0
$\begingroup$

I have an object that is broken into smaller pieces such that the sum of the pieces is the volume of the original object.

I have arranged the volumes from the smallest to largest and have calculated the cumulative volume starting at 0% and ending at 100%.

Initially I was thinking that this graph was the same as the probability of the size distribution but the more I think about it am not 100% sure.

**Vol       Cumm Vol    % of total**
0.002652009 0.004214928 100
0.00064838  0.001562919 37.08055596
0.000261065 0.000914539 21.69761768
0.000142893 0.000653474 15.50379186
9.25843E-05 0.00051058  12.11362071
6.63311E-05 0.000417996 9.917040157
5.06804E-05 0.000351665 8.343322696
4.05044E-05 0.000300985 7.140921227
3.34249E-05 0.00026048  6.179945411
2.82653E-05 0.000227055 5.386932085
2.4392E-05  0.00019879  4.716332593
2.13362E-05 0.000174398 4.137627787
1.89405E-05 0.000153062 3.631422336
1.69605E-05 0.000134121 3.182054867
1.53332E-05 0.000117161 2.77966324
1.39699E-05 0.000101828 2.415880905
1.27933E-05 8.78578E-05 2.084442725
1.17995E-05 7.50645E-05 1.780918818
1.09368E-05 6.32649E-05 1.500972549
1.01715E-05 5.23281E-05 1.241494728
9.49734E-06 4.21567E-05 1.000174814
8.9103E-06  3.26593E-05 0.774848551
8.38075E-06 2.3749E-05  0.563449821
7.90202E-06 1.53683E-05 0.364614847
7.46623E-06 7.46623E-06 0.177137873

So if I have this set of sizes is this how I calculate the size distribution?

If not then how do I do this?

$\endgroup$
0
$\begingroup$

Your percentages (the third column) are the probability that a point chosen uniformly from the object is in a piece of volume less than or equal to the value in the first column. For example, looking at the fourth row of numbers, there is a $15.50379186\%$ probability that a point chosen is in in a piece of volume less than or equal to $0.000142893$.

In that sense your data shows a cumulative distribution function.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.