On sums of monotone random integer variables

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On sums of monotone random integer variables. / Aamand, Anders; Alon, Noga; Houen, Jakob Bæk Tejs; Thorup, Mikkel.

In: Electronic Communications in Probability, Vol. 27, 64, 2022, p. 1-8.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Aamand, A, Alon, N, Houen, JBT & Thorup, M 2022, 'On sums of monotone random integer variables', Electronic Communications in Probability, vol. 27, 64, pp. 1-8. https://doi.org/10.1214/22-ECP500

APA

Aamand, A., Alon, N., Houen, J. B. T., & Thorup, M. (2022). On sums of monotone random integer variables. Electronic Communications in Probability, 27, 1-8. [64]. https://doi.org/10.1214/22-ECP500

Vancouver

Aamand A, Alon N, Houen JBT, Thorup M. On sums of monotone random integer variables. Electronic Communications in Probability. 2022;27:1-8. 64. https://doi.org/10.1214/22-ECP500

Author

Aamand, Anders ; Alon, Noga ; Houen, Jakob Bæk Tejs ; Thorup, Mikkel. / On sums of monotone random integer variables. In: Electronic Communications in Probability. 2022 ; Vol. 27. pp. 1-8.

Bibtex

@article{6aede41f9e70475d85bdb82cb9494586,
title = "On sums of monotone random integer variables",
abstract = "We say that a random integer variable X is monotone if the modulus of the characteristic function of X is decreasing on [0,π]. This is the case for many commonly encountered variables, e.g., Bernoulli, Poisson and geometric random variables. In this note, we provide estimates for the probability that the sum of independent monotone integer variables attains precisely a specific value. We do not assume that the variables are identically distributed. Our estimates are sharp when the specific value is close to the mean, but they are not useful further out in the tail. By combining with the trick of exponential tilting, we obtain sharp estimates for the point probabilities in the tail under a slightly stronger assumption on the random integer variables which we call strong monotonicity.",
author = "Anders Aamand and Noga Alon and Houen, {Jakob B{\ae}k Tejs} and Mikkel Thorup",
year = "2022",
doi = "10.1214/22-ECP500",
language = "English",
volume = "27",
pages = "1--8",
journal = "Electronic Communications in Probability",
issn = "1083-589X",
publisher = "Institute of Mathematical Statistics",

}

RIS

TY - JOUR

T1 - On sums of monotone random integer variables

AU - Aamand, Anders

AU - Alon, Noga

AU - Houen, Jakob Bæk Tejs

AU - Thorup, Mikkel

PY - 2022

Y1 - 2022

N2 - We say that a random integer variable X is monotone if the modulus of the characteristic function of X is decreasing on [0,π]. This is the case for many commonly encountered variables, e.g., Bernoulli, Poisson and geometric random variables. In this note, we provide estimates for the probability that the sum of independent monotone integer variables attains precisely a specific value. We do not assume that the variables are identically distributed. Our estimates are sharp when the specific value is close to the mean, but they are not useful further out in the tail. By combining with the trick of exponential tilting, we obtain sharp estimates for the point probabilities in the tail under a slightly stronger assumption on the random integer variables which we call strong monotonicity.

AB - We say that a random integer variable X is monotone if the modulus of the characteristic function of X is decreasing on [0,π]. This is the case for many commonly encountered variables, e.g., Bernoulli, Poisson and geometric random variables. In this note, we provide estimates for the probability that the sum of independent monotone integer variables attains precisely a specific value. We do not assume that the variables are identically distributed. Our estimates are sharp when the specific value is close to the mean, but they are not useful further out in the tail. By combining with the trick of exponential tilting, we obtain sharp estimates for the point probabilities in the tail under a slightly stronger assumption on the random integer variables which we call strong monotonicity.

U2 - 10.1214/22-ECP500

DO - 10.1214/22-ECP500

M3 - Journal article

VL - 27

SP - 1

EP - 8

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

SN - 1083-589X

M1 - 64

ER -

ID: 329694680