COMPARISON OF ORDER STATISTICS IN A RANDOM SEQUENCE TO THE SAME STATISTICS WITH I.I.D. VARIABLES

By J. Bon, Eugen Păltănea. 2006

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ORDERING PROPERTIES OF ORDER STATISTICS FROM HETEROGENEOUS POPULATIONS: A REVIEW WITH AN EMPHASIS ON SOME RECENT DEVELOPMENTS (2013, background): “For the exponential case, Bon and Pǎltǎnea [13] provided the necessary and sufficient condition on λ for Xk:n ≥st X∗k:n of the following form: Xk:n ≥st X∗k:n ⇐⇒ λ ≥ ⎡ ⎣(n k )−1 ∑ 1≤i1 ··· ik≤n λi1 . . . λik ⎤ ⎦ 1 k .”
On the skewness of order statistics in multiple-outlier models (2011, unknown): “…3 of Ahmed et al. (1986), which states that, under the condition that Xk:n ≥∗ Yk:n, a result proved in our Corollary 3.1, Xk:n ≥st Yk:n ⇒ Xk:n ≥disp Yk:n. Bon and Pǎltǎnea (2006) showed that Xk:n ≥st Yk:n is equivalent to λ̂ ≥ (( n k )−1 ∑ 1≤i1<···<ik≤n λi1 · · · λik )1/k = (( n k )−1 ∑ l∈L ( p…”