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What is a statistical fat tail?
By definition, fat tails are a statistical phenomenon exhibiting large leptokurtosis. This represents a greater likelihood of extreme events occurring similar to the financial crisis. Since the magnitude of fat tails are so difficult to predict, left tail events can have devastating effects on portfolio returns.
Is log-normal fat-tailed?
Relationship to fat-tailed distributions Since such a power is always bounded below by the probability density function of an exponential distribution, fat-tailed distributions are always heavy-tailed. An example is the log-normal distribution.
Which is the best description of a fat tailed distribution?
A fat-tailed distribution is a probability distribution that exhibits a large skewness or kurtosis, relative to that of either a normal distribution or an exponential distribution. In common usage, the term fat-tailed and heavy-tailed are synonymous, different research communities favor one or the other largely for historical reasons.
When does a distribution have a heavy tail?
Hope you enjoy at least one of the three. A heavy tailed distribution has tails that are heavier than an exponential distribution (Bryson, 1974) Distribution is said to have a heavy tail when the tail part decays more slowly than the exponential distribution.
Which is the right tail of the normal distribution?
Unfortunately, there is no single answer. Consider the normal distribution. Note that there are two tails: right and left. If we want to describe the ‘right’ tail of the distribution from the one standard deviation from the mean, for example, then the shaded part refers to the right tail of the normal distribution.
Do you know the definition of fat tail?
Instead, we were taught to use the student-t distribution and log normal distribution when modelling the financial return series to take into account the ‘fat-tail’ property. But we need to know the definition of fat tail. Unfortunately, there is no universal definition for the term fat.