A uniform approximation to the right normal tail integral

DOI10.1016/S0096-3003(01)00015-7zbMath1023.65015OpenAlexW2157364645WikidataQ127395611 ScholiaQ127395611MaRDI QIDQ1855650

Wlodzimierz Bryc

Publication date: 28 January 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0096-3003(01)00015-7

zbMATH Keywords

Mill's ratioprobability integralcalculator approximationcumulative normal distributionstandard normal tail probabilities

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Computation of special functions and constants, construction of tables (65D20) Numerical approximation and evaluation of special functions (33F05) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20)

Related Items (11)

Piecewise linear lower and upper bounds for the standard normal first order loss function ⋮ Double precision rational approximation algorithm for the inverse standard normal second order loss function ⋮ The computation of standard normal distribution integral in any required precision based on reliability method ⋮ New approximations for standard normal distribution function ⋮ Tail Probability Ratios of Normal and Student’stDistributions ⋮ Approximating Mills ratio ⋮ A sharp Pólya-based approximation to the normal cumulative distribution function ⋮ Double precision rational approximation algorithm for the inverse standard normal first order loss function ⋮ Some new approximations and proofs for Mills' ratio ⋮ Double precision rational approximation algorithms for the standard normal first and second order loss functions ⋮ A Fairly Accurate Approximation to the Area Under Normal Curve

Cites Work

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• Calculation of univariate and bivariate normal probability functions
• On Laplace continued fraction for the normal integral
• A sigmoid approximation of the standard normal integral
• An invertible approximation to the normal distribution function
• A Formula for the Approximation of Definite Integrals of the Normal Distribution Function
• Yet another series for the normal integral
• On the Calculation of the Inverse of the Error Function.
• A Close Approximation Related to the Error Function
• INEQUALITIES FOR THE NORMAL INTEGRAL INCLUDING A NEW CONTINUED FRACTION

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