Fr.: distribution binomiale
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)!] px.qn - 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.
Fr.: distribution de Bose-Einstein
For a → population of independent → bosons, a function that specifies the number of particles in each of the allowed → energy states.
→ boson; → Einstein; → distribution.
Fr.: distribution de brillance
A statistical distribution of the brightness of an astronomical extended object.
→ brightness; → distribution.
Vâbâžeš, → distribution; deraxšandegi, → brightness.
Fr.: distribution des charges
The way a number of → electric charges are arranged in space with respect to the point of observation.
→ charge; → distribution.
Fr.: loi du chi-deux
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.
cumulative distribution function
karyâ-ye vâbâžeš-e kumeši
Fr.: fonction de distribution cumulée
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
Fr.: fonction de distribution
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.
family of distributions
Fr.: famille de distributions
A set of distributions which have the same general mathematical → formula.
→ family; → distribution.
vâbâžeš-e Gaussi (#)
Fr.: distribution gaussienne
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.
Gibbs canonical distribution
vâbâžeš-e hanjârvâr-e Gibbs
Fr.: distribution canonique de Gibbs
The probability distribution of the various possible states of a certain → quasi-closed subsystem.
→ Gibbs free energy; → canonical; → distribution.
halo occupation distribution (HOD)
vâbâžeš-e hageš-e hâlé
Fr.: distribution d'occupation de halo
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.
Fr.: distribution logarithmico-normale
A → probability distribution in which the natural logarithm (logX) of the → random variable (X) has a → Gaussian distribution.
→ logarithm; → normal distribution.
Fr.: distribution de Maxwell-Boltzmann
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.
metallicity distribution function (MDF)
karyâ-ye vâbâžeš-e felezigi
Fr.: fonction de distribution de métallicité
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.
Fr.: distribution normale
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.
Fr.: distribution de Planck
The distribution of radiation with wavelength for a blackbody, given by → Planck's radiation law.
→ Planck; → distribution.
Fr.: distribution de Poisson
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) = (λxe-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.
vâbâžeš bâ qânun-e tavâni
Fr.: distribution en loi de puissance
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.
Fr.: distribution de probabilité
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.