A Simple Formula for Calculating the “Mass Density” of a Lognormally Distributed Characteristic: Applications to Risk Analysis

摘要: Statements such as “80% of the employees do 20% work” or “the richest 1% society controls 10% its assets” are commonly used to describe distribution concentration a variable characteristic within population. Analogous statements can be constructed reflect relationship between probability and for unvarying quantities surrounded by uncertainty. Both kinds represent specific usages general relationship, “mass density function,” that is not widely exploited in risk analysis management. This paper derives simple formula mass function when uncertainty and/or variability quantity lognormally distributed; gives analyst an exact, “back-of-the-envelope” method determining fraction total amount contained any portion distribution. For example, if exposures toxicant distributed with σin x= 2, 50% all exposure borne 2.3% persons most heavily exposed. Implications this various issues assessment explored, including: (1) marginal benefits reduction; (2) distributional equity perception; (3) accurate confidence intervals population mean limited set data available; (4) possible biases introduced uncritical assumption extreme “outliers” exist; (5) calculation value new information.