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Note again that you can enter the standard deviation and achieve the 84% or 16%. The second screenshot below shows how the NORMDIST and the NORMINV functions work. The numbers in the box show that when you either add one standard deviation to the mean AND deduct one standard deviation from the mean, you achieve the famous 68% probability number. The screen shot below shows various ways the normal distribution can be used.
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In this case, when you multiply the (RAND()-.5) by the volatility, you can use the volatility to estimate the probability of being above or below a level.Ī couple of files with some general exercise on working with the normal distribution are available for download below.
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In the case of a constant distribution, you can simply use the formula (RAND()-.5) instead of the NORMSINV() in the time series equation. Three alternative distributions illustrated below include a (1) a simple distribution with constant probabilities across the range (2) the normal distribution (3) a log-normal distribution and, (4) alternative distributions that can be created from the Weiblull distribution. When other distributions are used, the volatility does not have the same meaning. The reason for use of the normal distribution is that the volatility comes from standard deviation and can be used to create probability distributions. Alternative distributions allow you to assess risk in different ways and do things like including skewed distributions and fat-tailed distributions.
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