Statistics question

[Dauphin]

I have data that has generated a graph that has a remarkable likeness to the Maxwell-Boltzmann distribution. It's been a long time since I've done statistics, so hoping someone can tell me if this statistical distribution tells me anything interesting about my data. e.g. what types of phenomena (beside the thermodynamics of a gas) would be expected to have this distribution, and why?

My y-value is a $ amount (equating to the population in the M-B distribution), and my x-value is an age value (equivalent to velocity).

[Ben Kenobi]

someone can tell me if this statistical distribution tells me anything interesting about my data. e.g. what types of phenomena (beside the thermodynamics of a gas) would be expected to have this distribution, and why?

It means you did your work correctly. We'd expect that distribution for income because folks tend to have their peak earning years between 50 and 60. This is actually a pretty well known phenomenon.

[Lorizael]

So the way this got explained to me this past semester is that in any particular direction, there is a Gaussian distribution of speed, but to get the distribution within some volume element, you need to find the product of the three individual components, which ends up producing an MB distribution. So unless you want to conclude that your age variable exists along three independent dimensions of time, I don't know how useful my half-remembered derivation is. Oh ****, KH is viewing this thread.

[pchang]

It means that money is transferred by random Brownian transactions?

[pchang]

Thus, the longer you are alive, the greater chance you have if becoming rich.

[Dauphin]

So the way this got explained to me this past semester is that in any particular direction, there is a Gaussian distribution of speed, but to get the distribution within some volume element, you need to find the product of the three individual components, which ends up producing an MB distribution. So unless you want to conclude that your age variable exists along three independent dimensions of time, I don't know how useful my half-remembered derivation is. Oh ****, KH is viewing this thread.

This was about the limit to my memory too.

I'm not sure how I would count the degrees of freedom for my data. Each data point has a start date ($ value starts to accrue), an end date ($ value stops accruing), a crystallization date, and the $ value. The dates are bucketed into six month time brackets. My graph is attempting to show the number of six-month time periods between a $ amount accruing and it crystallizing. I'm not convinced my three time variables lead to three degrees of freedom, as I would have expected them to be non-independent, but maybe the distributions shows that they are?

[Dauphin]

In narrative terms:
- the more quickly a value is accrued, and the more quickly it is crystallized, the further to the left of the graph its $ values will be;
- the slower it is to crystallize, and the longer it takes to accrue, the further to the right of the graph its $ values will be.

Two of the variables affect its accruing length, and one its crystallization.

[Lorizael]

Well, I'm honestly not sure what you have is a distribution at all. If it's a distribution, then you're looking at a population of dollar bills spread over your set of age brackets, and integrating up along that spread will tell you the total number of dollar bills in the system. But when you talk about amounts "accruing" between periods of time, it sounds like later parts of the graph include stuff from earlier parts of the graph. In that case, you don't really have a distribution and I'm not sure that similarities to a M-B distribution (really, a chi-squared distribution with, as you said, three degrees of freedom) are meaningful.

^ might all be bull****.

[Dauphin]

Well, I'm honestly not sure what you have is a distribution at all. If it's a distribution, then you're looking at a population of dollar bills spread over your set of age brackets, and integrating up along that spread will tell you the total number of dollar bills in the system. But when you talk about amounts "accruing" between periods of time, it sounds like later parts of the graph include stuff from earlier parts of the graph. In that case, you don't really have a distribution and I'm not sure that similarities to a M-B distribution (really, a chi-squared distribution with, as you said, three degrees of freedom) are meaningful.

^ might all be bull****.

The accrual process just means that, for example, if $100 accrues in a year, and the crystallizes a year after the accruing period ends, then $50 gets assigned to the two relevant six month periods. i.e., $50 appears in period t=3 and $50 in period t=4; $0 appears in all other time periods. If $10,000 accrues over five years and crystallizes immediately after the accrual period ends, then $1,000 appears in each of t=1 to t=10.

When you add up all such accruals and crystallizations, it comes out looking very similar to the distribution described.

[Lorizael]

Okay, that makes sense.

[BeBMan]

Are you guys saying we should use logic???

*hides