Some Measures on the Standard Bivariate Lognormal Distribution

While univariate and bivariate lognormal distributions have demonstrated great utility in a number of applications related to decision sciences, practitioners find few - if any - tables of their cumulative distributions function available to support their work. This paper describes a "standardized" form of the univariate and bivariate lognor mal distributions and a methodology by which tables of their cumulative distribution functions can be generated. This paper, then, provides these reference tables and illustrates their use. Finally, it is noted that this methodology may be readily exten ded to the multivariate lognormal distribution. 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%, an d 10%) as a function of the shape parameter. Similarly, Broadbent (1956) provides upper and lower 1% and 5% values as a function of the coefficient of variation. Thomopoulos and Longinow (1984) utilize the bivariate lognormal distribution in a structural reliability application. It is the objective of this paper to provide practitioners with more comprehensive tables of the cumulative distribution function of the univariate and bivariate lognormal distributions. Additionally, we illustrate a methodology by which "critical values" of "standardized" lognormal distributions may be determined.