Fitting an Exponential Distribution

Abstract

Exponential distributions of the type N = N0 exp(??t) occur with a high frequency in a wide range of scientific disciplines. This paper argues against a widely spread method for calculating the ? parameter in this distribution. When the ln function is applied to both members, the equation of a straight line in t is obtained, which may be fit by means of linear regression. However, the paper illustrates that this is equivalent to a least squares fit with a weight function that assigns more importance to the higher values of t. It is argued that the method of maximum likelihood should be applied, because it takes into account all of the data equally. An iterative method for determining ? is proposed, based on the method of moments for cases in which only a truncated distribution is available.