An approximation to the inverse of left-sided truncated gaussian cumulative normal density function using Polya's model to generate random variates for simulation applications

Istrazivanja i projektovanja za privredu

Hamasha Sa'd¹  Ali Haneen²  Hamasha Mohammad M.³  Ahmed Abdulaziz⁴  Aqlan Faisal⁵ 

[1] Auburn University, Department of Industrial Engineering, Auburn, AL, USA;Auburn University, Health Services Administration Program, Auburn, AL, USA;Hashemite University, Faculty of Engineering, Department of Industrial Engineering, Zarqa, Jordan;University of Alabama at Birmingham, School of Health Professions, Department of Health Services Administration, Birmingham, Alabama, USA;University of Louisville, Industrial Engineering Department, Louisville, KY, USA;

关键词: gaussian distribution;    normal distribution;    random variate generation;    cumulative density function;    mathematical approximation;    truncated normal distribution;   

DOI  :  10.5937/jaes0-35413

来源: DOAJ

【 摘 要 】

The Gaussian or normal distribution is vital in most areas of industrial engineering, including simulation. For example, the inverse of the Gaussian cumulative density function is used in all simulation software (e.g., ARENA, ProModel) to generate a group of random numbers that fit Gaussian distribution. It is also used to estimate the life expectancy of new devices. However, the Gaussian distribution that is truncated from the left side is not defined in any simulation software. Estimation of the expected life of used devices needs left-sided truncated Gaussian distribution. Additionally, very few works examine generating random numbers from left-sided truncated Gaussian distribution. A high accuracy mathematical-based approximation to the left-sided truncated Gaussian cumulative density function is proposed in the current work. Our approximation is built based on Polya's approximation of the Gaussian cumulative density function. The current model is beneficial to approximate the inverse of the left-sided truncated Gaussian cumulative density function to generate random variates, which is necessary for simulation applications.

【 授权许可】

Unknown