Fitting an exponential distribution: Effect of discretization

The parameter λ of an exponential distribution with a probability density function f(x) = λ exp(–λx) may be calculated in different ways. The analysis carried out in this paper confirms the difference existing between the value of this parameter when it is calculated by means of the moments method using all the data and the value obtained when the data used have previously been classified into groups. This difference must be taken into account if the aim is to compare the parameter in two or more distributions. The present study develops a theoretical calculation of the error introduced when classifying the data into groups, and a correction is put forward. This error depends on the size of the group used and on the value of λ itself. Finally, the equations obtained have been applied to one particular case study: hailstone size distributions provided by the hailpad network installed in Italy. The data corroborate the validity of the results and the usefulness of the correction suggested for the value of λ when it is calculated from a classification into hailstone size groups.