Optimal cutpoints for random observations

For the discretisation of a continuous random variable into different categories the choice of cutpoints is essential. A popular application is the contingent valuation method. In a parametric approach, the choice of cutpoints directly effects the quality of the estimates. Therefore, optimal cutpoints are desirable in order to estimate the parameters most accurately. We consider an arbitrary number of cutpoints and determine optimal cutpoints for the exponential and Gumbel distribution and prove that the c-optimal cutpoints for the location parameter of the logistic distribution have corresponding equal category probabilities. Furthermore, we show that in the limiting case for infinitely many cutpoints there is no loss of information.