Tables And Characteristics of the Standardized Lognormal Distribution

Abstract

While lognormal distributions have demonstrated great utility in a number of applications related to decision sciences, practitioners find few - if any - tables of its cumulative distribution function available to support their work. This paper describes a standardized form of the lognormal distribution and a methodology by which tables of its cumulative distribution function can be generated. This paper, then, provides these reference tables and illustrates their use. Despite the lognormal distribution's utility, practitioners find few - if any - tables of its cumulative distribution function available to support their work. Moshman (1953) has published selected upper and lower percentile points (0.5%, 1%, 2.5%, 5%, and 10%) as a function of the shape parameter. Similarly, Broadbent (1956) provides upper and lower 1% and 5% as a function of the coefficient of variation. It is the objective of this paper to provide practitioners with more comprehensive tables of the cumulative distribution function of the lognormal distribution. Additionally, we will illustrate a methodology by which critical values of a standardized lognormal distribution may be calculated directly.