HP Forum Archive 17

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Area under normal curve Message #1 Posted by Paul Guertin on 2 June 2007, 10:32 a.m. I wonder who decided that hyperbolic functions and their inverses would be standard on basic scientific pocket calculators (not only HP but other brands, too), but Q and Q^-1 (area under the normal curve and its inverse function) would appear on only a few select models. Shouldn't they be considered basic, useful and common functions?

Re: Area under normal curve Message #2 Posted by Namir on 2 June 2007, 12:02 p.m., in response to message #1 by Paul Guertin I agree. The Student-t probability distribution function and its inverse should also be included. Together withe the inverse normal, the inverse Student-t are used to calculate confidence interval. Of couse including the Chi-square and F distributions makes the set complete.

Re: Area under normal curve Message #3 Posted by Les Wright on 3 June 2007, 2:29 a.m., in response to message #2 by Namir I have written 41C routines, also readily usable on the 42S, that compute the incomplete gamma and incomplete beta functions using series or continued fraction expansions, as appropriate. In the case of the continued fraction calculations, I use the Modified Lentz algorithm as spelled out in Numerical Recipes--seems to be faster and converges more reliably than the familiar 300-year-old Wallis method. The error function and cumulative normal and chi-square distributions are special cases of the incomplete gamma function. The t and F distributions are special cases of the incomplete beta function. I would hope that if the processor is fast as in the 33s and the programming paradigm is flexible enough it will be easy to adapt these routine to the 35s. The inverse normal and t distributions can be found using the corresponding cumulative distributions and the Solver. I have a routine for the 33s that computes the cumulative normal distribution fairly quickly (it is a direct routine that is not mediated through the incomplete gamma function), and I can use the Solver to find z scores associated with given percentiles fairly quickly--a few seconds at most in the typical case. Les

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