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- W4366999564 abstract "Let $X$ be a random variable with finite second moment. We investigate the inequality: $P{|X-E[X]|le sqrt{{rm Var}(X)}}ge P{|Z|le 1}$, where $Z$ is a standard normal random variable. We prove that this inequality holds for many familiar infinitely divisible continuous distributions including the Laplace, Gumbel, Logistic, Pareto, infinitely divisible Weibull, log-normal, student's $t$ and inverse Gaussian distributions. Numerical results are given to show that the inequality with continuity correction also holds for some infinitely divisible discrete distributions." @default.
- W4366999564 created "2023-04-27" @default.
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- W4366999564 date "2023-04-22" @default.
- W4366999564 modified "2023-10-01" @default.
- W4366999564 title "Variation comparison between infinitely divisible distributions and the normal distribution" @default.
- W4366999564 doi "https://doi.org/10.48550/arxiv.2304.11459" @default.
- W4366999564 hasPublicationYear "2023" @default.
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