Maximum Size Prediction in Wicksell's Corpuscle Problem for the Exponential Tail Data

In the Wicksell corpuscle problem, the maximum size of random spheres in a reference volume is to be predicted from the size distribution of circles which are planar sections of spheres cut by a plane. If the area of the great circle of spheres have the exponential tail, simple prediction methods are applied. Performance of the methods is evaluated by simulation and they are applied to a dataset of graphite nodule sizes in spheroidal graphite cast iron. The effect of left-truncation in Wicksell transform is discussed in a general framework.