(adsbygoogle = window.adsbygoogle || []).push({}); Converting Binomal cpk to a "fair dice" deviation.

Hi,

I would like to detect low probability in a "fair dice" problem being used for graphing of outliers.

The actual data is binned into cells of 1% probability which form a histogram of the dice faces can be drawn. (The original data distribution is not equal probability, however the histogram cell distribution *is*).

I have made the problem equivalent to a histogram of a 100 or 200 faced dice.

eg: there are 100 cells for binning positive only data, or 200 cells for binning signed data.

Now dice are merely a Bernoulli / binomial trial, and I have only two kinds:

100 cell version: n=#diceRolls p=0.010, q=0.990

200 cell version: n=#diceRolls p=0.005, q=0.995

For the 200 cell version, I compute:

μ = np = n(0.005)

σ**2 = n(0.005)(0.995)

But, I am uncertain of a few facts:

1) Does the standard deviation (σ) have a different meaning than the normal distribution? eg: Namely, that not ~68% of data is within 1 sigma of a 100 or 200 sided dice?

2) If the meaning is different, is there a simple formula to convert a { p, q = 50%,50% } binomial's precomputed cdf value into a { p, q = 1%, 99% } cdf probability?

For example: I'd like to compute 'a' for a single cell such that less than 5% of the time would a fair dice be above μ + 'a' samples out of 'n' dice rolls.

I'd also like to compute 'a' boundaries for 1%,0.1%,and 0.01%.

I am able to compute the 'a' value, exactly, even for large n when doing a 2 cell p,q=50%,50% cumulative binomial distribution.

So, I am just wondering if there is an easy way to convert the result of that computation to a 100 or 200 sided dice { p,q=0.01,0.99 } binomial? (eg: that won't cause computer overflow errors.)

Thanks.

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# Converting Binomal cpk to a fair dice deviation.

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