0
$\begingroup$

Does this formula (or a piece of it) have a name?

$$P = W \times \left[1 - (1-x_1)(1-x_2) \ldots (1-x_n) \right]$$

where $x_i$ are scores between 0 and 1. $W$ is a weight (so not really relevant I suppose).

It is used in an application to combine weighted scores. The documentation doesn't define it beyond writing it out. I'm curious if it's a standard calculation.

$\endgroup$
  • $\begingroup$ It looks a bit like a probability calculation, but if it is, it wouldn't have a standard name of which I am aware. $\endgroup$ – Adrian Keister Apr 26 '18 at 14:51
  • $\begingroup$ Please state what the $x_i,P $ are. Please give reference to the textbook $\endgroup$ – Narasimham Apr 26 '18 at 23:17
1
$\begingroup$

This is inclusion-exclusion in disguise.

\begin{align} 1 - &(1-x_1)(1-x_2) \cdots (1-x_n) \\ {}={} &1-1 \\ &+ [x_1 + x_2 + \cdots + x_2] \\ &- [x_1(x_2 + \cdots + x_n) + x_2(x_3 + \cdots x_n) + \cdots x_{n-1}x_n] \\ &+ [\text{sum of products of distinct $x_i$, taken three at a time}] \\ &- [\text{sum of products of distinct $x_i$, taken four at a time}] \\ &\vdots \\ &\pm x_1 x_2 \cdots x_n \end{align}

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.