Claims Reserving Manual, vol.2: Section D3: A curve fitting method and a regression method
This method models the run-off triangle row-by-row and then ties the rows together. Each row, or year of account, is modelled by a Weibull distribution function. This model was suggested by D H Craighead, and so the Weibull distribution function has become to be known as the Craighead curve when it is used in this context. It is not a linear model and the three parameters have to be estimated using an iterative search method. Once this has been done, the ultimate loss ratio for each year of account can be estimated.
The second part of the method relates the known loss ratios (paid or incurred) to the predicted ultimate loss ratio. Taking a particular development year, each row of the triangle has a known loss ratio for that development year and a predicted ultimate loss ratio from the first part of the method. There is thus a set of pairs of known and dependent variables: one pair for each year of account. A line of best fit is found, using standard regression methods. From this regression line, another estimate of the ultimate loss ratio for each year of account can be read off. This new estimate has the advantage that it takes into account the information from all years of account, rather than just one particular year of account. The regression line can also be used to produce a confidence interval for the estimated ultimate loss ratio, and to estimate loss ratios for future development years (ie the lower triangle).