(35S) Statistical Distributions Functions

11152015, 09:26 PM
(This post was last modified: 11172015 09:29 PM by Dieter.)
Post: #54




RE: HP 35s Statistical Distributions Functions
(11152015 03:04 PM)PedroLeiva Wrote: Much I would like to try the Fisher F function with the emulator (* .EP), please also send me the instructions for the incoming and outgoing data. I have attached a zip file that contains both the emulator .ep file and a PDF with instructions for Student's t distribution. The four distributions (XEQ N, S, C and F) are handled much the same, so instructions for one of them should do. Only the two asymmetric distributions (Chi² and F) of course do not return the twosided symmetric integrals A(x) resp. B(x) = 1–A(x). EDIT: the original attachment has been removed, please see note at the end of this post. The programs run either in cdf mode (flag 1 clear) or in quantile mode (flag 1 set). In cdf mode, various cumulative distribution functions and the density function are calculated and returned on the stack and in registers A...D. In quantile mode, the value of the random variable is determined for which the (lower tail) cdf equals the entered probability ("inverse cdf"). The quantile functions use Halley's method for the Chi² and Student case and a very effective extrapolation scheme due to Abramovitz & Stegun for the Normal distribution. The Fisher quantile is handled by a simple Newton iteration, it is intended for both degress of freedom larger than 2. Here and there the iteration may diverge, some code has been added to handle this, so you may also try 1 or 2 degrees of freedom, but this may require some time until the iteration converges. Please note: all this is experimental code! The programs may, and probably will, contain any arror you can imagine, and even those you can't. ;) So try this and see what you get. In the meantime I am waiting for your error reports. Some remarks:
Finally, here is a test case for the Fisher distribution: For 10 and 15 degrees of freedom, determine the probability for an Fvalue of 2,7. Code: Just to be sure, clear flag 1: For a twosided Ftest, find the critial Fvalues for a significance level of 5%. This means we are looking for the two Fvalues that yield a probability of 0,05/2 resp. 1–0,05/2. Code: Set quantile mode: Now try and see what you get. I am waiting for your error reports and other suggestions. ;) Dieter EDIT and WARNING: this post originally contained an attachment with an emulator file (.ep) and instructions for Student's t distribution. However, there were a few errors in the program that now have been corrected. Please see post #59 below for the latest version along with a complete set of instructions. Please do not use older program versions before Nov 17, 2015. 

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