In the 3-slope ski-rental problem, the player is asked to determine a strategy, that is, (i) whether to buy a ski wear and then a ski set separately, or to buy them at once for a discount price, and (ii) when to buy these goods. If the player has not got any thing, he/she can rent it for some price. The objective is to minimize the total cost, under the assumption that the player does not know how many times he/she goes skiing in the future. We reveal that even with a large discount for buying at once available, there is some price setting for which to buy the goods separately is a more reasonable choice. We also show that the performance of the optimal strategy may become arbitrarily worse, when a large discount is offered.

In the present paper, we focus ourselves on the turning point (TP) algorithm proposed by Mueller and evaluate its performance when applied to a Gaussian signal with definite covariance function. Then the ECG wave is modeled by Gaussian signals: namely, the ECG is divided into two segments, the baseline segment and the QRS segment. The baseline segment is modeled by a Gaussian signal with butterworth spectrum and the QRS one by a narrow-band Gaussian signal. Performance of the TP algorithm is evaluated and compared when it is applied to a real ECG signal and its Gaussian model. The compression rate (CR) and the normalized mean square error (NMSE) are used as measures of performance. These measures show good coincidence with each other when applied to Gaussian signals with the mentioned spectra. Our results suggest that performance evaluation of the compression algorithms based on the stochastic-process model of ECG waves may be effective.