gaussian distribution


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nor·mal dis·tri·bu·tion

a specific bell-shaped frequency distribution commonly assumed by statisticians to represent the infinite population of measurements from which a sample has been drawn; characterized by two parameters, the mean (x) and the standard deviation (σ), in the equation:

normal distribution

A bell-shaped frequency distribution of data, the plotted curve of which is symmetrical about the mean, indicating no significant deviation of the data set from the mean.

Properties of a normal distribution
Continuous and symmetrical, with both tails extending to infinity; arithmetic mean, mode, and median are identical. The curve’s shape is completely determined by the mean and standard deviation.

gaus·si·an dis·tri·bu·tion

(gow'sē-ăn dis'tri-byū'shŭn)
The statistical distribution of members of a population around the population mean. In a gaussian distribution, 68.2% of values fall within ± 1 standard deviation (SD); 95.4% fall within ± 2 SD of the mean; and 99.7% fall within ± 3 SD of the mean.
Synonym(s): bell-shaped curve, normal distribution.

Gaussian distribution

Normal distribution. The distribution of characteristics found in large populations subject to many causes of variability. The graph of the Gaussian distribution of any characteristic (such as body height) is a symmetrical bell shape, centred on the mean. (Johann Karl Friedrich Gauss, 1777–1855, German mathematician).

Gauss,

Johann K.F., German physicist, 1777-1855.
gauss - a unit of magnetic field intensity.
gaussian curve - a specific bell-shaped frequency distribution. Synonym(s): gaussian distribution; normal distribution
gaussian distribution - Synonym(s): gaussian curve

distribution

the arrangement of numerical data. The arrangement may be in accordance with magnitude, a frequency distribution, or in relation to geographical location, a spatial distribution.

age distribution
see age distribution.
bimodal distribution
the distribution has two regions of high frequency of observations separated by a zone of low frequency.
binomial distribution
a probability distribution associated with two mutually exclusive outcomes.
cluster distribution
a nonrandom distribution with observations aggregating about geographic or temporal variables. May be deceptive and merely reflect the distribution of an uneven population.
frequency distribution
a table or graph of the frequency of occurrence of each value of a variable.
Gaussian distribution
see normal distribution (below).
hypergeometric distribution
may apply to sampling without replacement of a finite population.
lognormal distribution
a distribution which is normal when the log values of the variable are considered.
normal distribution
a graph of the distribution appears as a bell-shaped curve which is symmetrical on the two sides of the vertical axis through the peak of the curve. Called also gaussian distribution.
parent distribution
the distribution (population) that was originally sampled.
Poisson distribution
regular distribution
distributed at regular intervals of time or space; all values within its given interval are equally likely.
sex distribution
an increase in frequency in one sex, which includes neutered males and neutered females. Called also sex-linked or sex-associated.
skewed distribution
a distribution in which the curve illustrating it is not symmetrical but has a long tail on one or other side of the graph.
spatial distribution
variations in distribution related to position in space, e.g. close to the door of a barn.
t-distribution
see t-test.
temporal distribution
variation in distribution related to time, e.g. occurrence of disease incidents after visits by veterinarians, inseminators, feed salesmen.
References in periodicals archive ?
In the first case, the pure CE method was utilised: we generate N samples from a Gaussian distribution which determines the parameters (weights) of the radial basis function.
5[sigma], which practically coincides with the estimates based on the relevant Gaussian distributions.
18A) that are lower than the mean rate (<1) compress the Gaussian distribution, as these animals' scope for growth is insufficient to permit normal fecundity.
A Gaussian distribution has an average to standard deviation ratio of [square root of (2/[pi])] [congruent to] 0.
In a Gaussian distribution, the mean divides the observations in two halves -50 percent above the mean and 50 percent below the mean.
For measured data, that distribution will generally be a normal or Gaussian distribution.
The statistics involved in SPC are elementary, little more than an understanding of the basic mathematics of the Gaussian distribution.
The best value for this has been calculated using a Gaussian distribution function which is defined as
Using data obtained from the wavelet analysis derived in the previous step we could obtain statistical parameters necessary for fitting the probability density function related to data (for Gaussian distribution just the mean and variance are necessary to estimate).
In the case of the market price development of many liquid financial instruments we observe not Gaussian distribution of returns with a positive kurtosis which is characterized by the fat tails at the borders and the sharpness in the mid-area of the distribution.
The estimation of original reliability of inverse Gaussian distribution from length-biased samples by way of stochastic transformations will be presented.
It is seen that the probability densities obtained by the nonstationary model based on WT comply with the Gaussian distribution better than those calculated by nonstationary model based on EMD and traditional stationary model.

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