# Accurate RMM-Based Approximations for the CDF of the Normal Distribution

```@article{Shore2005AccurateRA,
title={Accurate RMM-Based Approximations for the CDF of the Normal Distribution},
author={Haim Shore},
journal={Communications in Statistics - Theory and Methods},
year={2005},
volume={34},
pages={507 - 513}
}```
• H. Shore
• Published 1 March 2005
• Physics
• Communications in Statistics - Theory and Methods
Abstract A variation of the RMM error distribution, used to model the exponential distribution, has recently been applied to derive a three-parameter approximation for the standard normal CDF, with a maximum absolute error of order (10)−5. In this short communication, a simple modification enhances the accuracy to the order of (10)−6. Another RMM-based approximation, based on the original RMM error distribution, achieves an absolute maximum error of (10)−7. The simplicity of the new non…
A Sharp Polya-Based Approximation to the Normal CDF
• Mathematics, Computer Science
• 2016
We introduce a closed form approximation to the cumulative distribution function of the standard normal variable involving only five explicit constants with an approximation error of 5.79 x 10^{-6}
New approximations for standard normal distribution function
• Mathematics
Communications in Statistics - Theory and Methods
• 2019
Abstract This article proposes nine new approximations for the standard normal cumulative distribution function In addition, it collects most of the approximations existing in the literature. The
A Simple Approximation to the Area Under Standard Normal Curve
Of all statistical distributions, the standard normal is perhaps the most popular and widely used. Its use often involves computing the area under its probability curve. Unlike many other statistical
APPROXIMATIONS TO THE NORMAL DISTRIBUTION FUNCTION AND AN EXTENDED TABLE FOR THE MEAN RANGE OF THE NORMAL VARIABLES
• Mathematics
• 2008
This article presents a formula and a series for approx¬imating the normal distribution function. Over the whole range of the normal variable z, the proposed formula has the greatest absolute error
Very simply explicitly invertible approximations of normal cumulative and normal quantile function
• Mathematics
• 2014
For the normal cumulative distribution function: Φ(x) we give the new approximation 2**(-22**(1-41**(x/10))) for any x>0, which is very simple (with only integer constants and operations and / and
Response modeling methodology
This overview of response modeling methodology details the motivation that led to the development of RMM, explains RMM core concepts, and introduces RMM basic model and variations.
Profit Maximizing Warranty Period with Sales Expressed by a Demand Function
• Mathematics
Qual. Reliab. Eng. Int.
• 2007
The problem of determining the optimal warranty period, assumed to coincide with the manufacturer's lower specification limit for the lifetime of the product, is addressed and a general solution is derived using Response Modeling Methodology (RMM) and a new approximation for the standard normal cumulative distribution function.
Approximations to the Normal Probability Distribution Function using Operators of Continuous-valued Logic
• Computer Science, Mathematics
Acta Cybern.
• 2018
It is demonstrated here that application of the averaging Dombi conjunction operator to two symmetric Sigmoid fuzzy membership functions results in a function that is identical with Tocher’s approximation to the standard normal probability distribution function.
Sample-Size Determination
Sample data may be collected with different objectives in different scenarios. In some cases, one may wish to collect enough observations that would guarantee minimal prespecified reliability for the
A Fairly Accurate Approximation to the Area Under Normal Curve
• Mathematics
Commun. Stat. Simul. Comput.
• 2009
A new approximation to the cumulative distribution function of standard normal distribution is presented that outperforms other such approximations available in literature and is fairly accurate with minimum accuracy of seven decimal digits.