Right, so my understanding of how fractional randomness is implemented is that for each interspike interval, the interval is dependent on the values set for s.interval and s.noise (assuming s = new NetStim(x)). Specifically, the magnitude of the value of s.noise (from 0 to 1) will control the proportion by which the interval is dependent on s.interval vs random values sampled from a negative exponential distribution. For example if s.noise = 0.2, the actual interval will be 0.8*s.interval + a random duration sampled from a negative exponential distribution with a mean duration of 0.2*s.interval. I am mostly unsure about how this negative exponential distribution (i.e.

*X*) is represented mathematically. Honestly, from my limited understanding I would've written it as follows:

If given a PDF negative exponential distribution according to the following: lambda*exp(-lambda*x), and 1/lambda = the mean of the distribution, then lambda would be equal to (1/s.interval*s.noise). This would give the following:

*X ~ lambda*exp(-lambda*x)*
*X ~ (1/s.interval*noise) * exp( -x / (s.interval*s.noise) )*
In this case,

*x* would represent the range of durations that the exponential distribution covers, which can incorporate the proportion of the interval (i.e. (1-s.noise)*s.interval) according to the following:

*X ~ (1/s.interval*noise) * exp( -(t - (1-s.noise)*s.interval)) / (s.interval*s.noise) )*
Which ensures that

*x* (i.e. t - (1-s.noise)*s.interval) ) must be larger than 0 in order to get event probabilities greater than zero (i.e. negative duration probabilities would be impossible), such that the total time elapsed,

*t*, before a new event occurs is greater than (1-s.noise)*s.interval). Actually, going through this, again, I am thinking that the notation I had posted previously would be incorrect, because the PDF and the equation preceding it sort of incorporate the (1-s.noise)*s.interval twice, which I think could force the actual interval to be up to twice its set value. My corrected notation would be one of the following:

... or this (which I think would mean the same thing (?)):

Thank you for your time,

Alex GM