## One Citation

### Bernstein-type bounds for beta distribution

- MathematicsModern 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…

## References

SHOWING 1-10 OF 15 REFERENCES

### Inequalities and Bounds for the Incomplete Gamma Function

- Mathematics
- 2013

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

- MathematicsModern 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

- Mathematics
- 1999

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

- Mathematics
- 2004

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

- MathematicsAppl. Math. Comput.
- 2014

### On the sub-Gaussianity of the Beta and Dirichlet distributions

- Mathematics, Computer Science
- 2017

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

- Mathematics
- 2020

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

- Mathematics
- 1998

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

- MathematicsMemoirs of the American Mathematical Society
- 2019

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

- Computer ScienceBiometrika
- 2022

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.