Bivariate gamma distributions for extending annual streamflow records from precipitation: Some large‐sample results

This paper discusses the extension of streamflow records (commonly for annual time intervals) by correlation with longer records of precipitation for the purpose of estimating μY, the mean of the extended streamflow record. It is assumed that streamflow and precipitation have a bivariate gamma distribution, incorporating physical constraints on both variables, with μY estimated by maximum likelihood, by a ratio estimate, and by a regression estimate. Large‐sample variances of estimates given by these three estimation procedures are compared, and the effect on the ratio estimate of serial correlation in streamflow is calculated.