Fix moving function linear weighted avg

[Quentin18]

Closes #113751

There is a problem in the MovingFunctions.linearWeightedAvg method. The totalWeight is initialized to 1 whereas it should be initialized to 0.

In the issue example, the raw values are:

• 15.3984375
• 15.3984375
• 15.703125

Actually, the Linear Weighted Moving Average (LWMA) is calculated as follows:

$$ LWMA=\frac{\sum v_i\times w_i}{1+\sum w_i} $$

Where $v=\{15.3984375, 15.3984375, 15.703125\}$ and $w=\{1, 2, 3\}$. The extra 1 in the denominator is due to the wrong initialization. In the example:

$$ LWMA=\frac{15.3984375\times 1+15.3984375\times 2+15.703125\times 3}{1+1+2+3}=13.329241071 $$

The LWMA formula should be:

$$ LWMA=\frac{\sum v_i\times w_i}{\sum w_i} $$

In the example:

$$ LWMA=\frac{15.3984375\times 1+15.3984375\times 2+15.703125\times 3}{1+2+3}=15.55078125 $$

[elasticsearchmachine]

Pinging @elastic/es-analytical-engine (Team:Analytics)

[nik9000]

@elasticmcahine, test this please.

[nik9000]

Thanks @Quentin18! I've kicked this off with the robots and will get back to you. I imagine there might be a test failure, but the robots will find it.

[iverase]

@elasticmachine, test this please.

[nik9000]

Community PR needs a changelog YAML file at docs/changelog/118516.yaml

Looks like I do that myself.

[nik9000]

@elasticsearchmachine, test this please

[john-wagster]

@elasticmachine test this please

[nik9000]

I've pushed a few test fixes that ought to make the robots happy. It's an integration test, and it's forwards and backwards compatibility form.

@elasticsearchmachine, test this please.

[nik9000]

@elasticmachine test this please

[nik9000]

I have a spelling problem calling the right robot....

[nik9000]

@elasticmachine test this please

I had to merge main in. Again. BWC tests were sad.

[nik9000]

Ok robot, are you going to make backport commits or should I?

[elasticsearchmachine]

💔 Backport failed

Status	Branch	Result
❌	8.17	Commit could not be cherrypicked due to conflicts
❌	8.x	Commit could not be cherrypicked due to conflicts
❌	7.17	Commit could not be cherrypicked due to conflicts

You can use sqren/backport to manually backport by running backport --upstream elastic/elasticsearch --pr 118516

[nik9000]

💔 Backport failed

Ok robot. Monday, monday.

[iverase]

@nik9000 I will take care of the backports

[nik9000]

@nik9000 I will take care of the backports

Thanks @iverase !