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LAPLACE TRANSFORMATION FOR THE $\gamma$-ORDER GENERALIZED NORMAL, $N_\gamma\left(\mu, \sigma^2\right)$
Keywords:
$\gamma$-order generalized normal distribution, Laplace transformation, heat equation, Sobolev inequality.DOI:
https://doi.org/10.17654/0972086324001Abstract
We discuss a number of properties of the univariate $\gamma$-order generalized normal distribution, acting also as a solution to the heat equation. More emphasis is given on the Laplace transform of the introduced distribution. Logarithm Sobolev inequalities are discussed since they are the source of the introduced $N_\gamma(\mu, \Sigma)$.
Received: September 6, 2023
Revised: September 22, 2023
Accepted: October 10, 2023
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