I am trying to reach the answers "How likely would that be? ¿How can I know if that is X% likely?" numbers using Mathematica, so far it seems I can answer: How likely would that be? by writing this:
Probability[x<1.54,x[Distributed]PERTDistribution[0.25,5,1]] I get a 0.55 probability of X being smaller than 1.54. ¿Correct?
Yes your assumptions are correct and you have used the Mathematica function ( $Probability[x < 1.54, x \[Distributed] PERTDistribution[{0.25, 5}, 1]]$ ) in the right way.
You also have a 0.45 chance of your storage needs being larger than 60GB as well as 0.55 chance of it being smaller.
If you specify 128GB of storage you will have a 0.964 chance of your storage not being exceeded.
If you specify 256GB of storage you will have a probability of almost 1 that your storage will not be exceeded.
Unless you are using RAM or SSD why not specify 1 TB and be done with it :)
But it does not, it seems like estimating a single files size with 95% confidence and then multiplying it for 40,000 is very different... ¿where is the mistake? also ¿is there a way to deal with this mistake "symbolically" that is, without having to wait for slow generation of sizes?
Yes there is. Use the Mathematica function Probability and your chosen PERTDistribution, which will integrate the probability distribution correctly for you.
For your report perhaps you could consider including a graph such as this:
Produced using the following Mathematica command:
With[{uLim = 5},
Plot[CDF[PERTDistribution[{0.25, 5}, 1], x], {x, 0, uLim},
FrameTicks -> {With[{ts = Range[0, uLim, 0.25]}, {ts,
40 ts}\[Transpose]], Automatic},
GridLines -> {Range[0, uLim, 0.25], Range[0, 1, 0.05]},
Frame -> True, LabelStyle -> Directive[Bold, Larger],
FrameLabel -> {"Space (GB) ",
"Probability that Space is Sufficient"}]]
which uses the Cumulative Distribution Function for the PERT distribution, CDF in Mathematica, which is effectively an aggregate of the probability that is below some value ( think of it as a plot of instantaneous values of the Probability function ).
You can then pose the question "What probability of storage exhaustion is acceptable to the organisation ?".
I'd be a little wary of the values of storage size for probabilities approaching unity, as the real distribution of file sizes is likely to have heavier tails than accounted for by the PERT distribution.
You may also want to consider your estimate of user numbers. You have a nice distribution estimate for file size, accounting for the potential variability in that quantity. However,you have a single fixed estimate for user numbers, 40,000, with no equivalent allowance for the potentially significant variation in this value. It might be wise to account for this uncertainty on your model.
