Influence size distribution of voronoi diagramm

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Hey everybody,
I tried so "simmulate" a grin distribution with a voronoi diagramm. Plotting the area distribution and the radius distribution for equiareal circles i saw that compared to real grain distributions, the lognormal distribution that comes naturally from the voronoi diagrmm is not wide enough. Since the radius goes with ~sqrt(area), the radius distribution has a normal distribution. In realit the area distribution is so wide, that even the radius distribution is lognormal.
I now try to find a way to influence the area distribution resulting from the voronoi diagramm. A constraint is that the different sized areas should be distributed normal over the whole area, so just taking a lognormal distribution or ny otherdistribution fpr the random seed doesnt work since it will results in an inhomogenious map.
I tried to add some noise to my normal distribution, but that didnt work either, since all sin or cos noises also add inhomogenity.
Does anyone has a better idea to come up with?

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