A functional equation and its application to the characterization of gamma distributions |
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Authors: | Fruzsina Mészáros |
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Institution: | 1. Institute of Mathematics, University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary
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Abstract: | The functional equation $$ f\left(x\right)g\left(y\right)=p\left(x+y\right)q\left(\frac{x}{y} \right) $$ is investigated for almost all ${\left(x,\,y\right)\in\mathbb{R}^{2}_{+}}$ and for the measurable functions ${f,\,g,\,p,\,q:\mathbb{R}_{+}\rightarrow\mathbb{R}_{+}}$ . This equation is related to the Lukács characterization of gamma distribution. |
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