## 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.