normal distribution

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Related to Normal random variable: Standard normal distribution, normal distribution


1. the specific location or arrangement of continuing or successive objects or events in space or time.
2. the extent of a ramifying structure such as an artery or nerve and its branches.
3. the geographical range of an organism or disease.
frequency distribution in statistics, a mathematical function that describes the distribution of measurements on a scale for a specific population.
normal distribution a symmetrical distribution of scores with the majority concentrated around the mean; for example, that representing a large number of independent random events. It is in the shape of a bell-shaped curve. Called also gaussian distribution. See illustration.
 Normal distribution. The approximate percentage of the area (or frequency) lying under the curve between standard deviations is indicated. From Dorland's, 2000.
probability distribution a mathematical function that assigns to each measurable event in a sample group the probability that the event will occur.

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.

normal distribution

Gaussian distribution, a distribution which when expressed graphically is bell-shaped. The distribution to which many frequency distributions of biological variables, such as height, weight, intelligence, etc correspond.


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

nor·mal dis·tri·bu·tion

(nōr'măl dis'tri-byū'shŭn)
Specific bell-shaped frequency distribution commonly assumed by statisticians to represent the infinite population of measurements from which a sample has been drawn.
References in periodicals archive ?
Since there is a strong heterogeneity among students who differ from each other in these exogenous dimensions, inefficiency is allowed to change according to variations among students, due to the variance of the half normal random variable. This explains the heteroscedasticity assumption.
Toward this goal, we begin by approximating the sequence of single period log normal random variables in (2) by a sequence of discrete random variables.
In particular, we approximate the sequence of conditional normal random variables by a sequence of discrete random variables.
To account for the inherent variability in material properties and test conditions, the fatigue strength exponent m and the fatigue coefficient A of the S-N curve are considered normal random variables with the parameters of Table 8.
The proposed functional form of Cobb-Douglas stochastic frontier production function has country effects that are assumed to be distributed as half normal random variables and, also, are permitted to vary systematically with time.
From theorem 3 and Continuous Mapping Theorem, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [U.sub.j] (y) are the normal random variables with mean zero and covariance structure:
Shocks to endowment growth and inflation, ([[Epsilon].sub.[Zeta],t], [[Epsilon].sub.[Phi],t]), are assumed to be jointly distributed normal random variables such that E([[Epsilon].sub.[Zeta],t]) = E([[Epsilon].sub.[Phi],t]) = 0, [Mathematical Expression Omitted], [Mathematical Expression Omitted], and cov([[Epsilon].sub.[Zeta],t], [[Epsilon][Phi],t]) = [[Sigma].sub.[Zeta][Phi]].
Computer generation of normal random variables, Journal of the American Statistical Association 71, 3 56, 1976, 893-896.
So the program can operate without the use of the Statistics Toolbox (an extracost addition to Matlab), the random data has been generated from the two random number generators supplied with the basic Matlab program: randn for normal random variables, and rand for continuous uniform random variables.
where [Z.sub.i], i = 1, ...,4 are standard normal random variables and [[mu].sub.v] (t) is the mean velocity.
So there exists a lower triangular and nonsingular matrix [D.sub.[gamma]], [[mu].sub.[gamma]] [member of] [R.sup.n], and a random vector [xi] with components being independent standard normal random variables such that [[eta].sub.[gamma]] = [D.sub.[gamma]][xi] + [[mu].sub.[gamma]].
Next, the following standard results regarding bivariate normal random variables are employed.