Estimation of Statistical Parameters for Annual River Flows
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A first order Markov process is chosen as representative for annual river flows. The normalized standard errors of the estimates of the mean, the variance, and the first autocorrelation coefficient are shown as functions of the sample size for a river which is considered to have average statistical characteristics. The theoretical analysis is complemented with a study of the variations with sample size of the main statistical parameters of three rivers with a large amount of data. The results show that on the average between 40 and 60 years of data are desirable to estimate the mean and the variance. The normalized standard error grows rapidly with any diminishing of the sample size. Beyond this range the normalized standard error of estimate decreases slowly with lengthening sample size. Large errors appear to be common in estimating the first autocorrelation coefficient, even for series whose length is much longer than is normally found. Copyright 1969 by the American Geophysical Union.
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