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.

  • $\begingroup$ 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

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}


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