7.3.2 Distribution of Gravity, Temperature and Radiation

I was under the impression that the grav temp and rad randomizing were some sort of Gaussian centered around the center for each bar.

It is not a Gaussian, but a trapezoid. The last 10 clicks on each end are less likely to occur, each progressively less likely in linear fashion. The program generates the actual values for those two ranges as RANDOM(10) + RANDOM(90), which gives the trapezoid. And that is for grav and temp only - rad is just RANDOM(100), with all values equally likely.

By the way, as another fellow mentioned the actual endpoint values don't occur, in any of the three ranges. Probably for rounding reasons - RANDOM(x) just uses RANDOM(1) times x then does something with the excess fraction (rounded or dropped, etc). The rounding may be ``inwards" rather than ``up or down" (e.g. if it is distance from the center and rounded down).

Are you sure about the above distributions? I can think of other curves!

Total data points(planets) collected in each variable = 19900 . The data was sorted into 101 bins for each variable. A histogram was constructed for all 3 (rad, temp, grav).

First, the findings:

Radiation

Totally flat minus the endpoints which do not exist. We can say this with certainty since the average bin contained 201 planets. A value of 0 for the endpoints lies 14 standard deviations away from the mean. This is about as certain as you get. In truth I can only conclude that the endpoints are 1/50th as likely as every other point, but I will consider 0 to be a d### good bet. There were fluctuations outside of 2SD (standard deviation) for the whole data set, but nothing unexpected. Since 95% of the data should fall between 2 standard deviations of the mean you should expect 5% to fall outside of this and that is what I found.

I should also note that there were no significant deviations from the mean. By this I mean that I found no data points with twice the likelyhood of the rest of the data points, or something extreme like that.

In short: No surprises in the radiation range

Temperature

The theory is that the temp range starts at 0 at the endpoints, goes linearly up to the full percentage at 10 clicks in from the end and is flat from there on out. Theoretically this gives a 1/90 probability for each bin in the flat section.

Taking an average of the numbers in bins 10-90 we get 221.1 planets. This works out to 1 / 90.39 which is quite close to the predicted value of 1/90.

Next I looked at the end region and compared the actual data to the predicted data. I took into acount statistical fluctuations and compared the data to the expected line you should get if the theory is correct. The fit is quite nice. There are fluctuations in the results but all in all it looked good. I also compared the data to the theoretical line you should get if the corner fell 8 clicks out instead of 10. The fit was not as good this time. The line fell outside of 2SD for quite a few data points.

From the data it would appear that the theoretical distribution is accurate. At least with 19,900 data points the fit was good. Can I conclude that this ``IS" the right distribution...no, but I can conclude that using this distribution will give you no bad results. Either the theoretical distribution is correct, or there is no noticable d