What is the 'Normal Distribution'
The normal distribution, also known as the Gaussian or standard normal distribution, is the probability distribution that plots all of its values in a symmetrical fashion, and most of the results are situated around the probability's mean. Values are equally likely to plot either above or below the mean. Grouping takes place at values close to the mean and then tails off symmetrically away from the mean.
BREAKING DOWN 'Normal Distribution'
The normal distribution is the most common type of distribution and is often found in stock market analysis. Given enough observations within a sample size, it is reasonable to make the assumption that returns follow a normally distributed pattern, but this assumption can be disproved.As with any distribution, the distribution's mean, skewness and kurtosis coefficients should be calculated to determine the type of distribution. The standard normal distribution has two parameters: the mean and the standard deviation. In the Gaussian distribution, the mean, or mu, is equal to zero, while the standard deviation, or sigma, is equal to one. Under normal circumstances, independent identically distributed random variables, or outcomes, are said to converge to a standard normal distribution under the central limit theorem.
Skewness and Kurtosis
The skewness measures the symmetry of a distribution. The standard normal distribution has a skewness of zero, and therefore, it is said to be symmetric. If the distribution of a data set has a skewness less than zero, the data is skewed to the left. Conversely, data that has a positive skewness is said to be skewed to the right. For example, asset prices follow a lognormal distribution, which is skewed to the right because asset prices are nonnegative.
The kurtosis measures the tail ends of a distribution and whether the distribution of a data set has skinny tails or fat tails in relation to the normal distribution. The standard normal distribution has a kurtosis of three, which indicates data that follow a Gaussian distribution have neither fat or thin tails. Therefore, if observed data have a kurtosis greater than three, it 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.
For example, stock market returns are said to follow a normal distribution in theory. However, in reality, asset returns tend to have fat tails. Observed asset returns have typically had moves greater than three standard deviations beyond the mean more than expected under the assumptions of the normal distribution.

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Kurtosis
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Probability Distribution
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Mesokurtic
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Symmetrical Distribution
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Leptokurtic
A statistical distribution where the points along the Xaxis ...

Investing
What a Normal Distribution Means
Normal distribution describes a symmetrical data distribution, where most of the results lie near the mean. 
Trading
Trading With Gaussian Models Of Statistics
The entire study of statistics originated from Gauss and allowed us to understand markets, prices and probabilities, among other applications. 
Investing
Find The Right Fit With Probability Distributions
Discover a few of the most popular probability distributions and how to calculate them. 
Trading
What's Skewness?
Skewness describes how a data distribution leans. 
ETFs & Mutual Funds
Stock Market Risk: Wagging The Tails
The bell curve is an excellent way to evaluate stock market risk over the long term. 
Managing Wealth
Using Normal Distribution Formula To Optimize Your Portfolio
Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk. 
Managing Wealth
The Uses And Limits Of Volatility
Check out how the assumptions of theoretical risk models compare to actual market performance. 
Investing
Quantitative Analysis Of Hedge Funds
Hedge fund analysis requires more than just the metrics used to analyze mutual funds. 
Markets
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. 
Trading
A Simplified Approach To Calculating Volatility
Though most investors use standard deviation to determine volatility, there's an easier and more accurate way of doing it.

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