Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Univariate Data Distributions Common Distributons Continuous Distributions Cauchy Distribution  
See also: t Distribution, Pareto Distribution  
Cauchy Distribution
ExampleThe following figure shows the average of means of Cauchy distributed random numbers as a function of n for n=1..500 (C(n), blue line). Since the probability density function of the Cauchy distribution has long tails, the odds for large values to occur are not negligible. This makes the mean jump considerably even when several hundred or thousand random numbers are averaged. The gray symbols show the individual random numbers, the red arrows indicate occasions where a random number exceeds the visible limits of the diagram.In contrast to the Cauchy distribution the mean of normally distributed data G(n) moves only slightly for n > 50 and the variation of the average decreases with increasing n. Thus the average can converge on the true mean of the distribution, since the probability of very small or very large numbers is so low that, on the long run, extreme values have no effect.


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