Contents
Are bounded random variables sub-Gaussian?
Using the inequality (2n + 1)! ≥ n! 2n, we see that X is a-subgaussian. More generally, any centered and bounded random variable is subgaussian, as we demonstrate now (see e.g. [13, Theorem 9.9]).
Is Bernoulli a sub-Gaussian?
This allows us to conclude that any Bernoulli variable is sub-Gaussian with variance factor ν=14.
Is binomial distribution sub-Gaussian?
Furthermore, we show that most probability distributions used in practice such as the binomial, Poisson, normal and gamma distributions are locally sub-Gaussian.
Is a Gaussian random variable sub Gaussian?
Sub Gaussian random variables exist, for example the Gaussian random variable is subgaussian. Hoeffding’s Lemma (1963) asserts that bounded random variables are also sub Gaussian. .
What is moment in normal distribution?
Moments Suppose again that has the normal distribution with location parameter μ ∈ R and scale parameter σ ∈ ( 0 , ∞ ) . As the notation suggests, the location and scale parameters are also the mean and standard deviation, respectively. The mean and variance of are. E ( X ) = μ var ( X ) = σ 2.
Where did the name subgaussian random variables come from?
The name \\subgaussian” is the English counterpart of the French \\sous-gaussienne” coined by Kahane in [3]. Subsequent works have studied subgaussian random variables and processes either per se or in connection with various other subjects.
Which is an example of a sub Gaussian distribution?
A sub-Gaussian distribution is any probability distribution that has tails bounded by a Gaussian and has a mean of zero. It is well known that the sum of independent sub-Gaussians is again sub-Gaussian. This note generalizes this result to sums of sub-Gaussians that may not be independent, under the assumption a certain conditional
When did Kahane introduce the subgaussian random variable?
To the best of the author’s knowledge, subgaussian random variables were introduced by Kahane in [3], where they played a role to establish a sucient condition for the almost-sure uniform convergence of certain random series of functions.
Is the tail of a Gaussian random variable zero?
The fact that a Gaussian random variable Z has tails that decay to zero exponentially fast can also be seen in the moment generating function (MGF) M : s → M(s) = IE[exp(sZ)].