(35S) UTPN Formula

11212014, 05:47 PM
(This post was last modified: 06152017 01:59 PM by Gene.)
Post: #1




(35S) UTPN Formula
For a given Zscore the formula calculates the value of Q, the area under the upper tail of the Normal Distribution.
Best to use values of Z > 0. For a given probability Q the corresponding Zscore is evaluated. Best to use Q < 0.5. Do NOT solve for X. All answers are approximate. UTPN Q = ABS( ( ( ( ( ( 1.330274429 * ( 1 ÷ ( 1 + 0.23164419 * ABS( Z ) ) ► X ) ) ) – 1.821255978 ) * X + 1.781477937 ) * X – 0.35653782 ) * X + 0.31938153 ) * X ÷ ( SQRT( 2 * π ) * EXP( SQ( Z ) ÷ 2 ) ) 

11212014, 08:50 PM
Post: #2




RE: HP 35S: UTPN Formula
(11212014 05:47 PM)Gerald H Wrote: For a given Zscore the formula calculates the value of Q, the area under the upper tail of the Normal Distribution. This implements the well known 1955 approximation from C. Hastings' "Approximations for digital computers", resp. Abramovitz & Stegun 26.2.18. It was also used in various HP software pacs, e.g. for the 41 series. Please let me add three remarks:
So how about your own improved customdesigned approximation ?) Dieter 

11222014, 06:29 AM
Post: #3




RE: HP 35S: UTPN Formula
(11212014 08:50 PM)Dieter Wrote:(11212014 05:47 PM)Gerald H Wrote: For a given Zscore the formula calculates the value of Q, the area under the upper tail of the Normal Distribution. Many thanks for the correction of the erroneous coeffficients. The accuracy of the approximation is really surprisingly good. Sadly my own maths abilities are inferior to the task of producing a formula attaining the same level of simplicity & accuracy. 

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