Assume that we generate forecasts from a model y=cx+d+. “c” and “d” are placement parameters estimated from observations on x and y, and is the residual.
If the residual is observed to be symmetric about the mode, it is usually assumed to be distributed by the Gaussian family of functions. If the residual is skew to the left of the mode, or to the right of the mode, it cannot be assumed to be normally distributed. A family of functions will then have to be found which will correctly represent the observed skew values for . The analyst has to search for a family on a case-by-case basis, trying one family of functions first, then another, till one is found which fits the observed non-symmetric -values correctly. This chapter aims to eliminate this time consuming estimation process. The chapter introduces a family of functions. The family is capable of taking any skew or symmetric locus by varying its placement parameters. The family will simplify the effort to correctly measure the densities of because the estimation problem is reduced to fitting only one function to the data if it is symmetric or skew.
Waage, F. (2008), "A new method for estimating forecasting functions", Lawrence, K.D. and Geurts, M.D. (Ed.) Advances in Business and Management Forecasting (Advances in Business and Management Forecasting, Vol. 5), Emerald Group Publishing Limited, Leeds, pp. 227-248. https://doi.org/10.1016/S1477-4070(07)00213-9
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