On the landmark hybrid computation of the generalized parabolic cylinder function distribution
Ilir F. Progri · Journal of Geolocation Geo-information and Geo-intelligence · 2024
Use in connection with any form of information storage and retrieval, electronic adaptation, computer software or by similar or dissimilar methodology now known or hereafter developed is forbidden.The use of the publication of trade names, trademarks, service marks, or similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.This paper discusses the landmark hybrid computation ii (LHC) of the Generalized Parabolic Cylinder Function (or GPCF) distribution (or GPCFD) cumulative probability distribution function (cdf) that consists of two segments: the inner segment and the outer segment.First, the inner segment consists of the absolute values of the main variable minus a parameter are less than equal to another parameter.Second, the outer segment consists of all the values of the main variable that are outside of the inner segment.Although in the past the computation of the Efficient GPCFD (or EGPCFD) cdf existed for both of these segments; only the outer segment computation was optimized for both speed and accuracy.Third, the LHC of the GPCFD cdf is the currently fastest computation of the GPCFD cdf for the inner segment.Numerical results are derived for the first and second special cases to validate the theoretical models presented in the paper.According to the numerical results the LHC of the GPCFD cdf is several orders of magnitude more accurately and two orders of magnitude faster than any of the previous computations of the EGPCFD cdf.