This is the second of the three-part paper and generalises the least squares method to the weighted least squares (WLS) method in order to deal with the trend in the first two moments. The generalised method applies when the assumption of constant variance does not hold and the functional form of a trend in the variance is given. In the generalised method, the parameters of trend in the mean and variance are estimated simultaneously. To keep the weights as power functions of variances only, the restrictions on distribution functions are formulated, which, in fact, are not difficult to fulfil in hydrological studies. It is shown that the WLS method coincides with the maximum likelihood method in the case of the normal distribution.
Financed by the National Centre for Research and Development under grant No. SP/I/1/77065/10 by the strategic scientific research and experimental development program:
SYNAT - “Interdisciplinary System for Interactive Scientific and Scientific-Technical Information”.