New Approximation Formulas for Tighter Bounds of the Q-Function and its Applications

Chen, Xiao-Diao; Yu, Junle; Ma, Jingfei; Jiang, Nichang

doi:10.1007/s11277-021-08811-7

Cited by 1 publication

(3 citation statements)

References 37 publications

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“…The first one is related to the field of transport phenomena in chemical engineering [29]. The second case is in the field of wireless communications and wireless networks [37].…”

Section: Applications To Sciencementioning

confidence: 99%

“…The integrals in these formulae are the product of the fading probability density function and the Gaussian Q-function. The following is how the integral is represented [37]:…”

Section: Symbol Error Probability (Sep)mentioning

confidence: 99%

“…The design of a function to approximate these functions typically involves a trade-off between accuracy and complexity. Achieving high accuracy often necessitates complex expressions or multi-term polynomials, as evidenced in prior studies [11,12,16,22,23,31,32,33]. Furthermore, today meta-heuristic algorithms are widely used in solving optimization problems with high complexity, if the problem can be implemented as an optimization problem, these algorithms can provide high quality solutions.…”

Section: Introductionmentioning

confidence: 99%

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New Mathematical Approximations for the Cumulative Normal Distribution Function

Etesami,

Madadi,

Keynia

et al. 2024

Preprint

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The normal cumulative distribution function and its derivatives, such as the error function, the Q-function, and the Mills ratio, are widely used in engineering, mathematics, statistics, computer science, diffusion theory, communication theory, physics, and chemistry. However, their non-closed form nature has led to the development of new approximations with varying levels of accuracy and complexity. These new approximations are often more accurate; nevertheless, they can also be more complex, which may limit their practical utility. In this article, a new approach for approximating is proposed. which combines Taylor series expansion and logistic function to create an initial approximation, to enhance the accuracy of the initial approximation, the Hunter-Prey Optimization algorithm is utilized to minimize both the maximum absolute error and the mean absolute error, leading to a significantly more precise approximation. Furthermore, this algorithm is employed to enhance the accuracy of other existing approximations introduced by researchers. The results showed that the improved approximations have much higher accuracy. To show the effectiveness of the new findings of this article, two case studies with applications are presented.

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“…The first one is related to the field of transport phenomena in chemical engineering [29]. The second case is in the field of wireless communications and wireless networks [37].…”

Section: Applications To Sciencementioning

confidence: 99%

“…The integrals in these formulae are the product of the fading probability density function and the Gaussian Q-function. The following is how the integral is represented [37]:…”

Section: Symbol Error Probability (Sep)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New Mathematical Approximations for the Cumulative Normal Distribution Function

Etesami,

Madadi,

Keynia

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

New Approximation Formulas for Tighter Bounds of the Q-Function and its Applications

Cited by 1 publication

References 37 publications

New Mathematical Approximations for the Cumulative Normal Distribution Function

New Mathematical Approximations for the Cumulative Normal Distribution Function

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