Best (and Newest?) Approximations for Popular Inverse Distributions

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(03-15-2019 12:48 PM)Namir Wrote:  … I am looking for the best (and I assume newest) approximations for the Inverse Normal … distribution … I am looking for better approximations that the ones appearing the HP 65/65 Stat Pacs ….Namir

You may find An Approximation to the Probability Normal Distribution and its Inverse, Una aproximación a la distribución de probabilidad normal y su inversa, Alamilla-López Jorge Luis, Instituto Mexicano del Petróleo, Dirección de Investigación en Transformación de Hidrocarburos (MAR 2015), useful.

Abstract
Mathematical functions are used to compute Normal probabilities, which absolute errors are small; however their large relative errors make them unsuitable to compute structural failure probabilities or to compute the menace curves of natural hazards. In this work new mathematical functions are proposed to compute Normal probabilities and their inverses in an easy and accurate way. These functions are valid over a wide range of random variable and are useful in applications where computational speed and efficiency are required. In addition, these functions have the advantage that the numerical correspondence between the random value Χ = x and its Normal probability Φ (-x) is bijective.

BEST!
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