Bounds for covariances and variances of truncated random variables

N. Hemachandra; V. Cheriyan

Bounds for covariances and variances of truncated random variables

Probability 2007-05-23 v1

Authors: N. Hemachandra , V. Cheriyan

Abstract

We show that a lower bound for covariance of $\min(X_1,X_2)$ and $\max(X_1,X_2)$ is $\cov{X_1}{X_2}$ and an upper bound for variance of \\ $\min(X_2,\max(X,X_1))$ is $\var{X} + \var{X_1} +\var{X_2}$ generalizing previous results. We also characterize the cases where these bounds are sharp.

Keywords

truncated random variables covariance bounds variance bounds min max functions sharp bounds

Cite

@article{arxiv.math/0212006,
  title  = {Bounds for covariances and variances of truncated random variables},
  author = {N. Hemachandra and V. Cheriyan},
  journal= {arXiv preprint arXiv:math/0212006},
  year   = {2007}
}

Comments

7 pages. Revised during October 2002

Related papers

View all related →