AN EMPIRICAL-TEST FOR THE RELIABILITY OF QUANTAL ANALYSIS BASED ON PASCAL STATISTICS

We have previously shown that amplitude distributions of excitatory postsynaptic potentials (EPSPs) can be better described by Pascal distribution when the mean quantal content (m) is not stationary but fluctuating according to gamma distribution. We have developed the procedure of estimating quantal parameters by the method of maximum likelihood. In this study, we examined empirically the reliability of this quantal parameter estimation procedure by using Monte Carlo simulations. The reliability was evaluated by absolute values of error (/ error /) of estimated parameters relative to the known 'true' parameters. The mean values of relative / error / were relatively small unless the probability of failures was too large ( > 0.7) or too small ( < 0.1). The values of relative / error / became smaller in association with increases in the sample size. When the probability of failure was between 0.1 and 0.7, the sample size was 1000, coefficient of variation of quantal size was 0.45, the values of relative / error / of estimated parameters were below 0.1. These results mean that this procedure gives relatively reliable estimates of quantal parameters with the limitation that the probability of failure is neither too large ( > 0.7) nor too small ( < 0. 1); it is preferable that the sample size is as large as 1000.