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Normal Distribution
Message posted by Paul on November 29, 1999 at 12:00 AM (ET)
If variable X is normally distributed, x ranges from -infinity to +infinity. However, in most of the statistics example problems I have seen, x can not be negative. Nonetheless, the normal distribution is assumed. If I want to calculate a probability from Z=(X-mu)/sigma, Z can never be less than -mu/sigma. For example, if Zmin= -2, then there is a 2.28% probability that X<0, even though X cannot be negative.
I want to rank Z’s from different sets of data. Each set has its own Zmin. How do I account for (adjust for) the distortion in the statistics caused by the constraint on Z.
READERS RESPOND:
(In chronological order. Most recent at the bottom.)
Re: Normal Distribution
Message posted by JG on November 30, 1999 at 12:00 AM (ET)
Usually the assumption of normality is only an approximation so that cutting of a piece of the lower tail in not serious. We call this a truncated normal.
Re: Normal Distribution
Message posted by Paul on December 1, 1999 at 12:00 AM (ET)
How much of the tail can I cut without invalidating the statistics? What Is the relationship between Zmin and the confidence level of the statistics?
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