Transcription of The Truncated Normal Distribution
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The Truncated Normal Distribution
The Truncated Normal DistributionJohn BurkardtDepartment of Scientific ComputingFlorida State jburkardt/ October 2014 AbstractThe Normal Distribution is a common model of randomness. Unlike the uniform Distribution , itproposes a most probable value which is also the mean, while other values occur with a probabilitythat decreases in a regular way with distance from the mean. This behavior is mathematically verysatisfying, and has an easily observed correspondence with many physical processes. One drawback ofthe Normal Distribution , however, is that it supplies a positive probability density to every value in therange ( ,+ ), although the actual probability of an extreme event will be very low. In many cases, itis desired to use the Normal Distribution to describe the random variation of a quantity that, for physicalreasons, must be strictly positive.
Note that the standard deviation of any distribution, represented by std(ˆ()), is simply the square root of the variance, so for the standard normal distribution, we also have that std(˚(0;1;)) = 1. 1.3 The Cumulative Distribution Function Recall that any probability density function ˆ(x) can be used to evaluate the probability that a random
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