Optimal selection based on relative ranks of a sequence by ties

The optimal selection of a maximum of a sequence with the possibility of ties is considered. The object is to examine each observation in the sequence of known length n and, based only on the relative rank among predecessors, either to stop and select it as a maximum or to continue without recall. Rules which maximize the probability of correctly selecting a maximum from a sequence with ties are investigated. These include rules which randomly break ties, rules which discard tied observations, and minimax rules based on the atoms of a discrete distribution function. If the sequence is random from F, a random distribution function from a Dirichlet process prior with non-atomic parameter, optimal rules are developed. The limiting behavior of these rules is studied and compared with other rules. The selection of the parameter of the Dirichlet process regulates the ties.

Optimal selection based on relative ranks of a sequence by ties

The optimal selection of a maximum of a sequence with the possibility of ties is considered. The object is to examine each observation in the sequence of known length n and, based only on the relative rank among predecessors, either to stop and select it as a maximum or to continue without recall. Rules which maximize the probability of correctly selecting a maximum from a sequence with ties are investigated. These include rules which randomly break ties, rules which discard tied observations, and minimax rules based on the atoms of a discrete distribution function. If the sequence is random from F, a random distribution function from a Dirichlet process prior with non-atomic parameter, optimal rules are developed. The limiting behavior of these rules is studied and compared with other rules. The selection of the parameter of the Dirichlet process regulates the ties.

Structure cristalline et moléculaire du cyclopentadiényle dicarbonyle triphénylphosphine manganèse, MnC5H5(CO)2P(C6H5)3

The crystalano molecular structure of cyclopentadienyl manganese dicarbonyl-triphenyl phosphine has been determined by means of three dimensional data obtained by a Buerger precession camera. 2931 independent intensities were utilized in the refinement of the structure using the least-squares method. The final disagreement factor is 0.11. MnC5H5(CO)2P(C6H5)3 crystallizes in the triclinic space group.[Formula: see text]The molecule shows atomic parameter almost identical to those of MnC5H5(CO)3 except for the Mn—C bond lengths which change from 1.80 to 1.73 Å. The Mn—P distance (2.236 Å) and the unchanged parameters for the Mn—C5H5 group confirm the strong donating power of the cyclopentadienyl group. [Journal translation]