# normal distribution

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Related to Error Distribution: normal curve

## distribution

[dis″trĭ-bu´shun]
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.

## 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

## 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 ?
On the whole, the analysis showed that each of the objective variables considered had an impact on the delivery, but none of them is correlated with the error distribution. However, the subjective variable represented by trainees' skills does appear to be an accurate predictor of error patterns.
Furthermore, efficiency test should be conducted to ensure that the statistical method of the predicted error distribution characteristic is valid.
This function is very valuable tool for describing the extent of relationship between the transformed experimental data and the predicted isotherms and minimization of error distribution [93].
Assuming that the error distributions shown in Table 5 are applicable, we could say it is probable that absolute Percentage Error will not exceed 4.1 per cent and very likely (though not impossible) lie within 5.9 per cent.
Therefore, the above results show that the adaptive modulation is possible under Zero-Mean phase error distribution without any estimates.
Although transforms may achieve the desired linearisation and normal distribution, back-transformation of the predicted results to raw data format is subsequently required, leading to skewness and/or increasing bias in the back-transformed error distribution. We therefore propose that the usual regression statistics are inappropriate for describing prediction performance, and that a more detailed assessment of error for a particular analyte value may be required.
This paper complements and extends an earlier study by Baker, Rahman and Saadi (2008) showing that weekday effect in one stock market index (i.e., S&P/TSX Canadian index) is sensitive to the specification of error distribution. The present study is different in several ways.
Despite the drawbacks of the arithmetic mean in the absolute percentage error distribution, and in spite of the existence of simple procedures with the advantages already outlined, this is still used practically exclusively as if it were the only available location estimator.
It can be observed that the error distribution within the [+ or -] 5 dB window dominates the frequency counts.
With no [+ or -] allowable error distribution for the acceptable range limit points, 10 g/dL and 12 g/dL, the clinical goal and the reimbursement reduction risk resides within the Hgb measurement error and the ability to resolve an Hgb result of 10 g/dL and one of 9.9 g/dL.
1) Kriging accompanied by any estimation reduces its error, and not only the average error can be calculated but also the error distribution (estimation variance) can be determined in the whole area under study.
In his next paragraph, Huebner states, "The author ignores the clear lack of expected randomness in many of the entries of Table 1." This also is mistaken: the article addresses randomness, expected or otherwise, in the sections on the error distribution, statistical independence, Benford's law, rounding, and the systematic properties expressed by the equation for longevity.

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