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0

$begingroup$

Let's say you have a balance which changes by $Delta$, where the change is net of an increase less a decrease i.e. $Delta := uparrow - downarrow$. Both the increase and decrease are caused by 2 components: A and B

$ uparrow:= uparrow^A + uparrow^B$ and similarly,

$ downarrow:= downarrow^A + downarrow^B$

Clearly

How do I create a metric $hatDelta^A$ (which is supposed to represent the proportion of the total change that is attributable to A) such that:

1. $hatDelta^A + hatDelta^B = 1$ (propotions add to 1)



2. 
   

   For $k in A,B$, we have:

   
   
   

   (a) $0 leq hatDelta^k leq 1$ (proportions are not greater than 1 or negative)

   
   
   

   (b) $If Delta^k = Delta implies hatDelta^k = 1$ (If the change attributable to $k$ is the same as the total change, then $k$ is responsible for the total change.

   
   

metric-spaces

share|cite|improve this question

asked 17 hours ago

Vykta WakandigaraVykta Wakandigara

11

$endgroup$

add a comment | 

0

$begingroup$

Let's say you have a balance which changes by $Delta$, where the change is net of an increase less a decrease i.e. $Delta := uparrow - downarrow$. Both the increase and decrease are caused by 2 components: A and B

$ uparrow:= uparrow^A + uparrow^B$ and similarly,

$ downarrow:= downarrow^A + downarrow^B$

Clearly

How do I create a metric $hatDelta^A$ (which is supposed to represent the proportion of the total change that is attributable to A) such that:

1. $hatDelta^A + hatDelta^B = 1$ (propotions add to 1)



2. 
   

   For $k in A,B$, we have:

   
   
   

   (a) $0 leq hatDelta^k leq 1$ (proportions are not greater than 1 or negative)

   
   
   

   (b) $If Delta^k = Delta implies hatDelta^k = 1$ (If the change attributable to $k$ is the same as the total change, then $k$ is responsible for the total change.

   
   

metric-spaces

share|cite|improve this question

asked 17 hours ago

Vykta WakandigaraVykta Wakandigara

11

$endgroup$

add a comment | 

$begingroup$

Let's say you have a balance which changes by $Delta$, where the change is net of an increase less a decrease i.e. $Delta := uparrow - downarrow$. Both the increase and decrease are caused by 2 components: A and B

$ uparrow:= uparrow^A + uparrow^B$ and similarly,

$ downarrow:= downarrow^A + downarrow^B$

Clearly

How do I create a metric $hatDelta^A$ (which is supposed to represent the proportion of the total change that is attributable to A) such that:

1. $hatDelta^A + hatDelta^B = 1$ (propotions add to 1)



2. 
   

   For $k in A,B$, we have:

   
   
   

   (a) $0 leq hatDelta^k leq 1$ (proportions are not greater than 1 or negative)

   
   
   

   (b) $If Delta^k = Delta implies hatDelta^k = 1$ (If the change attributable to $k$ is the same as the total change, then $k$ is responsible for the total change.

   
   

metric-spaces

share|cite|improve this question

asked 17 hours ago

Vykta WakandigaraVykta Wakandigara

11

$endgroup$

share|cite|improve this question

asked 17 hours ago

Vykta WakandigaraVykta Wakandigara

11

share|cite|improve this question

asked 17 hours ago

Vykta WakandigaraVykta Wakandigara

11

asked 17 hours ago

Vykta WakandigaraVykta Wakandigara

11

asked 17 hours ago

Vykta WakandigaraVykta Wakandigara

11