Normal probability plot

The Probability or probability paper is one of the mathematical papers. With a probability paper can examine the data in a statistical feature to determine whether they are based on certain probability distribution is based. It is provided with a coordinate grid in which the abscissa equidistant from the quantiles of the distribution, whereas the ordinate is the corresponding function values ​​of the distribution are plotted in a linearized form. When entering the value pairs ( quantile, distribution), one obtains a straight line.

The probability plot is a conventional tool, which was used primarily before the introduction of electronic data processing wide application in order to achieve a distribution of verification of data fairly quickly and efficiently. Is primarily the well-known power probability of the normal distribution, but also the Weibull distribution represented in probability networks.

The normal distribution in probability network

The abscissa shows the quantiles x are removed for a standard normal random variables, as well as on the ordinate. On the ordinate, but not the values ​​of x, but the distribution function values

Displayed. If one arranges the ordinate scale lines in a way that calculated the distances between the distribution function values ​​are equal, we obtain the typical pattern of the Gaussian probability network.

Due to this linearization results for the pairs of values ​​a straight line. So probability paper allows a simple drawing of such a function, or the simple check whether given value pairs fit to a normal distribution (they must then lie on a line ).

As an example, the following function for the mean μ = 100 and the dispersion σ = 20 drawn on probability paper.

Practical application on the example of the normal distribution

In practice, the procedure is such that the observation values ​​collected are sorted by size. The ordered values ​​() the corresponding values ​​of an empirical distribution function are then assigned. To determine the empirical distribution function, there are various proposals and estimation formulas, eg

Results from the pairs of values ​​approximate a straight line, a normal distribution can be assumed for the population of the data. Estimates for the parameters median and standard deviation can be read directly from the probability paper.