Physical Sciences and Mathematics Commons^™

The Pitman Inequality For Exchangeable Random Vectors, J. Behboodian, Naveen Bansal, Gholamhossein Hamedani, Hans Volkmer

Naveen Bansal

In this short article the following inequality called the “Pitman inequality” is proved for the exchangeable random vector (X₁,X₂,…,X_n)(X1,X2,…,Xn) without the assumption of continuity and symmetry for each component X_iXi:

P(|1n∑i=1nXi|≤|∑i=1nαiXi|)≥12 ,

where allαi≥0 are special weights with∑i=1nαi=1.