# Lognormal

• Nick T. Thomopoulos
Chapter

## Abstract

When the logarithm of a variable, x, yields a normal variable, y, x is distributed as a lognormal distribution. The reverse occurs when the exponent of y transforms back to the lognormal x. The lognormal distribution has probabilities that peak on the left of its range of values and has a tail that skews far to the right. The mean and variance of the lognormal are related to the mean and variance for the counterpart normal. Further, the parameters of the lognormal are the mean and variance of the counterpart normal. In the pursuit to develop percent-point values for the lognormal in this chapter, some mathematical maneuvering is needed. When the normal variable y has its mean shifted to zero, to produce another normal variable y, the exponent of y transfers back to a lognormal that becomes a standard lognormal variable where percent-point values can be computed. Table values for the standard lognormal are listed in the chapter. The way to start with sample data from a lognormal variable and convert to a standard lognormal variable is described so that analysts can readily apply the tables.

## References

1. 1.
Galton, F. (1909). Memories of my life. New York: E.P. Dutton & Co.Google Scholar
2. 2.
Thomopoulos, N. T., & Johnson, A. C. (2003). Tables and characteristics of the standardized lognormal distribution. Proceeding of the decision sciences institute, 103, 1–6.Google Scholar