andysif
andysif
Joined: Aug 8, 2011
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August 18th, 2014 at 10:29:04 PM permalink


Is it possible to calculate the cumulative distribution function with a hand held scientific calculator (obviously without the function built in)?
ChesterDog
ChesterDog
Joined: Jul 26, 2010
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August 19th, 2014 at 5:29:00 AM permalink
Quote: andysif



Is it possible to calculate the cumulative distribution function with a hand held scientific calculator (obviously without the function built in)?



Yes.

Sum the following terms starting at k = 0. The 0th term is the value of x. The kth term is the (k-1)th term times (-1) * x^2 * [2(k-1)+1] / [2 * k * (2*k + 1)]. Stop when the terms are sufficiently small. Then divide the sum by sqrt(2*pi) and add 0.5.

Here's an example for x = 0.6. Term 0 = 0.60000; term 1= -0.03600; term 2 = 0.00194; term 3 = -0.00008; term 4 = 0.00000. Sum = 0.56586. CDF(0.6) = 0.56586/sqrt(2*pi) + 0.50000 = 0.72575.

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