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

#### Abstract

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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