geometric distribution


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geometric distribution

[¦jē·ə¦me·trik ‚dis·trə′byü·shən]
(statistics)
A discrete probability distribution whose probability function is given by the equation P (x) = p (1 -p) x- 1for x any positive integer, p (x) = 0 otherwise, when 0 ≤ p ≤ 1; the mean is 1/ p.
References in periodicals archive ?
The value of the inverse fine structure constant reflecting the 2-sided geometric distribution of the frequencies of the path of the electron in the ground state of Hydrogen atom can be calculated with the help of equations (1), (4), (5) and (6):
The value of the inverse fine structure constant reflecting the k-sided geometric distribution of the path of the electron in the ground state of Hydrogen atom is found with the help of equations (1), (4), (5), (10) and (11):
6 The inverse fine structure reflecting the geometric distribution
In fact, for the geometric distribution to emerge, seed 1 must be better than the rest of the field by the same margin as seed 2 is better than the lower-seeded teams; the same is true for seeds 2 and 3, 3 and 4, and so on.
j=1] 1/j for the the nth harmonic number, Exp([lambda]) denotes the exponential distribution with parameter [lambda], and Geo(p) is the geometric distribution with parameter (success probability) p.
The length of these carry intervals has a geometric distribution with parameter (b - 1)/2, but the number of such intervals started up to time n is now a random quantity [N.
Topics include optimal deterministic bounds on L-statistics, sharp upper bounds for expectations on kTH record increments from restricted families, maximal correlation between order statistics, characterizations of distributions by equalities of order statistics, records from discrete distributions, stochastic ordering of record and inter-record values, progress on sums of records, characterizations of geometric distributions by weak records, mean residual and past lifetime of k-out of n structures at the system level, linear estimation of location and scale parameters based on generalized order statistics from generalized Pareto distributions, and Bayesian estimation and prediction for the three-parameter generalized exponential model.
Topics of representative session papers include a source coding theory for sets, new lower and upper bounds on the expected length of optical one-to-one codes, efficient quantizer designs for robust distributed source coding and a practical approach to joint network-source coding, optical prefix codes for some families of two-dimensional geometric distributions, fast compression of scientific floating-point data without loss, low density codes that achieve the rate distortion bound, compression by the suffix tree, vector quantization with model selection, optical index assignment for multiple description of lattice vector quantization, a fast and low complexity image condec based on the backward coding of wavelet trees and a methods of making the correct mistakes.