The infimum values of three probability functions for the Laplace distribution and the student's $t$ distribution
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866908817990615040 |
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| author | Hu, Rong-Sheng Hu, Ze-Chun Huang, Zhen Li, Mu-Xuan |
| author_facet | Hu, Rong-Sheng Hu, Ze-Chun Huang, Zhen Li, Mu-Xuan |
| contents | Let $\{X_α\}$ be a family of random variables satisfying some distribution with a parameter $α$, $E(X_α)$ be the expectation, and $Var(X_α)$ be the variance. In this paper, we study the infimum values of three probability functions: $P(X_α\leq y E(X_α))$, $P\left(|X_α-E(X_α)|\leq y\sqrt{Var(X_α)}\right)$ and $P\left(|X_α-E(X_α)|\geq y\sqrt{Var(X_α)}\right), \forall y>0$, with respect to the parameter $α$ for the Laplace distribution and the student's $t$ distribution. Our motivation comes from three former conjectures: Chvátal's conjecture, Tomaszewski's conjecture and Hitczenko-Kwapień's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06758 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The infimum values of three probability functions for the Laplace distribution and the student's $t$ distribution Hu, Rong-Sheng Hu, Ze-Chun Huang, Zhen Li, Mu-Xuan Probability Let $\{X_α\}$ be a family of random variables satisfying some distribution with a parameter $α$, $E(X_α)$ be the expectation, and $Var(X_α)$ be the variance. In this paper, we study the infimum values of three probability functions: $P(X_α\leq y E(X_α))$, $P\left(|X_α-E(X_α)|\leq y\sqrt{Var(X_α)}\right)$ and $P\left(|X_α-E(X_α)|\geq y\sqrt{Var(X_α)}\right), \forall y>0$, with respect to the parameter $α$ for the Laplace distribution and the student's $t$ distribution. Our motivation comes from three former conjectures: Chvátal's conjecture, Tomaszewski's conjecture and Hitczenko-Kwapień's conjecture. |
| title | The infimum values of three probability functions for the Laplace distribution and the student's $t$ distribution |
| topic | Probability |
| url | https://arxiv.org/abs/2602.06758 |