The x-distribution

In case of continuous distributions, the "x-distribution" φ(x) defined in some interval [x_min,x_max] is by definition the number of x values (for a long chain of random numbers) in the interval [x,x+dx], divided by dx and the number n of random numbers.

In practice, we divide the interval [x_min,x_max] into M subintervals of width dx, with x_i being the center of the i-th interval, and we count the number of random numbers N_i which fall into the i-th interval. The x-distribution is then given as φ_i = N_i / (n × dx), together with the x-values x_i .

In the program, we use the table phi[i] for φ_i , the table xmi[i] for x_i , Nsim for the number n of simulated random numbers and Nsub the number M of subdivisions of the x-axis.

In case of discrete distributions (discrete values x_i), the "x-distribution" φ(x_i) is obtained by counting the number N_i of x values with x = x_i. Instead of Nsub, we use here Nval, being the number of possible x_i values. The x-distribution is then given as φ_i = N_i / n , together with the x-values x_i .

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