caa a22 4500 475827007 CHVBK 20180406123831.0 cr unu---uuuuu 170329e20000601xx s 000 0 eng 10.1023/A:1004153419736 doi (NATIONALLICENCE)springer-10.1023/A:1004153419736 Quantitative Approximation to the Ordered Dirichlet Distribution under Varying Basic Probability Spaces [Elektronische Daten] [Tomoya Yamada, Tadashi Matsunawa] An approximate expansion of a sequence of ordered Dirichlet densities is given under the set-up with varying dimensions of the relating basic probability spaces. The problem is handled as the approximation to the joint distribution of an increasing number of selected order statistics based on the random sample drawn from the uniform distribution U(0, 1). Some inverse factorial series to the expansion of logarithmic function enable us to give quantitative error evaluations to our problem. With the help of them the relating modified K-L information number, which is defined on an approximate main domain and different from the usual ones, is accurately evaluated. Further, the proof of the approximate joint normality of the selected order statistics is more systematically presented than those given in existing works. Concerning the approximate normality the modified affinity and the half variation distance are also evaluated. The Institute of Statistical Mathematics, 2000 Ordered Dirichlet distribution nationallicence approximate distribution nationallicence sample quantiles nationallicence modified K-L information number nationallicence modified affinity nationallicence half variation distance nationallicence approximate main domain nationallicence approximate joint normality nationallicence Yamada Tomoya The Graduate Universities for Advanced Studies, 4-6-7 Minami-Azabu, Minato-ku, 106-8569, Tokyo, Japan aut Matsunawa Tadashi The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106-8569, Tokyo, Japan aut Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/2(2000-06-01), 197-214 0020-3157 52:2<197 2000 52 10463 https://doi.org/10.1023/A:1004153419736 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004153419736 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yamada Tomoya The Graduate Universities for Advanced Studies, 4-6-7 Minami-Azabu, Minato-ku, 106-8569, Tokyo, Japan aut NATIONALLICENCE 700 1- Matsunawa Tadashi The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106-8569, Tokyo, Japan aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/2(2000-06-01), 197-214 0020-3157 52:2<197 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer