I determined the distribution law of a random variable. Sample size - 110 measurements. According to different statistical criteria, different distribution laws were obtained: by the Kolmogorov-Smirnov criterion - the Johnson SU distribution law ; by the Anderson-Darling criterion - a generalization of extreme values; according to the Chi-square criterion - the Rayleigh distribution law. So what distribution law is the random variable under investigation? What is the criterion to decide?
Dear Sergei Azemsha ,
I suggest you start with a histogram the calculate standard summary statistic (mean, standard deviation, skewness and kurtosis). This will give you a feel for the distribution of your random variable.
However, the hypothesis testing process is usually deductive rather than inductive. The distribution you are looking for is often determined from this context, which you have not mentioned.
You need to determine the asymmetry of the distribution and distribution of the distribution through the Pearson coefficients.
Suggest that you do the graphs as suggested above to get ideas. Then choose the hypotheses for your test to represent the data vs a reasonable choice of distribution. Best wishes, David Booth
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