A Technique for Calculating the Parameters of a Normal or Lognormal Cumulative Distribution.

摘要

The statistical distribution of biological phenomena is generally assumed to be normal or Gaussian. In some instances, however, the distribution is lognormal, that is, the logarithm of the variable is normally distributed. This report presents a technique for determining the mean and standard deviation of these distributions from the cumulative distribution function. The actual distribution is compared against a standardized cumulative distribution function of mean, 5, and standard deviation, 1, (probit transformation). The relationship between the random variable and the probit is found by linear regression and the corresponding mean and standard deviation determined. Two programs are presented for solving this problem, one written for a Hewlett-Packard 9820A programmable calculator with plotter, and the other written for a digital computer in Fortran IV. As an example of the use of these programs, the platelet size distribution in a fresh blood sample, obtained from rats subjected to hyperbaric exposures and subsequently decompressed, is solved. (Author)