Normal Distribution (Gaussian)
This distribution is the one that most frequently is representing natural and social events. Much of the evidence from classical statistics, as well as the estimation of uncertainties, is based on the assumption that the data conform to a normal distribution. From the theoretical perspective, the Central Limit Theorem maintains that given a random sample of sufficiently large size, it will be observed that the distribution of means follows an approximately normal distribution. The general formula of this distribution is:
where μ represents the location and σ the scale of the function. In order to estimate a measurement uncertainty, μ corresponds to the mean and mode value of the random variable, while σ is the standard deviation.
Input parameters:
- Mean. Average value, or average of the random variable. The data collection of this variable, therefore, will be distributed on both sides of this function. In the case of this Normal or Gaussian distribution, the mean will coincide with fashion.
- Standard deviation. Measure of the dispersion of the values with respect to the sample mean. If this distribution is used for Type A (statistical) uncertainty components, this value can be calculated according to the equation:
where n is the number of values or repetitions. On the other hand, if what you want to know is the standard deviation of the sample’s mean, this value can be obtained by dividing s / √ n .
If the parameter to which this distribution is assigned corresponds to the uncertainty contribution from a calibration certificate, the standard deviation corresponds to the standard uncertainty ( u ), or to the expanded uncertainty divided by the coverage factor k.
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