An Etymological Dictionary of Astronomy and Astrophysics
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A probability distribution for independent events for which there are only two possible outcomes i.e., success and failure. The probability of x successes in n trials is: P(x) = [n!/x!(n - x)!] p^x.q^{n - x}, where p is the probability of success and q = 1 - p the probability of failure on each trial. These probabilities are given in terms of the → binomial theorem expansion of (p + q)ⁿ.

→ binomial; → distribution.

For a → population of independent → bosons, a function that specifies the number of particles in each of the allowed → energy states.

→ boson; → Einstein; → distribution.

A statistical distribution of the brightness of an astronomical extended object.

→ brightness; → distribution.

Vâbâžeš, → distribution; deraxšandegi, → brightness.

The way a number of → electric charges are arranged in space with respect to the point of observation.

→ charge; → distribution.

A probability density function, denoted χ², that gives the distribution of the sum of squares of k independent random variables, each being drawn from the normal distribution with zero mean and unit variance. The integer k is the number of degrees of freedom. The distribution has a positive skew; the skew is less with more degrees of freedom. As degrees of freedom increase, the chi-square distribution approaches a normal distribution. The most common application is chi-square tests for goodness of fit of an observed distribution to a theoretical one. If χ² = 0 the agreement is perfect.

Chi Gk. letter of alphabet; → square; → distribution.

Vâbâžeš, → distribution; do, → two.

A function that gives the probability that a → random variable X is less than or equal to x, at each possible outcome: F(x) = P(X ≤ x), for -∞ < x < ∞. Same as → distribution function.

→ cumulative; → distribution; → function.

An act or instance of distributing; the state or manner of being distributed; something that is distributed. → binomial distribution, → Bose-Einstein distribution, → brightness distribution, → chi-square distribution, → cumulative distribution function, → distribution function, → Gaussian distribution, → Gibbs canonical distribution, → lognormal distribution, → Maxwell-Boltzmann distribution, → normal distribution, → Poisson distribution, → power-law distribution, → probability distribution, → spectral energy distribution.

Verbal noun of → distribute

A function that gives the relative frequency with which the value of a statistical variable may be expected to lie within any specified interval. For example, the Maxwellian distribution of velocities gives the number of particles, in different velocity intervals, in a unit volume.

→ distribution; → function.

A set of distributions which have the same general mathematical → formula.

→ family; → distribution.

A theoretical frequency distribution for a set of variable data, usually represented by a bell-shaped curve with a mean at the center of the curve and tail widths proportional to the standard deviation of the data about the mean.

→ Gaussian; → distribution.

The probability distribution of the various possible states of a certain → quasi-closed subsystem.

→ Gibbs free energy; → canonical; → distribution.

The → probability distribution of the → number of galaxies that a host → dark matter halo of a given mass contains. HOD is a powerful theoretical frame to populate dark matter halos with luminous galaxies. More specifically, it describes the bias between galaxies and dark matter by specifying (a) the probability P(N|M) that a halo of → virial mass M contains N galaxies of a particular class and (b) the relative spatial and velocity distributions of galaxies and dark matter within halos.

→ halo; → occupation; → distribution.

A → probability distribution in which the natural logarithm (logX) of the → random variable (X) has a → Gaussian distribution.

→ logarithm; → normal distribution.

The distribution law for kinetic energies (or, equivalently, speeds) of molecules of an ideal gas in equilibrium at a given temperature.

→ maxwell; → Boltzmann's constant; → distribution.

A plot representing the number of stars (or systems) per metallicity interval, usually expressed in [Fe/H] (abundance of → iron relative to → hydrogen).

→ metallicity; → distribution; → function.

A theoretical frequency distribution for a set of variable data, usually represented by a bell-shaped curve with a mean at the center of the curve and tail widths proportional to the standard deviation of the data about the mean. Same as → Gaussian distribution.

→ normal; → distribution.

The distribution of radiation with wavelength for a blackbody, given by → Planck's radiation law.

→ Planck; → distribution.

A → probability function that characterizes → discrete  → random events occurring independently of one another within some definite time or space. It may be regarded as an approximation of the → binomial distribution when the number of events becomes large and the probability of success becomes small. The Poisson distribution is expressed by: f(x) = (λ^xe^-λ)/x!, where λ is the mean number of successes in the interval, e is the base of the → natural logarithm, and x is the number of successes we are interested in.

Named after Siméon Denis Poisson (1781-1840), French mathematician, who developed the application of Fourier series to physical problems and made major contributions to the theory of probability and to the calculus of variations; → distribution.

For a → random variable X, any → distribution which has the form: P(X ≥ x) = (k/x)^α, where x is a value in the range defined for X, k > 0 is a parameter termed location parameter, and α > 0 is the → slope parameter.

→ power; → law; → distribution.

The function that describes the range of possible values that a random variable can attain and the probability that the value of the random variable is within any (measurable) subset of that range.

→ probability; → distribution.