A Mathematical Approximation of the Left-sided Truncated Normal Distribution Using the Cadwell Approximation Model

  • M. M. Hamasha Department of Engineering Management, Prince Sultan University, Saudi Arabia
Keywords: truncated normal distribution, normal distribution, mathematical approximation


In the case that life distribution of new devices follows the normal distribution, the life distribution of the same brand used devices follows left-sided truncated normal distribution. In spite of many mathematical models being available to approximate the normal distribution density functions, there is a few work available on modeling/approximating the density functions of left-sided truncated normal distribution. This article introduces a high accuracy mathematical model to approximate the cumulative density function of left-sided truncated standard normal distribution defined on the range of [truncation point (ZL): ∞]. The introduced model is derived from the Cadwell approximation of the normal cumulative density. The accuracy level change with Z score is discussed in details. The maximum deviation of the model results, from the real results for the whole region of [-∞<Z<-2:∞], is 0.006877.


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