Wikipedia:Reference desk/Archives/Mathematics/2014 August 6

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August 6

What is the best way to indicate high sales in this situation?

Hello!

I have a collection of data which represents the quantity held of a certain part number over a period of time. For instance:

Part# TPD-506

8/1/2014 7000

8/2/2014 7000

8/3/2014 5000

8/4/2014 4000

8/5/2014 6000

What i am interested in is looking at how much is sold. (If the quantity decreases some was sold, if it increases, the company received more into stock than what they sold that day). Note that from Aug 3 to Aug 4, for instance.... we don't know if 1000 were sold... maybe 2000 were sold and 1000 were brought in, maybe 3000 were sold and 2000 brought in, etc. This is because the data we have is ONLY the quantity. However, this data at least gives us SOME idea of what is happening.

Considering this data as a set of quantities for the specific part number, i want to compare two different part numbers and see which has more sales, or is more active. Thus, a number indicating the sales or activity of this part number is preferable, so that two part numbers can be compared numerically and sorted. Let us call this variable "S", and the set of quantities representing a single part "X". There are many different ways to make such an indicator number. Here are a couple i thought of:

1) S = Mean Absolute Deviation

2) S = Average decrease per day, where an increase in stock is counted as "Zero decrease" (The idea behind this is trying to see that AT LEAST a certain amount was sold.

For clarity i will compute these values for the given data set, as option 1 is probably more obvious, but i wish to make 2 more clear.

1) Mean = 5800, S = MAD = ( |7000 - 5800| + |7000 - 5800| + |5000 - 5800| + |4000 - 5800| + |6000 - 5800| ) / 5 = 1040

2) (0 + 2000 + 1000 + 0) / 4 = S = 750

The formula for S should be chosen so that among perhaps hundreds of parts, one can look at their "S values" and observe the highest values of this, so as to easily construct a "Top 10 selling parts list".

Please advise what the best formula or way to do this would be, and why. Thanks!

216.173.144.188 (talk) 13:21, 6 August 2014 (UTC)

I'd suggest using Volatility_(finance). The idea is to measure how much the the stock tends to change over time. You can compute it for various time frames, e.g. the whole data series, past 10 days, etc. Each period will mean a slightly different thing, but that will be useful. E.g product X had highest total volatility for the year 2013, but for the month of December 2013, Y had highest volatility. If I were making business decisions, this is the kind of information I'd like to know. As a bonus, there's a decent chance some people involved will already be familiar with the concept. SemanticMantis (talk) 19:25, 6 August 2014 (UTC)

Of my understanding is correct volatility is equivalent to standard deviation, according to the wiki article. If this is the case, I would choose the population standard deviation. Is this what type of path you are suggesting?

It would at least make sense to me. If a company has 7000 of a part in stock but doesn't sell a single one, the deviation would be nothing at all.

204.16.69.173 (talk) 15:12, 7 August 2014 (UTC)

Yes, I think you took my meaning correctly. I just linked to the volatility article because it is written in terms of the application you have in mind. And, if you use the terminology from that article, some financial types of people might find it easier to understand what you are doing. It's a bit too subtle to get into in this format, but I believe there are good reasons why the financial industry defines volatility the way it does, and does not use MAD as much. SemanticMantis (talk) 17:01, 7 August 2014 (UTC)

Solved. Thanks! 216.173.144.188 (talk) 19:01, 7 August 2014 (UTC)

Dilations

I want to pose a few questions related to a situation I do not fully understand. Let say I have a 2-sphere. I will introduce a set of spherical coordinates and define a function F(θ,φ) on it. For simplicity sake and visualization, let's assume that this function looks like this: $\vee$.

I can then expect to expand this function into a series of spherical harmonics, the natural basis on 2-sphere which is invariant under rotations. It is also a basis in the Hilbert space of functions on 2-sphere.

Then I "dilate" this function on 2-sphere and after the dilation it looks like this $\bigvee$. Likewise I will express this function via the spherical harmonics transform.

Then I want to move to a different subject: the Dilation operator on Hilbert spaces. These are my questions.

• Does the "physical" dilation of the function on 2-sphere have anything to do with Dilation operator in Hilbert spaces? I have a feeling they are not related, but I may be wrong.

• Given two functions $\vee$ and $\bigvee$, is it possible to define an operator which can "convert" the expansion of $\vee$ into the basis in Hilbert space into the expansion of $\bigvee$ in the same space on 2-sphere and vice versa provided this dilation can be expressed mathemaically with a formula? Thanks, --AboutFace 22 (talk) 18:12, 6 August 2014 (UTC)

I think there is no relation between the notion in operator theory and the physical dilation you describe. As for the other question, if you multiply the function by a number (that is "dilate" it), then the corresponding coefficients in the spherical harmonic expansion will also get multiplied by that number. But I think that's probably not what you're after here. There is a sense in which dilation transforms functions on $R^{n}$ (although not on the sphere) by $f(x)\to f(\lambda x)$. This is also unrelated to the notion in Hilbert spaces. If you're reading a book on special functions, very likely this is the kind of dilation that you're after. Sławomir Biały (talk) 20:10, 6 August 2014 (UTC)

Thank you very much. It what you are saying is correct, then it is a great news. It resolves one of the most serious problems I face. I really appreciate your message. I may have a few more questions concerning some details of what you posted but it will take me a day or two to formulate them. --AboutFace 22 (talk) 21:42, 6 August 2014 (UTC)