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

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.