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- W2886433229 abstract "For a subexponential density, so far, there has been no positive conclusion or counter example to show whether it is almost decreasing. In this paper, a subexponential density supported on $mathbb{R}^+cup{0}$ without the almost decrease is constructed by a little skillful method. The density is a positive piecewise linear function with a more normal shape. Correspondingly, there exists a local subexponential distribution which is not locally almost decreasing. Based on an example of Cline cite{C1986}, some similar results are also obtained for the long-tailed density excluding the subexponential density and the local long-tailed distribution excluding the local subexponential distribution. Finally, the paper shows that, for the local subexponentiality of a distribution supported on $mathbb{R}$, the local almost decreasing condition is necessary in some sense." @default.
- W2886433229 created "2018-08-22" @default.
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- W2886433229 date "2018-08-20" @default.
- W2886433229 modified "2023-10-17" @default.
- W2886433229 title "On the almost decrease of a subexponential density" @default.
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- W2886433229 doi "https://doi.org/10.48550/arxiv.1808.06433" @default.
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