• Corpus ID: 248571862

Improvements of Polya Upper Bound for Cumulative Standard Normal Distribution and Related Functions

  title={Improvements of Polya Upper Bound for Cumulative Standard Normal Distribution and Related Functions},
  author={Omar M. Eidous},
Although there is an extensive literature on the upper bound for cumulative standard normal distribution Ξ¦(π‘₯) , there are relatively not sharp for all values of the interested argument π‘₯ . The aim of this paper is to establish a sharp upper bound for Ξ¦(π‘₯) , in the sense that its maximum absolute difference from Ξ¦(π‘₯) is less than 5.785 Γ— 10 βˆ’5 for all values of π‘₯ β‰₯ 0 . The established bound improves the well-known Polya upper bound and it can be used as an approximation for Ξ¦(π‘₯) itself… 



Very Simple Tight Bounds on the Q-Function

  • G. Abreu
  • Mathematics
    IEEE Transactions on Communications
  • 2012
New lower and upper bounds on the Gaussian Q-function are presented, unified in a single and simple algebraic expression which contains only two exponential terms with a constant and a rational coefficient, respectively, which are found to be as tight as multi-term alternatives obtained e.g. from the Exponential and Jensen-Cotes families of bounds.

New approximations for standard normal distribution function

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…

New inequalities of Mill's ratio and Its Application to The Inverse Q-function Approximation

This paper investigates the Mill’s ratio estimation and gets two new inequalities and presents a conjecture on the bounds of inverse solution on Q-function and some useful results on the inverse solution.

Inequalities and Bounds for the Incomplete Gamma Function

Inequalities involving the incomplete gamma function are established. They are obtained using logarithmic convexity of some function associated with the function in question. Lower and upper bounds…

Inequalities related to the error function

In this note we consider inequalities involving the error function $\phi$. Our methodes give new proofs of some known inequalities of Komatsu, and of Szarek and Werner, and also produce two families…

Bounding the Error Function

  • R. Iacono
  • Mathematics
    Computing in Science & Engineering
  • 2021
Using an integral representation of the error function of a real argument, two simple and accurate lower bounds are obtained which complement a well-known upper bound given long ago by PΓ³lya.

Probability distributions involving Gaussian random variables : a handbook for engineers and scientists

Basic Definitions and Notation.- Fundamental One-Dimensional Variables.- Fundamental Multidimensional Variables.- Difference of Chi-Square Random Variables.- Sum of Chi-Square Random Variables.-…

Error function inequalities

  • H. Alzer
  • Computer Science
    Adv. Comput. Math.
  • 2010
The inequalities for the error function are presented and one of the theorems states that α β‰₯ 1 is true for all x,y > 0.

New Refinements for the Error Function with Applications in Diffusion Theory

  • G. Bercu
  • Mathematics, Computer Science
  • 2020
These approximations for the error function are provided using the Pade approximation method and the Fourier series method and they are used in diffusion theory.

Bit Error Rate Analysis for Reconfigurable Intelligent Surfaces With Phase Errors

This letter investigates the error probability of reconfigurable intelligent surfaces (RIS)-enabled communication systems with quantized channel phase compensation with Monte Carlo simulations and derives exact and asymptotic bit error rate expressions.