binomial distribution vâbâžeš-e donâmin 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)!] 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. |
Bose-Einstein distribution vâbâžeš-e Bose-Einstein 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. |
brightness distribution vâbâžeš-e deraxšandegi Fr.: distribution de brillance A statistical distribution of the brightness of an astronomical extended object. → brightness; → distribution. Vâbâžeš, → distribution; deraxšandegi, → brightness. |
charge distribution vâbâžeš-e bâr Fr.: distribution des charges The way a number of → electric charges are arranged in space with respect to the point of observation. → charge; → distribution. |
chi-square distribution vâbâžeš-e Xi-do Fr.: loi du chi-deux A probability density function, denoted χ^{2}, 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 χ^{2} = 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. |
distribution vâbâžeš (#) Fr.: distribution 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 |
distribution function karyâ-ye vâbâžeš 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 xânevâde-ye vâbâžešhâ Fr.: famille de distributions A set of distributions which have the same general mathematical → formula. → family; → distribution. |
Gaussian 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. |
lognormal distribution vâbâžeš-e logâritmi-hanjârvar 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. |
Maxwell-Boltzmann distribution vibâžš-e Maxwell-Boltzmann 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. |
normal distribution vâbâžeš-e hanjârvar 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. |
Planck distribution vâbâžeš-e Planck Fr.: distribution de Planck The distribution of radiation with wavelength for a blackbody, given by → Planck's radiation law. → Planck; → distribution. |
Poisson distribution vâbâžeš-e Poisson 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) = (λ^{x}e^{-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. |
power-law 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. |
probability distribution vâbâžeš-e šavânâyi 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. |