. Last check: 2007-10-19)
The cumulative distribution functions and their inverses are computed separately for the upper and lower tails of the distribution, allowing full accuracy to be retained for small results.
Continuous random number distributions are defined by a probability density function, p(x), such that the probability of x occurring in the infinitesimal range x to x+dx is p dx.
For \alpha = 2 it is a Gaussian distribution with \sigma = \sqrt{2} c.
www.gnu.org /software/gsl/manual/gsl-ref_19.html   (3818 words)

  
 extRemes web tutorial: Appendix
The problem with the above exact distribution is that F is not generally known in practice and subsequently must be estimated.
The above three families of distributions can be combined into one family of distributions known as the generalized extreme value (GEV) family.
The asymptotic distribution approximation of maximums and exceedances over a threshold assumes that data are independent and identically distributed (iid), but this is often not the case with real data.
www.esig.ucar.edu /extremevalues/tutorial/Appendix.html   (1177 words)

  
 Dehaan
Estimate the parameters of a generalized Pareto distribution using the Dehaan method.
The generalized Pareto distribution (GPD) is an asymptotic distribution developed by using the fact that exceedances of a sufficiently high threshold are rare events to which the Poisson distribution applies.
The cumulative distribution function of the generalized Pareto distribution is
www.itl.nist.gov /div898/software/dataplot/refman1/auxillar/dehaan.htm   (513 words)

  
 Extreme value theory
Extreme value theory is a branch of statistics dealing with the extreme deviations from the median of probability distributions.
Most common at this moment is the tail-fitting approach based on the second theorem in extreme value theory (Theorem II Pickands (1975), Balkema and de Haan (1974)).
Limiting forms of the frequency distribution of the largest and smallest member of a sample, Proc.
www.brainyencyclopedia.com /encyclopedia/e/ex/extreme_value_theory.html   (353 words)

  
 Improved amino acid flexibility parameters -- Smith et al. 12 (5): 1060 -- Protein Science
The observed distribution was smoothed and the area under the curve was normalized to 1.
Gumbel distribution was used as the estimator of each amino
Wampler, J.E. Distribution analysis of the variation of B-factors of X-ray crystal structures: Temperature and structural variations in lysozyme.
www.proteinscience.org /cgi/content/full/12/5/1060   (5753 words)

  
 DISTRIB.RTF
Consider the probability distribution as the sum of the probability mass at 0.0 and a probability distribution over the remainder of the range.
A Distribution analysis is automatically performed on the data in the main spreadsheet, simply by clicking the button corresponding to the distribution type desired.
The maximum likelihood estimates the distribution parameters such that product of the likelihoods of the individual events (L) is maximized.
www-cee.engr.ucf.edu /software/distrib   (1342 words)

  
 Statistics of Weather and Climate Extremes
This web page is intended to serve as a resource for the use of the statistical theory of extreme values in the analysis of weather and climate extremes and their impacts.
One important theorem states that the maximum of a sequence of observations, under very general conditions, is approximately distributed as the generalized extreme value distribution.
In terms of the tail of a distribution, the corresponding theorem states that the observations exceeding a high threshold, under very general conditions, are approximately distributed as the generalized Pareto distribution [of which the exponential (light tail) and Pareto (heavy tail) are special cases].
www.isse.ucar.edu /extremevalues/extreme.html   (939 words)

  
 [No title]   (Site not responding. Last check: 2007-10-19)
We will use the Normal and Gumbel probability distribution functions to approximate the frequency characteristics of observed annual peak floods.
Criticize the applicability of Gumbel distribution function for the estimation of floods in the Flat River basin.
In other words, the changes of precipitation pattern and landcover pattern of the watershed over the monitoring period are assumed to exert negligible influence on the flood frequency occurring during the period.
www.unc.edu /courses/2003fall/geog/141/001/inprogress/ex2/tutorial.doc   (1253 words)

  
 2002 Building Publications - Extreme Wind Load Estimates Based on Gumbel Distribution of Dynamic Pressures: An ...   (Site not responding. Last check: 2007-10-19)
We present a contribution to the current debate on whether it is more appropriate to fit a Gumbel distribution to the time series of the extreme dynamic pressures (i.e.
In addition, we show results of probability plot correlation coefficient (PPCC) analyses of 100 records of sample size 23 to 54, according to which the fit of reverse Weibull distributions to largest yearly wind speeds is considerably better than the fit of Gumbel distributions to the corresponding largest yearly dynamic pressures.
We interpret the data and results presented in the paper as indicating that there is no convincing support to date for the hypothesis that the Gumbel distribution should be used as a model of extreme dynamic pressures.
fire.nist.gov /bfrlpubs/build02/art032.html   (258 words)

  
 Stat 567 Homework Log
from the JMP output of the Gumbel fit of the log of the ball bearings data.
Reproduce the JMP output of the Gumbel fit of the log of the ball bearings data.
Reproduce the JMP output of the Gumbel fit of the log of the ball bearings data with sigma locked at the value one.
web.utk.edu /~leon/rel/class/class97/homework.html   (1999 words)

  
 Emil Gumbel - Wikipedia, the free encyclopedia
Emil Julius Gumbel (July 18, 1891 - September 10, 1966), was a German mathematician, pacifist and anti-Nazi campaigner.
Emil J. Gumbel: Weimar German Pacifist and Professor
This page was last modified 15:35, 15 October 2005.
en.wikipedia.org /wiki/Emil_Gumbel   (61 words)

  
 HESS, Vol.6, No. 1, 2002   (Site not responding. Last check: 2007-10-19)
The widely-used hydrological procedures for calculating events with T-year return periods from data that follow a Gumbel distribution assume that the data sequence from which the Gumbel distribution is fitted remains stationary in time.
The paper describes an alternative model in which the Gumbel distribution has a (possibly) time-variant mean, the time-trend in mean value being determined, for the present purpose, by a single parameter
The large-sample variance of the ML estimate is compared with the variance of the trend
www.copernicus.org /EGS/hess/hs6/6-17.htm   (227 words)

  
 A Higher Order Expansion for the Joint Density of the Sum and the Maximum under the Gumbel Domain of Attraction ...   (Site not responding. Last check: 2007-10-19)
Abstract: An asymptotic expansion is developed for the joint density of the sum and maximum of an i.i.d.
sequence when the parent distribution is in the domain of extreme value attraction of the Gumbel distribution.
Previous results by Chow and Teugels, extended by Anderson and Turkman, show that in this situation, the normalized sum and normalized maximum of the sample converge to independent normal and Gumbel distributions, but they have not characterized the rate of convergence.
citeseer.ist.psu.edu /591085.html   (248 words)

  
 Gumbel distribution   (Site not responding. Last check: 2007-10-19)
The Gumbel distribution is also known as the Extreme Value distribution (type I).
Its opposite is also known as the Euler constant.
You can take a value from a Gumbel distribution with parameter
www.fundp.ac.be /~fbastin/computing/rangen/doc/node16.html   (93 words)

  
 Learn more about Extreme value theory in the online encyclopedia.   (Site not responding. Last check: 2007-10-19)
Hint: Play with putting spaces before and after your words to see the different results you get.
Extreme value theory is a branch of statistics dealing with the extreme deviations from the mean of probability distributions.
Founded by the German mathematician, pacifist, and anti-Nazi campaigner Emil Julius Gumbel who described the Gumbel distribution in the 1950s.
www.onlineencyclopedia.org /e/ex/extreme_value_theory.html   (174 words)

  
 casino roulette   (Site not responding. Last check: 2007-10-19)
In American roulette the croupier collects and distributes chips by hand.Roulette is a casino and gambling game (Roulette is a French word meaning "small wheel").Slot machines are commonplace in casinosThe term originally meant a small villa, summerhouse or pavilion built for pleasure, usually on the grounds of a larger Italian villa or palazzo.
These schemes work by determining that the ball is more likely to fall at certain numbers.
Different authors have different opinions on which casinos are worth avoiding, so always read the reason that they are on the fllist and decide for yourself if you want to play there.
www.document-sugery.co.uk /casino-roulette.aspx   (4374 words)

  
 Mathematical Statistics with Mathematica - Index   (Site not responding. Last check: 2007-10-19)
as limit distribution of a Binomial 93, 281, 299
asymptotic distribution of MLE of (m, s2) 372-374
as limit distribution of Binomial 95, 280, 300
www.mathstatica.com /book/bookindex.html   (313 words)

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