k and k' values
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Definition
Given a probability, [ilmath]p\in[0,1]\subseteq\mathbb{R} [/ilmath] the corresponding values are:
- [math]k:\eq\frac{-\ln(p) }{\ln(10) } [/math], higher values indicate the event we have the probability for is rarer, eg [ilmath]k\eq 6[/ilmath] is 1 in 1,000,000 (1 million), or [ilmath]p\eq 0.000001[/ilmath]
- [math]k':\eq\frac{-\ln(1-p)}{\ln(10)} [/math], higher values indicate the event we have the probability for is more common, eg [ilmath]k'\eq 6[/ilmath] is 999,999 in 1,000,000, or [ilmath]p\eq 0.999999[/ilmath]
Given a k-value, [ilmath]k\in\mathbb{N}_{\ge 0} [/ilmath] then the corresponding probability is:
- [math]p:\eq 10^{-k} [/math]
Given a k'-value, [ilmath]k'\in\mathbb{N}_{\ge 0} [/ilmath] then the corresponding probability is:
- [math]p:\eq 1-10^{-k} [/math]
Selected examples
| value, [ilmath]v[/ilmath] | [ilmath]v\ \mathbf{k} [/ilmath] (rarity) | [ilmath]v\ \mathbf{k}' [/ilmath] (commonality) | ||
|---|---|---|---|---|
| (As probability) | ||||
| 0 | 1 (certainty) | 0 (impossibility) | ||
| 1 | 0.1 | 1 in 10 | 0.9 | 9 in 10 |
| 2 | 0.01 | 1 in 100 | 0.99 | 99 in 100 |
| 3 | 0.001 | 1 in 1,000 | 0.999 | 999 in 1,000 |
| 4 | 0.0001 | 1 in 10,000 | 0.9999 | 9,999 in 10,000 |
| [ilmath]\vdots[/ilmath] | | |||
| [ilmath]\infty[/ilmath] | 0 (impossibility) | 1 (certainty) | ||
