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Topic: Distribution function

Related Topics

Cumulative distribution function

Probability mass function

Beta distribution

Probability distribution

Normal distribution

Lebesgue integration

Lebesgue measure

Gigakelvin

Stieltjes integral

Extreme value theory

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	Distribution functions for identical particles
		The distribution function f(E) is the probability that a particle is in energy state E. The distribution function is a generalization of the ideas of discrete probability to the case where energy can be treated as a continuous variable.
		The term A in the denominator of each distribution is a normalization term which may change with temperature.
		The Maxwell-Boltzmann distribution is the classical distribution function for distribution of an amount of energy between identical but distinguishable particles.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/disfcn.html (249 words)

	Cumulative distribution function - Wikipedia, the free encyclopedia
		It is conventional to use a capital F for a cumulative distribution function, in contrast to the lower-case f used for probability density functions and probability mass functions.
		Continuity of the distribution implies that P(X = a) = P(X = b) = 0, so the difference between "<" and "≤" ceases to be important in this context.) The function f is equal to the derivative of F almost everywhere, and it is called the probability density function of the distribution of X.
		The Kolmogorov-Smirnov test is based on cumulative distribution functions and can be used to test to see whether two empirical distributions are different or whether an empirical distribution is different from an ideal distribution.
	en.wikipedia.org /wiki/Cumulative_distribution_function (556 words)

	Encyclopedia: Distribution (Site not responding. Last check: 2007-10-27)
		If f : R → R is an integrable function, and φ : R → R is a smooth (that is, infinitely differentiable) function with compact support (that is, it is identically zero except on some bounded set), then ∫fφdx is a real number which linearly and continuously depends on φ.
		These distributions are useful if one studies the Fourier transform in generality: all tempered distributions have a Fourier transform, but not all distributions have one.
		Tempered distributions generalize the bounded (or slow-growing) locally integrable functions; all distributions with compact support and all square-integrable functions can be viewed as tempered distributions.
	www.nationmaster.com /encyclopedia/Distribution (1660 words)

	1.3.6.2. Related Distributions
		That is, for a distribution function we calculate the probability that the variable is less than or equal to x for a given x.
		The hazard function is the ratio of the probability density function to the survival function, S(x).
		The cumulative hazard function is the integral of the hazard function.
	www.itl.nist.gov /div898/handbook/eda/section3/eda362.htm (597 words)

	Computation - Operations Research Models and Methods
		If the mass of the function is concentrated to the left of the mean and the distribution has a tail that decreases to the right, the skewness is positive, as for the example.
		The kurtosis measures the relative thickness of the tails of the distribution.
		When a function is not a probability distribution function or does not have a closed form, it might also be interesting to compute moments.
	www.me.utexas.edu /~jensen/ORMM/computation/unit/functions/moments.html (1293 words)

	Maxwell-Boltzmann distribution - Open Encyclopedia (Site not responding. Last check: 2007-10-27)
		The Maxwell-Boltzmann distribution can be derived using statistical mechanics (see the derivation of the partition function) or by using the principle of extreme physical information.
		The denominator in this equation is known as the partition function.
		Although Equation 11 gives the distribution of speeds or in other words the fraction of molecules having a particular speed, we are often more interested in quantities such as the average speed of the particles rather than the actual distribution.
	open-encyclopedia.com /Maxwell-Boltzmann_distribution (1056 words)

	A Potpourri of Partons (Site not responding. Last check: 2007-10-27)
		Parton distribution functions (in the "MS-bar" convention) are precisely defined in terms of matrix elements of operators.
		The code interpolates the desired parton distribution function from a table written in a standard form.
		One application of parton distributions is the calculation of the structure functions measured in deeply inelastic scattering.
	zebu.uoregon.edu /~parton (362 words)

	1.3.6.6.1. Normal 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 normal survival function can be computed from the normal cumulative distribution function.
		The sampling distribution of the mean becomes approximately normal regardless of the distribution of the original variable.
	www.itl.nist.gov /div898/handbook/eda/section3/eda3661.htm (458 words)

	1.3.6.6.7. Exponential Distribution
		Maximum likelihood estimation for the exponential distribution is discussed in the chapter on reliability (Chapter 8).
		The exponential distribution is primarily used in reliability applications.
		The exponential distribution is used to model data with a constant failure rate (indicated by the hazard plot which is simply equal to a constant).
	www.itl.nist.gov /div898/handbook/eda/section3/eda3667.htm (318 words)

	Statistics Glossary - Probability
		The probability-probability (P-P) plot is constructed using the theoretical cumulative distribution function, F(x), of the specified model.
		The quantile-quantile (Q-Q) plot is constructed using the theoretical cumulative distribution function, F(x), of the specified model.
		The Geometric distribution is related to the Binomial distribution in that both are based on independent trials in which the probability of success is constant and equal to p.
	www.cas.lancs.ac.uk /glossary_v1.1/prob.html (3540 words)

	Electron Energy Distribution Function (Site not responding. Last check: 2007-10-27)
		The package is intended for quick calculation of the electron energy distribution function and correspondent collisional rate coefficients in the gas-discharge or electron beam formed plasma under arbitrary non-stationary conditions.
		The distribution function may be calculated in accordance with the kinetics of population densities, determined basing on the real rate coefficients.
		The package is intended for a quick calculation of the electron energy distribution function, formed as a result of energy degradation process, initiated by electron beam or other high-speed particle beam propagation through a gas mixture.
	www.astrokettle.com /p_distr.html (288 words)

	Cumulative distribution function (Site not responding. Last check: 2007-10-27)
		It is conventional to use acapital F for a cumulative distribution function, in contrast to the lower-case f used for probability density functions and probability massfunctions.
		Every cumulative distribution function F is monotoneincreasing and continuous from the right.
		The Kolmogorov-Smirnov test is based on cumulativedistribution functions and can be used to test to see whether two empirical distributions are different or whether an empiricaldistribution is different from an ideal distribution.
	www.therfcc.org /cumulative-distribution-function-128713.html (395 words)

	Carrier distribution functions
		The distribution function of impurities differs from the Fermi-Dirac distribution function although the particles involved are Fermions.
		This distribution function is also called the classical distribution function since it provides the probability of occupancy for non-interacting particles at low densities.
		A plot of the three distribution functions, the Fermi-Dirac distribution, the Maxwell-Boltzmann distribution and the Bose-Einstein distribution is shown in Figure 2.5.4.
	ece-www.colorado.edu /~bart/ecen3320/newbook/chapter2/ch2_5.htm (1129 words)

	Distributions (Site not responding. Last check: 2007-10-27)
		The function is symmetric about the mean, it gains its maximum value at the mean, the minimum value is at plus and minus infinity.
		The exponential distribution is a special case of the gamma distribution where a=1 and B = 1/lambda.
		The Rician probability density function is derived as for the Rayleigh distribution by considering the in-phase and quadrature components.
	astronomy.swin.edu.au /~pbourke/analysis/distributions (901 words)

	SCATMECH: Slope_Distribution_Function
		Exponential_Slope_Distribution_Function: A slope distribution function that is exponentially distributed in slope.
		Exponential_Angle_Distribution_Function: A slope distribution function which is exponential in the polar angle of the surface normal.
		Table_Angle_Distribution_Function: A slope distribution function which is given by a table specifying the distribution in the polar angle of the surface normal.
	physics.nist.gov /Divisions/Div844/facilities/scatmech/html/sdf.htm (325 words)

	Gaussian distribution: FAQ. D'Errico.
		Even when the right conditions are not met however, the distributions found for many experimentally generated sets of data still tend to have a bell shaped curve that often looks quite like that of a normal.
		Even when a distribution may not be truly normal, it may still be convenient to assume that a normal distribution is a good approximation.
		The standard (mean=0 and variance=1) normal density function is 1 -(1/2)x^2 Z(x) = ---------- e sqrt(2pi) For mean=mu and variance=sigma^2 1 -(1/2)((x-mu)/sigma)^2 Z(x) = ---------------- e sigmasqrt(2pi) The normal distribution* with mean=mu and variance=sigma^2 is customarily referred to as N(mu,sigma^2).
	www.pitt.edu /~wpilib/statfaq/gaussfaq.html (1510 words)

	No Title
		As we have seen, not all distribution functions are continuous.
		In fact, the distribution function of a discrete random variable has a jump discontinuity at every point where the probability mass function is not 0, and the size of the jump is the value of the probability mass function.
		It is clear from calculus that a random variable with an absolutely continuous distribution is a random variable with a continuous distribution.
	www.uwm.edu /~ericskey/361material/361F98/L09/index.html (360 words)

	2.4 Distribution functions (Probability density functions)
		The derivation starts from the basic notion that any possible distribution of particles over the available energy levels has the same probability as any other possible distribution, which can be distinguished from the first one.
		The fact that the distribution function does not depend on the density of states is due to the assumption that a particular energy level is in thermal equilibrium with a large number of other particles.
		A plot of the three distribution functions, the Fermi-Dirac distribution, the Maxwell-Boltzmann distribution and the Bose-Einstein distribution is shown in the figure below, where the Fermi energy was set equal to zero.
	ece-www.colorado.edu /~bart/book/distrib.htm (1292 words)

	Distribution - Wikipedia, the free encyclopedia
		In physics, a distribution function, for example the Maxwell-Boltzmann distribution, describes the number of particles per unit volume in phase space.
		For the computer science concept, see distributed computing.
		For the meaning of distribution in the terminology of the Linux operating system, see Linux distribution.
	en.wikipedia.org /wiki/Distribution (132 words)

	distribution function -- Encyclopædia Britannica
		The binomial distribution gives the probabilities that heads will come up a times and tails n a times (for 0 a n), when a fair coin is tossed n times.
		This distribution was first set forth by the Scottish physicist James Clerk Maxwell in 1859, on the basis of probabilistic arguments, and gave the distribution of velocities among the molecules of a gas.
		They are often classified with the B vitamins because of similarities in function and distribution in foods.
	www.britannica.com /eb/article-9030657 (742 words)

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