2018/08/20 by Tao Jiang, Jiang, Tao, Yuebao Wang +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1808.06433
openalex publication_date 2018/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℝ+∪\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 \citeC1986, 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 ℝ, the local almost decreasing condition is necessary in some sense.