Abstract:
In this paper, two very high accurate models to approximate the lower truncated normal cumulative distribution have been developed. Mill's ratio with an order of2 1 and is used to develop two models to approximate the density of normal cumulative distribution, and then these two models are modified to approximate the density of the lower truncated normal cumulative distribution. The first model (i.e., order of 1) was very simple and very accurate with maximum absolute error of about 0.0015 over the domain [ZL :∞] . ZL is the truncation point and it takes any value from negative infinity to zero (i.e., ZL ∈ [-∞:0]). The second model (i.e., order of 2) is more advanced and can provide a superior accuracy of a maximum absolute error of less than 0.00004. Particularly, the first model can be used whenever an industrial engineer/practitioner needs to estimate probabilities and statistics associated with the lower truncated normal distribution due to its simplicity and accuracy. Further, we strongly recommend using the first model in the case of manual solutions. Although the second model provides superior accurate results, it is complicated and hard to be used manually.
Page(s):
369-382
DOI:
DOI not available
Published:
Journal: Pakistan Journal of Statistics, Volume: 33, Issue: 5, Year: 2017
Keywords:
Normal Cumulative Distribution
,
Normal Distribution
,
Mills Ratio
,
Truncated