A monotonicity property of the composition of regularized and inverted-regularized gamma functions with applications |
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| Authors: | Edward Furman Ri?ardas Zitikis |
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| Affiliation: | a Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada
b Department of Statistical and Actuarial Sciences, University of Western Ontario, 1151 Richmond Street North, London, Ontario N6A 5B7, Canada |
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| Abstract: | The gamma function and its various modifications such as the (upper) incomplete, regularized and inverted-regularized incomplete gamma functions are of importance in both theory and applications. In this note we observe an ‘if and only if ’ relationship between a certain axiom of insurance risk management and a monotonicity property of the composition of regularized and inverted-regularized incomplete gamma functions, assuming that the risks follow gamma distributions. We derive the monotonicity property by utilizing the above noted relationship and a probabilistic technique. The aforementioned insurance axiom, called consistent no-undercut, is explained in detail and related to several techniques of analysis. |
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| Keywords: | Regularized gamma function Incomplete gamma function Inverted gamma function Composition Monotonicity Inequalities Insurance |
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