Analytic error function and numeric inverse obtained by geometric means

Autor:	Martila, Dmitri, Groote, Stefan
Rok vydání:	2023
Předmět:	Physics - Data Analysis Statistics and Probability 62E15 62E17 60E15 26D15
Zdroj:	Stats 2023, 6(1), 431-437
Druh dokumentu:	Working Paper
DOI:	10.3390/stats6010026
Popis:	Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same geometric means finally help to systematically derive handy formulas that approximate the inverse error function. Our approach can be used for applications in e.g.\ high-speed Monte Carlo simulations where this function is used extensively. Comment: 10 pages, 2 figures, 2 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.12639 Zobrazit plný text záznamu View this record from Arxiv