I have a query regarding the Laplace (double exponential) distribution.

I have conducted some experiments measuring the orientation of fibres within a material. The orientations are biased towards 0 degrees. I have summarised the orientations in a histogram between (Pi/2) and (-Pi/2) and then fitted a curve to the data to give me a continuous function. I used NLREG non-linear regression software to do this.

Upon first inspection, the experimental data appeared to follow a normal distribution, but this gave a poor fit for intermediate orientations between 0.35-1.22 radians. A Laplace distribution (double exponential distribution) was selected as the most appropriate model, based on the coefficient of determination values (R2). It was assumed that the fibre orientations were symmetrical about the origin (i.e. the probability of 0.5 radians is the same as for -0.5 radians).

All was fine up to this point.

I then submitted the results in a scientific journal and I got the following response form one of the reviewers:

"It is troublesome to see the sharp tip on the density curves – implying that the change rate of the probability density is infinite at the center, something first impossible and also a reflection of ignorance about the probability distributions."

I presume what he is talking about is that when you differentiate the Laplace distribution there is no solution at zero.

In the current context why does this matter? All I am doing is plotting probability against orientation, between (Pi/2) and (-Pi/2). Personally, I am not interested in the differential. I have successfully integrated the distribution to find the percentage of fibres between +10degrees and -10degrees, but why would I ever need to differentiate it? Am I missing something vital?

I am happy to challenge the reviewer on this point, but I first want to check that I am correct, especially since he has already implied that I am ignorant .