For discrete data

Table 2

Number of Interval	Value of variables	Frequency	Relative frequencies

2)Choose the appropriate theoretical distribution law if it is possible.

3)Calculate the statistical characteristics (mean and variance ) of the experimental distribution. The complete sample size is defined by the formula , where is the number of groups (intervals) of the sample; is the midpoint of i ^th interval for the continuous data and the value of the i th group for the discrete data; is the frequency.

Table 3

 

Determination of the statistical parameters for the second group of data is illustrated by the table 4.

Table 4

4)Research the hypothesis about the low difference between the empiric and the theoretical distributions, using the criterion.

This criterion is defined by the expression:

where is the observed frequency for every group or interval; is the expected frequency for every group or interval; is the quantity of intervals or groups.

Check up accordance of data of the table 2 to the Poisson distribution law for the confidence probability 0,95.

The Poisson distribution law is determined by the formula

,

where [ ], is the positive constant, which simultaneously represents the mathematical expectation and the variance, . In our case

Calculations of are represented in the table 5.

Table 5

The last 3 groups are united to get the value of frequency, at least, equal to 5.

Calculate value The critical tabular value for the confidence probability 0,95 and the number of degree of freedom is . So, the calculated value is less than the critical value and the hypothesis is not cast aside.

If , the observed and the theoretical values of frequencies coincide.

Using this method, it is necessary to take into account the following factors:

a)It is necessary to use the absolute values of frequencies.

b)The values of the observed frequencies must not be less than 5 (). If this is not the case, groups or intervals must be united.

c)Number of degrees of freedom is equal to , where is number of groups or intervals, is number of the parameters determined by the experimental way.

5)Research the hypothesis about the low difference between the empiric and the theoretical distributions, using the Kolmogorov – Smirnov criterion.

For this criterion the integral probabilities for the theoretical and empiric distributions must be determined and the absolute difference comparable with the critical tabular values will be obtained.

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