Basic concepts of probability and statistics

Sample estimators of distribution moments

Sample moments are calculated using the observed values x1, x2, ..., xn of the variable X. Sample moments about the origin are: 

and sample moments about the mean are:

The sample estimate of the mean is the sample moment m'1, which is actually the arithmetic mean, or the average, of the sample values:

Sample moments m2 and m3 are not usually used to estimate distribution moments because they can be biased. Instead, so called unbiased estimators are used:

where s is the usual notation for sample standard deviation. Coefficients of variation and skewness are then estimated with:

 


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Hydrology of Floods
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HYDROLOGY OF FLOODS



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