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Topic: Gamma distribution

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Probability distribution

Exponential distribution

Uniform distribution (continuous)

Laplace distribution

Erlang distribution

Negative binomial distribution

Exponential family

Weibull distribution

Poisson distribution

Beta distribution

Joint distribution

Normal distribution

Cumulative distribution function

Bernoulli distribution

Probability density function

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	BioMed Central \| Full text \| Statistical distributions of optimal global alignment scores of random protein sequences
		The normal distribution also agrees well with the score distribution frequencies when the shape parameter of the gamma distribution is sufficiently large, for this is the scenario when the normal distribution can be viewed as an approximation of the gamma distribution.
		Both the gamma and normal distributions fit the score frequencies of the former well (Figure 3), whereas for the latter, the normal distribution disagrees with the majority of the score curve.
		The score distribution was fitted with (A) the three-parameter gamma distribution; (B) the normal distribution; and (C) the Gumbel distribution.
	www.biomedcentral.com /1471-2105/6/257 (4036 words)

	Random Number Generator - Gamma Distribution
		The Gamma distribution is most often used to describe the distribution of the amount of time until the nth occurrence of an event in a Poisson process.
		For example, when a Gamma distribution has an alpha of 1, Gamma(1, b), it becomes an Exponential distribution with scale parameter of b, Expo(b).
		And a Chi-Square distribution with k df is the same as the Gamma(k/2, 2) distribution.
	www.anthony-vba.kefra.com /vba/vbar8.htm (173 words)

	The Generalized Gamma Distribution
		While not as frequently used for modeling life data as the previous distributions, the generalized gamma distribution does have the ability to mimic the attributes of other distributions such as the Weibull or lognormal, based on the values of the distribution's parameters.
		While the generalized gamma distribution is not often used to model life data by itself, its ability to behave like other more commonly-used life distributions is sometimes used to determine which of those life distributions should be used to model a particular set of data.
		It is important to also note that as in the case of the mixed Weibull distribution, in the case of regression analysis, using a generalized gamma model, the choice of regression axis, i.e.
	www.weibull.com /LifeDataWeb/generalized_gamma_distribution.htm (725 words)

	The Gamma, Beta and Erlang distribution online. (Site not responding. Last check: )
		Input for the gamma distribution parameters in the 'c' and 'b' box.
		The Erlang distribution is a special case of the Gamma distribution were one value, in the c-box, has to be an integer.
		To revert the cummulative gamma distribution fill in the c and b box and additionally in the % box a value between 0 and 1.
	home.clara.net /sisa/gammahlp.htm (454 words)

	gamma distribution - OneLook Dictionary Search
		Gamma Distribution : AMEX Dictionary of Financial Risk Management [home, info]
		Gamma Distribution : Eric Weisstein's World of Mathematics [home, info]
		Phrases that include gamma distribution: inverted gamma distribution
	www.onelook.com /?loc=rescb&w=gamma+distribution (118 words)

	Gamma Distribution
		Typically, the gamma distribution is defined in terms of a scale factor and a shape factor.
		A chi-squared distribution is a gamma distribution in which the shape parameter set to the degrees of freedom divided by two and the scale parameter set to two.
		The Erlang distribution is used to model the total interval associated with multiple Poisson events, The shape parameters represents the number of events and the scale parameter the average interval between events.
	www.brighton-webs.co.uk /distributions/gamma.asp (487 words)

	Gamma Distribution (Site not responding. Last check: )
		The gamma distribution (continuous) could be used to model the time required to perform some task.
		If a gamma distribution has parameters mean = m and shape = a, then b = m/a is a scale parameter.
		A gamma distribution with mean = m and shape = 1 is an exponential distribution with mean = m.
	www.simprocess.com /docs/sp412/webhelp/SPHelp/gamma_distribution.html (105 words)

	DAKOTA: Variables Commands
		Distribution lower and upper bounds are explicit portions of the normal, lognormal, uniform, loguniform, triangular, and beta specifications, whereas they are implicitly defined for histogram and interval variables from the extreme values within the bin/point/interval specifications.
		The inclusion of lower and upper distribution bounds for all uncertain variable types (either explicitly defined, implicitly defined, or inferred; see Variables Description) allows the use of these variables with methods that rely on a bounded region to define a set of function evaluations (i.e., design of experiments and some parameter study methods).
		In addition, distribution bounds can be used to truncate the tails of distributions for normal and lognormal uncertain variables (see "bounded normal", "bounded lognormal", and "bounded lognormal-n" distribution types in [Wyss and Jorgensen, 1998]).
	www.cs.sandia.gov /DAKOTA/licensing/votd/html-ref/VarCommands.html (3499 words)

	Gamma Ray Bursts Tutorial - Chapter 4
		The angular distribution of the bursts is the batting average of the gamma-ray bursts - the first statistic any astronomer seems to be interested in - and it can provide important clues to the origin of these events.
		The non-uniformity of the angular distribution of objects on the sky lends insight into their nature, just as a right-handed batter who gets a majority of hits to left-field consistently might lead one to believe that the batter's nature is to pull the ball.
		Neither distribution is known for the gamma-ray bursts that we observe.
	science.msfc.nasa.gov /newhome/help/tutorials/batse/chapter4.htm (5499 words)

	A Mystery: Gamma Ray Bursts
		In addition to the constant flux of gamma rays illustrated in the adjacent image, there are also observed sudden pulses of gamma rays lasting typically seconds in which enormous amounts of energy appear to be poured out in gamma rays by still unknown sources.
		Furthermore, the mechanism producing the gamma rays must be such as to allow the gamma rays to escape without too much interaction with surrounding matter, because that interaction would convert the gamma rays to light of longer wavelength.
		Assuming these transients to be near the location of the gamma ray burst and the Doppler shifts to be Hubble redshifts, these observations have almost conclusively shown that gamma ray bursts are at cosmological distances and not in the halo of the local galaxy.
	csep10.phys.utk.edu /astr162/lect/cosmology/gammaray.html (765 words)

	Generalized gamma parameter estimation and moment evaluation (Site not responding. Last check: )
		We derive approximations for the log-density function and moments of the generalized gamma distribution that are smooth in the nearly log-normal case and involve only finite summations.
		The approximation for the first moment is applied to the problem of estimating the parameters of a generalized gamma distribution under the constraint that the distribution have mean one.
		This enables the development of a correspondence between the parameters in a mean one generalized gamma distribution and certain parameters in acoustic scattering theory.
	www.premier1.net /~bradbell/gamma.htm (198 words)

	ContinuousDistributions
		The extreme value distribution is sometimes referred to as the log-Weibull distribution because it describes the distribution of the log of a Weibull distributed random variable.
		Each distribution has a unique characteristic function, which is sometimes used instead of the pdf to define a distribution.
		This is a pseudorandom array with elements distributed according to the gamma distribution.
	documents.wolfram.com /v5/Add-onsLinks/StandardPackages/Statistics/ContinuousDistributions.html (588 words)

	Gamma Distribution Probability Tables (Site not responding. Last check: )
		The gamma distribution is widely used in climatological applications for representing variations in precipitation, ranging from seasonal and monthly totals (e.g., Ropelewski et al.
		The gamma distribution is characterized by mean µ=aß; and variance o^2=aß^2.
		Gamma distribution probabilities are calculated by integrating the probability density function.
	met-www.cit.cornell.edu /reports/RR_91-2.html (262 words)

	1.3.6.6.11. Gamma Distribution
		Since the general form of probability functions can be expressed in terms of the standard distribution, all subsequent formulas in this section are given for the standard form of the function.
		The formula for the percent point function of the gamma distribution does not exist in a simple closed form.
		The formula for the survival function of the gamma distribution is
	www.itl.nist.gov /div898/handbook/eda/section3/eda366b.htm (356 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)

	Press Info on the Gamma-Ray Halo
		Gamma rays are photons, or particles of light, with the highest energies of all forms of radiation, higher even than X-rays.
		Gamma rays are of great interest to astrophysicists because they may offer clues to some of the most violent events in the universe, such as the process of a dying star becoming a supernova and the birth of a galaxy.
		The high-energy gamma rays seen in the halo could be the result of collisions of high-energy cosmic rays, in the form of electrons, traveling at near the speed of light and colliding with low energy photons they encounter is space, Dixon said.
	tigre.ucr.edu /halo/halo.html (1424 words)

	Lecture 6—Monday, January 23, 2006
		One distribution that satisfies all three requirements is the gamma distribution.
		We conclude that the marginal density of a nonhomogeneous Poisson process when the gamma distribution is used as a mixing distribution, is negative binomial with parameters μ and α.
		The gamma probability distribution with these values of α and β then can be used to explicitly characterize, as a distribution, the way in which the heterogeneity manifests itself in your sample.
	www.unc.edu /courses/2006spring/ecol/145/001/docs/lectures/lecture6.htm (1290 words)

	S Archive: Poisson Gamma Distribution
		The Poison-gamma distribution is a Tweedie distribution with index p between 1 and 2.
		The distribution approaches gamma as p -> 2 and phi * Poisson(mu) as p -> 1.
		Since p = 1 corresponds to Poison and p = 2 corresponds to gamma, the Poison-gamma distribution is genuinely intermediate between the Poisson and gamma distributions.
	www.statsci.org /s/poisgam.html (250 words)

	A short digression on ``randomness''
		The normal distribution specifies the mean and variance separately, with two parameters, which means that one often assumes constant variance (as the mean changes), in contrast to the Poisson and binomial distribution (which are each defined by one parameter), where the variance is a fixed function of the mean.
		In this respect, the gamma is the continuous counterpart of the negative binomial, which is the distribution of a number of trials until a certain number of events occur.
		It is the continuous counterpart of the geometric distribution and a special case (for shape parameter=1) of the gamma distribution.
	www.zoo.ufl.edu /bolker/emd-2000/lect7.html (2834 words)

	Lecture 8—Wednesday, January 25, 2006
		The notion of a mixing distribution is a completely general one and appears in a number of other situations.
		The gamma distribution is a continuous distribution that should be viewed as a viable alternative to the normal distribution whenever the data in question are heteroscedastic.
		The lognormal distribution is a continuous distribution that should be viewed as a viable alternative to the normal distribution whenever the data in question are heteroscedastic.
	www.unc.edu /courses/2006spring/ecol/145/001/docs/lectures/lecture8.htm (2087 words)

	Probability Distributions (Site not responding. Last check: )
		The Gamma Distribution is a general distribution covering many special cases, including the Chi-squared distribution and Exponential distribution.
		The Log-Normal Distribution is useful when the raw data are highly skewed whereas the natural log of the data are normally distributed.
		The Beta Distribution is a continuous distribution bounded between 0 and 1.
	www.stat.vt.edu /~sundar/java/applets/Distributions.html (494 words)

	Example 27.3: Gamma Distribution Applied to Life Data
		Although PROC GENMOD does not analyze censored data or provide other useful lifetime distributions such as the Weibull or lognormal, it can be used for modeling complete (uncensored) data with the gamma distribution, and it can provide a statistical test for the exponential distribution against other gamma distribution alternatives.
		A value of 1 for the index parameter corresponds to the exponential distribution .
		The hypothesis of an exponential distribution for the data is, therefore, rejected at the 0.05 level.
	www.okstate.edu /sas/v7/sashtml/books/stat/chap27/sect44.htm (415 words)

	Unidentified gamma-ray sources
		Gamma ray bursts are flashes of high energy radiation that can be brighter, during their brief existence, than any other gamma ray source in the sky.
		The temporal distribution of the bursts is one of the most striking signatures of the GRB phenomenon.
		Based on the study of temporal asymmetry of 631 gamma ray bursts from the BATSE 3B catalog, we identified the population of bursts whose rising times are longer than their decays, thus showing atypical profiles.
	www.iar.unlp.edu.ar /garra/garra-unid.html (1360 words)

	Gamma Distribution -- from Wolfram MathWorld
		A gamma distribution is a general type of statistical distribution that is related to the
		This is the probability function for the gamma distribution, and the corresponding distribution function is
		The gamma distribution is closely related to other statistical distributions.
	mathworld.wolfram.com /GammaDistribution.html (233 words)

	Anthony's Excel VBA Page - Excel Tutorial - Excel Consultant - Excel Consulting
		The probability distribution derived from this simulation happens to be a Hypergeometric distribution.
		This tutorial shows how to create random numbers from a normal distribution given the standard deviation and the mean, and then computes the confidence interval given the level of significance.
		Use resampling with replacement, a probability distribution for the median is created, along with the standard deviation of the median, which cannot be computed under mathematical formula (since there is none).
	www.anthony-vba.kefra.com (1509 words)

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