I'm running a bunch of simulations that are modeling the first time a neuron fires when it receives stochastic input and has intrinsic noise. The program I wrote creates a dataset of a bunch of time values which refers to the first time the neuron fires from trial-to-trial. A paper I'm looking at defines the mean latency (ML) as follows:

$$ML = \left<t \right> = \frac{1}{N}\sum_{i=1}^n t_i$$

where $t_i$ is the first spike time of the $i^{th}$ realization, and the "jitter" (which is what is of interest) is defined as follows:

$$J = \sqrt{\left<t^2 \right>- \left<t \right>^2}$$

I question whether or not $J$ is an accurate representation to describe the variability in first spiking times. I believe that when scientists use $J$ to discuss the variation in data, they frequently assume the data is normally distributed or close to it, which in my case, it is definitely not. I ran a sample of size $500$ and produced the following histogram:

enter image description here

As you can see, there is a heavy tail. I then used minitab (which I'm super novice at) to try and run a "Individual Distribution Identification" test in hopes that the data fits a known distribution, and then I could compute the standard deviation of that distribution which would give a more accurate measure of the variation. But I got the following:

enter image description here

I'm not sure what the $*$ means for p-values, but based on what I was reading and from the plots, it seems like my data follows reasonably close to the 3-parameter lognormal model?

Thus my question is: To understand the "jitter", am I better off using the value $J$ or am I better off approximating the parameters of the parent distribution, and then compute the variance and hence the standard deviation that way? Or is there a better way altogether to understand how changing parameters of the model changes the trial-to-trial variation?


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