Is the gamma distribution stable?
The gamma distributions (5. 5) are not stable: the sum of two variables with the same gamma distribution has another gamma distribution.
What is a stable variable?
A stable (sociolinguistic) variable is a variable which is not undergoing linguistic change. Such a variable exhibits the regular age pattern. A stable variable, thus, reflects change in the speech of the individual speaker as (s)he progresses through life.
How do you know if a distribution is stable?
A distribution is said to be stable if summing independent random variables from that distribution results in a random variable from that same distribution. These distributions are called stable because their shape is unchanged (stable) when they are being summed.
Is Laplace a stable distribution?
The Laplace distribution and asymmetric Laplace distribution are special cases of the geometric stable distribution. The Laplace distribution is also a special case of a Linnik distribution. The Mittag-Leffler distribution is also a special case of a geometric stable distribution.
What makes a distribution stable?
In probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable.
What is stable distribution statistics?
Is Poisson distribution stable?
The most well-known discrete stable distribution is the Poisson distribution which is a special case as the only discrete-stable distribution for which the mean and all higher-order moments are finite.
What is a Laplace distribution used for?
The Laplace distribution is used for modeling in signal processing, various biological processes, finance, and economics. Examples of events that may be modeled by Laplace distribution include: Credit risk and exotic options in financial engineering.