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PARAMETERS STABLE DISTRIBUTION ESTIMATE
Keywords:
parameter estimation, Levy distribution, characteristic function, α-stable law, MLE, normal law, stable distribution, infinitely divisible, maximum likelihood estimator, α-distribution.DOI:
https://doi.org/10.17654/0972361722064Abstract
In this work, we propose a new version of the methods for estimating the parameters of an a-stable distribution based on the characteristic function. For this purpose, we started with two properties in the cases where the parameter of stability $\alpha \neq 1$ and $\alpha=1$. The two properties consist in standardizing the a-stable distribution. These properties were then used to propose two theorems and their generalizations on the estimates of the parameters of an $\alpha$-stable distribution. Finally, numerical simulations are performed to test whether these estimators respect the set of conditions on the parameters of an $\alpha $-stable distribution. The result found is positive.
Received: April 16, 2022
Revised: June 25, 2022
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