STATS 151 | Normal Probability Distributions |

NORMAL DISTRIBUTION • A normal distribution is usually the proper term for a probability bell curve. • In a normal distribution the mean is usually zero and the standard deviation is usually1. It has zero skew and also a kurtosis of 3. • Normal distributions are symmetrical, though not all symmetrical distributions are normal. • Most pricing distributions are not perfectly normal. Understanding normal distribution • The normal distribution is the most common type of distribution which is assumed in technical stock market analysis and also in other types of statistical analyses. • The standard normal distribution has two parameters which are the mean and the standard deviation. In a normal distribution, 68% of the observations are within +/- one standard deviation of the mean, 95% are within +/- two standard deviations, and again 99.7% are within +- three standard deviations. • The normal distribution model is usually motivated by the central limit theorem. This theory states that averages which are calculated from independent, identically distributed random variables they have approximately normal distributions, regardless of the type of distribution from where the variables are sampled. Skewness and Kurtosis • The skewness and kurtosis coefficients measure how different is a given distribution from a normal distribution. The skewness measures the symmetry of a distr...

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