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The lognormal distribution has a number of properties that do not lend themselves to simple "back-of-the-envelope" calculations. Mathematical relationships are presented for the basic parameters of the large population lognormal distribution as a function of characteristics available to, or needed by, the risk analyst. A freeware computer program called LOGNORM4 has been written to take the tedium out of determining various characteristics of lognormal distributions, given 1 of 15 sets of values that uniquely specify a lognormal distribution.
Keywords: aerosol size distribution, computer program, environmental health, lognormal distribution, parameters, probabilistic risk assessment
In considering the health effects of a hazardous or potentially hazardous agent in the indoor or outdoor environment, the person assessing the risks often wishes to compute more than just the central estimate or just the upper estimate of the risk. To compute a distribution of health risks, the distribution of the amount of the agent to which an individual or a group of individuals is exposed must be known. Often the distribution of pollutants in the environment is lognormally distributed because many environmental processes are governed by the product of independent random variables.(1) However, the risk analyst may not have ready access to the entire set of original data. Instead, he or she might be able to find minimal information published, or otherwise documented, giving the mean and standard deviation (SD) with no distribution specified, or perhaps the geometric mean and geometric standard deviation (GSD) without a complete justification of why a lognormal distribution was assumed.
Often, a risk analyst must address a problem with only such minimal data. Whenever one assumes a type of underlying statistical distribution without the data to show that such an assumption is correct or at least plausible, there is a danger of drawing erroneous conclusions. Those who read this article or use...