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

Adam M. Finkel

Risk Analysis, 1990, vol. 10, issue 2, 291-301

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

Date: 1990
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https://doi.org/10.1111/j.1539-6924.1990.tb01050.x

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Persistent link: https://EconPapers.repec.org/RePEc:wly:riskan:v:10:y:1990:i:2:p:291-301

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