Questions tagged [distribution-tails]

This tag is for questions relating to "tail-distribution" which essentially means how much probability is distributed over the largest values(usually) of the random variable.

The tail behavior of a probability distribution is known to be closely related to the behavior of the characteristic function of the distribution in the neighborhood of the origin.

A distribution may be viewed as 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 terms fat-tailed and heavy-tailed are sometimes synonymous; fat-tailed is sometimes also defined as a subset of heavy-tailed. - if it assigns smaller probabilities for larger values of the variable, or heavy tailed - if it assigns larger probabilities for larger values of the variable.
Again 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 terms fat-tailed and heavy-tailed are sometimes synonymous; fat-tailed is sometimes also defined as a subset of heavy-tailed.

For more about this you can see the following (also the references therein):

https://en.wikipedia.org/wiki/Heavy-tailed_distribution

https://en.wikipedia.org/wiki/Long_tail

https://en.wikipedia.org/wiki/Fat-tailed_distribution

231 questions
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Is there a tail bound for the sum of Bernoulli RVs where $\Pr[X_i = 1]$ is a decreasing function of $X_1, \dots, X_{i - 1}$?

Suppose I have a sequence $X_1, \dots, X_n$ of Bernoulli RVs with the property that for all $i = 1, \dots, n$, the function $$f(x_1, \dots, x_{i - 1}) := \Pr[X_i = 1 \mid X_1 = x_1, \dots, X_{i - 1} = x_{i - 1}]$$ is (non-strictly) decreasing. Is…
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Counter example to heavy/light tailed and mean excess loss

In a course we have been given the following proposition: For a random variable $X\geq0$ with essup$(X)=\infty$ i) $F$ is heavy tailed if $\lim_{u\rightarrow\infty}e_F(u)=\infty $ ii) $F$ is light-tailed if $\limsup_{u\rightarrow\infty}e_F(u)<\infty…
user407813
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Levy flight distribution

Can somebody help me with C++ code, how to make a Levy distribution like a function? I need to make one dimensional Levy flight model, but I don't know the function how to choose the right step.
Jenny
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