What is the 'Normal Distribution'
The normal distribution, also known as the Gaussian distribution, is a probability distribution that is a symmetric about the mean, showing that data near the mean are more frequent than data far from the mean. Â
BREAKING DOWN 'Normal Distribution'
The normal distribution is the most common type of distribution assumed in technical stock market analysis and in other types of statistical analyses. The standard normal distribution has two parameters: the mean and the standard deviation. For a normal distribution, 68% of the observations are within +Â one standard deviations of the mean, 95% are within + two standard deviations, and 99.7% are within + three standard deviations.
While real data are usually not precisely normally distributed, the normal model is motivated by the Central Limit Theorem, which states that averages calculated from independent identically distributed random variables have approximately normal distributions, regardless of the type of distribution that the variables are sampled from (provided it has finite variance).
Skewness and Kurtosis
Real data rarely if ever come from normal distributions. The skewness and kurtosis coefficients measure how different the real distribution is from a normal distribution. The skewness measures the symmetry of a distribution. The normal distribution is symmetric and has a skewness of zero, as is the case with all symmetric distributions. If the distribution of a data set has a skewness less than zero, the distribution of the data is skewed to the left; positive skewness implies that the distribution is skewed to the right. Asset prices can be modelled using a lognormal distribution, which is skewed to the right because asset prices are nonnegative, and because there are occasional assets with extremely high prices relative to the majority.
The kurtosis statistic measures the tail ends of a distribution in relation to the tails of the normal distribution. The normal distribution has a kurtosis of three, which indicates the distribution has neither fat nor thin tails. Therefore, if observed data have a kurtosis greater than three, the distribution is said to have heavy tails when compared to the normal distribution. If the data have a kurtosis less than three, it is said to have thin tails when compared to the normal distribution.
Stock market returns are often assumed to follow a normal distribution. However, in reality, return distributions tend to have fat tails, and therefore have kurtosis greater than three. Such returns have typically had moves greater than three standard deviations beyond the mean more often than expected under the assumption of a normal distribution.

Tail Risk
A form of portfolio risk that arises when the possibility that ... 
Probability Distribution
A statistical function that describes all the possible values ... 
Leptokurtic
A statistical distribution where there are extreme points(or ... 
Excess Kurtosis
Excess kurtosis describes a probability distribution with fat ... 
Platykurtosis
Platykurtosis is a statistical term that refers to the relative ... 
Platykurtic
A type of statistical distribution where the points along the ...

Trading
Trading with Gaussian models of statistics
The study of statistics originated from Carl Friedrich Gauss and helps us understand markets, prices and probabilities, among other applications. 
Investing
What's Skewness?
Skewness describes how a data distribution leans. 
Investing
Optimize your portfolio using normal distribution
Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk. 
Insights
SKEW Index Suggests a Market Downturn is Possible
The CBOE SKEW Index is at record highs. Does that mean a crash is coming? 
Financial Advisor
How to Save Clients from RMD Aggregation Mistakes
Advisors can help clients avoid required minimum distribution mistakes in their retirement plans. 
Investing
Calculating volatility: A simplified approach
Though most investors use standard deviation to determine volatility, there's an easier and more accurate way of doing it: the historical method. 
Financial Advisor
Stretch Your Savings By Working Into Your 70s
Staying employed a little longer may allow for a more comfortable retirement. 
Investing
Fat Tail Risk Makes Global Warming Scarier
The cost of global warming does not take into account climate changerelated catastrophes. Here's where fattail distributions come in. 
Investing
Expect Big Capital Gains Distributions from These Funds (AGTHX, ACRNX)
The steady rise in the markets since 2009 has led to some outsized gains in a few funds that are finally being realized as longterm winning holdings. 
Retirement
9 PenaltyFree IRA Withdrawals
If you need to take early distributions, find out which exemptions allow you to avoid expensive consequences.

Is my nonqualified Roth IRA distribution subject to taxes or early distribution ...
The ordering rules must be applied to determine whether the distribution is subject to income taxes and/or the early distribution ... Read Answer >>