Some new inequalities for beta distributions

@article{Henzi2022SomeNI,
  title={Some new inequalities for beta distributions},
  author={Alexander Henzi and Lutz Duembgen},
  journal={Statistics \& Probability Letters},
  year={2022}
}
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  • 2023
This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-Gaussian and sub-gamma bounds previously studied…

References

SHOWING 1-10 OF 15 REFERENCES

Inequalities and Bounds for the Incomplete Gamma Function

Inequalities involving the incomplete gamma function are established. They are obtained using logarithmic convexity of some function associated with the function in question. Lower and upper bounds…

Bernstein-type bounds for beta distribution

  • M. Skorski
  • Mathematics
    Modern Stochastics: Theory and Applications
  • 2023
This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-Gaussian and sub-gamma bounds previously studied…

Some Inequalities of the Incomplete Gamma and Related Functions

In the article, many inequalities of the integrals f 00 z e'dt, e"dt, j for p > 0, which are related to the incomplete gamma function, are established. The approach used in the paper could yield more…

Handbook of beta distribution and its applications

Foundations. Limit Theorems. Characterization. Interacting particles. Arithmetical functions. Miscellaneous results. Author Index. Subject Index.

Monotonicity properties and bounds for the chi-square and gamma distributions

On the sub-Gaussianity of the Beta and Dirichlet distributions

The optimal proxy variance for the sub-Gaussianity of Beta distribution is obtained, thus proving upper bounds recently conjectured by Elder (2016), and the proxy variance relation to log-Sobolev inequalities and transport inequalities is discussed.

Exact lower and upper bounds on the incomplete gamma function

Lower and upper bounds $B_a(x)$ on the incomplete gamma function $\Gamma(a,x)$ are given for all real $a$ and all real $x>0$. These bounds $B_a(x)$ are exact in the sense that…

New goodness-of-fit tests and their application to nonparametric confidence sets

Suppose one observes a process V on the unit interval, where dV = f 0 +dW with an unknown parameter f 0 ∈ L 1 [0, 1] and standard Brownian motion W. We propose a particular test of one-point…

One-dimensional empirical measures, order statistics, and Kantorovich transport distances

This work is devoted to the study of rates of convergence of the empirical measures μn = 1 n ∑n k=1 δXk , n ≥ 1, over a sample (Xk)k≥1 of independent identically distributed real-valued random…

Honest calibration assessment for binary outcome predictions

This work proposes honest calibration assessment based on novel confidence bands for the calibration curve, which are valid only subject to the natural assumption of isotonicity, and shows that they have a finite sample coverage guarantee, are narrower than existing approaches, and adapt to the local smoothness of the calibration Curve p and the local variance of the binary observations.