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I'm writing a report and I need to use an equation to represent a relationship in the Methodology section.

Here's how it works:

  • Everything in between 3 and 8 is between 0% and 100%
  • Everything below the number 3 is 100%
  • Everything above the number 8 is 0%

For example, the number 2.9 is 100%, 3.5 is 90%, 4.8 is 64%, 8.05 is 0% etc.

How do I express this with an equation?

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ObiHill
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1 Answers1

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This reminds me of a multinomial distribution. Here's one possibility. Say your data is $$ X=\left\{ \begin{array}{cc} x_1 & \textrm{with probability p_1}\\ x_2 & \textrm{with probability p_2} \\ \vdots & \vdots \\ x_n & \textrm{with probability p_n} \end{array} \right. $$ Then one possible way to express this as an equation is $$ P(X=x_1)=\prod_{i=1}^n(p_i)^{I[X=x_i]} $$ where $I$ is the indicator function which equals one if the event is true and zero otherwise.

user103828
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  • Thanks. I can put this in a conditional script, but have no idea how to express it mathematically [almost total noob]. Does this adequately capture the range/scale i.e. everything between 3 and 8 is between 0% and 100%? – ObiHill Feb 01 '15 at 19:03
  • I need to have more information about the problem... for example, why do you need to put it in an equation instead of just graphing it, I don't exactly understand what the numbers mean (it looks like some cdf). – user103828 Feb 01 '15 at 19:14
  • What happens is that I have about 3000 numbers (obtained from an unrelated operation). These numbers vary significantly, but when they are evaluated with the above scale, they are somewhat normalized to 0, 100, and everything in between. Is there a way to represent a series of conditional statements (like those I listed in the question above) in a single expression? If not, I'll have to skip math and just use step-by-step bullet points or something. – ObiHill Feb 02 '15 at 04:12
  • If you want a single expression then the expression I have is the only way I know how... if you want to just present it to other people or in a paper then I would recommend either a graph (e.g. histogram) or if you want the exact numbers then as $x_i$ with probability $p_i$ (basically a step-by-step). – user103828 Feb 02 '15 at 06:53
  • Thanks. Being that the report's audience might not be math-savvy, I might just have to use a step-by-step description instead. Longer than I would want, but easier to understand, I reckon. Cheers. – ObiHill Feb 02 '15 at 19:39