By construction, the sum of the pi=s is equal to one. For goods that have ownership rates that are relatively equal across deciles, regardless of the level of the ownership rate, the probability distributions are fairly flat with values for pi close to 0.1. For goods that are more concentrated among the affluent households, the probability distributions tend to rise across the income deciles.
BIS Review 67/1998  -5*  *  *  Footnotes 1 Arthur B. Kennickell and R. Louise Woodburn, “Consistent Weight Design for the 1989, 1992 and 1995 SCFs, and the Distribution of Wealth,” manuscript, August 1997.