The distribution of the logarithm of survival times when the true law is exponential

In a recent paper Withell (1942) has shown that for a wide range of microorganisms and disinfectants or poisons the logarithms of the survival times are approximately normally distributed. Even when the number of survivors is adequately represented by an exponential function of the time ( e − kt ) say, the former hypothesis still gives approximately correct results. This suggests that in many cases the data are not good enough to distinguish between the two hypotheses (1) of a constant force of mortality k and (2) of a normal distribution of the logarithms of survival times. It is worth while, therefore, to examine the form of the distribution of the logarithms of survival times when the exponential law is true, and to see how nearly normal it is. We shall show that except for the position of the mean, this distribution is independent of k .