Simulation and evaluation of different statistical functions for describing lag time distributions of a bacterial growth curve

Although different in shapes, the simulation results showed that the performance of normal, lognormal, Gumbel, and gamma distributions was practically the same when used to fit the growth curve, yielding the same estimates of initial and stationary phase bacterial concentrations, specific growth rate, and mean lag time as well as RSS. The lognormal, Gumbel, and gamma distributions of the lag times were slightly skewed to the right of the mean. The standard deviations of the lag times with these distributions were relatively small, suggesting that cells may leave the lag phase almost simultaneously. The Weibull and exponential distributions were also suitable for describing the distribution of lag times, but with larger standard deviations. In general, all these statistical distributions were found suitable for simulating the distribution of lag times of individual cells in a population.