Question about use of term "Expected value of x" (E[x]

Hello Everybody,


My question concerns not the algebra per se but rather use of the expression "Expected value of x" (and the symbol: E[x]) which I understand (from Wikipedia) is mostly used in statistics (so I post it here). I hope someone can tell me whether I can use it for the next value of a moving average. Let's say the following is a 3-month moving average:


(M1+M2+M3)/3


Example: (5+6+1)/3=4.


Now, let's say that for some reason we want the value of the overall average in the next round to equal (say) 8, or:


(6+1+x)/3=8


We can then calculate what the next value in the series must be:


6+1+x=3*8
7+x=24
x=24-7
x=17


Checking:


(6+1+17)/3=?
24/3=8


My question is this: Can I use the expression E[x] (expected value of x) to refer to the next value of the data series? If not, what expression should I use and how should I write it?


Many thanks.


Charles

CharlesW said:

Hello Everybody,


My question concerns not the algebra per se but rather use of the expression "Expected value of x" (and the symbol: E[x]) which I understand (from Wikipedia) is mostly used in statistics (so I post it here). I hope someone can tell me whether I can use it for the next value of a moving average. Let's say the following is a 3-month moving average:


(M1+M2+M3)/3


Example: (5+6+1)/3=4.


Now, let's say that for some reason we want the value of the overall average in the next round to equal (say) 8, or:


(6+1+x)/3=8


We can then calculate what the next value in the series must be:


6+1+x=3*8
7+x=24
x=24-7
x=17


Checking:


(6+1+17)/3=?
24/3=8


My question is this: Can I use the expression E[x] (expected value of x) to refer to the next value of the data series? If not, what expression should I use and how should I write it?


Many thanks.


Charles

Click to expand...

Short answer: Expected Value [note the caps] is a precise term as defined in statistics and shouldn't be used here.

Longer, possibly irrelevant answer: In statistics, trying to find relationships between variables falls under a broad category of regression analysis. What it appears to me that you are talking about is more a predictor or tracker formula which might fall under the same general broad umbrella.

Actually, I would put what you have under a class of alpha-beta trackers which, in the simple case, can be defined as
\(\displaystyle \overline{x}_{i+1}\, =\, \alpha\, x_{i}\, + \beta\, x_{i-1}\, ;\,\, \alpha+\beta\, =\, 1\)
where \(\displaystyle \overline{x}\) is a predictor for \(\displaystyle x\).

The number of coefficients [the \(\displaystyle \alpha\) and \(\displaystyle \beta\)] can be extended. In fact, one way of looking at a way of extending the number of coefficients "to infinity" is the exponential smoother
\(\displaystyle \overline{x}_{i+1}\, =\, \alpha\, x_{i}\, + \beta\, \overline{x}_{i}\, ;\,\, \alpha+\beta\, =\, 1\)
which allows all past events to influence the prediction of the future event albeit with less and less influence on the prediction the farther it is in the past.

Ishuda said:

In statistics, trying to find relationships between variables falls under a broad category of regression analysis. What it appears to me that you are talking about is more a predictor or tracker formula which might fall under the same general broad umbrella. However, Expected Value [note the caps] is a precise term as defined in statistics and shouldn't be used here.

Actually, I would put what you have under a class of alpha-beta trackers which, in the simple case, can be defined as
\(\displaystyle \overline{x}_{i+1}\, =\, \alpha\, x_{i}\, + \beta\, x_{i-1}\, ;\,\, \alpha+\beta\, =\, 1\)
where \(\displaystyle \overline{x}\) is a predictor for \(\displaystyle x\).

The number of coefficients [the \(\displaystyle \alpha\) and \(\displaystyle \beta\)] can be extended. In fact, one way of looking at a way of extending the number of coefficients "to infinity" is the exponential smoother
\(\displaystyle \overline{x}_{i+1}\, =\, \alpha\, x_{i}\, + \beta\, \overline{x}_{i}\, ;\,\, \alpha+\beta\, =\, 1\)
which allows all past events to influence the prediction of the future event albeit with less and less influence on the prediction the farther it is in the past.

Click to expand...

So, I understand that I absolutely must not use "E[x]"?

Then, could I use a symbol like: "Px" or "P[x]" for "predicted value of x" perhaps?

Or, what would you suggest?

Thanks,

Charles

CharlesW said:

So, I understand that I absolutely must not use "E[x]"?

Then, could I use a symbol like: "Px" or "P[x]" for "predicted value of x" perhaps?

Or, what would you suggest?

Thanks,

Charles

Click to expand...

If what you are writing would be seen a lot in the statistics community, you might want to use something different than E[x]. However, you could use anything you would like, even E[x], just don't call it an Expected Value [again, note the caps].

Ishuda said:

If what you are writing would be seen a lot in the statistics community, you might want to use something different than E[x]. However, you could use anything you would like, even E[x], just don't call it an Expected Value [again, note the caps].

Click to expand...

Many thanks.

Okay then, I will call it the "projected value" and use "P[x]" as the symbol. This way, it won't be confused with E[x] in statistics.

Thanks again,

Charles