Saleh, A. K. Md. Ehsanes; Hassanein, K. M.; Ali, Mir Masoom Linear estimation and tests of quantiles of logistic distribution based on selected order statistics. (English) Zbl 0665.62032 J. Inf. Optim. Sci. 9, No. 3, 445-464 (1988). Asymptotically best linear unbiased estimates (ABLUE) and tests of hypotheses on quantiles of the location-scale family of the logistic distribution are considered based on a few selected order statistics from a large sample. The optimum spacings, the coefficients and the ARE of ABLUE compared to maximum likelihood estimators are provided in tabular form for \(k=2(1)10\) and \(\xi =.01\),.05(.05).50. It is shown that the same spacings may be also used for testing and confidence intervals. MSC: 62F12 Asymptotic properties of parametric estimators 62F03 Parametric hypothesis testing 62G10 Nonparametric hypothesis testing 62Q05 Statistical tables 62F25 Parametric tolerance and confidence regions 62G05 Nonparametric estimation Keywords:Asymptotically best linear unbiased estimates; hypotheses on quantiles; location-scale family; logistic distribution; order statistics; optimum spacings; ARE; maximum likelihood estimators PDFBibTeX XMLCite \textit{A. K. Md. E. Saleh} et al., J. Inf. Optim. Sci. 9, No. 3, 445--464 (1988; Zbl 0665.62032) Full Text: DOI References: [1] Masoom Ali M., Commun. Statist.–Theor. Meth. 12 (19) pp 2261– (1983) · Zbl 0553.62048 · doi:10.1080/03610928308828604 [2] Ali M. Masoom, Sankhya B 44 (2) pp 135– (1982) [3] Masoom Ali M., Commun Statist.–Theor. Meth. 10 (19) pp 1921– (1981) · doi:10.1080/03610928108828161 [4] Masoom Ali M., Aligarh J Statist. 1 (2) pp 139– (1981) [5] Ali M. Masoom, Sankhya B 47 pp 310– (1985) [6] Chernoff H., Tech. Report 70, in: A note on optimal spacings for systematic statistics (1971) [7] Gupta S.S., Biometrika 53 pp 565– (1966) · Zbl 0203.21102 · doi:10.1093/biomet/53.3-4.565 [8] Gupta S.S., Technometrics 9 pp 43– (1967) · doi:10.1080/00401706.1967.10490440 [9] Hatter J.L., JASA 62 pp 675– (1967) · doi:10.1080/01621459.1967.10482940 [10] Hassanein K.M., Biometrika 56 pp 684– (1969) · doi:10.1093/biomet/56.3.684 [11] Hassanein K.M., Statist. Hafte 15 pp 65– (1974) · Zbl 0281.62033 · doi:10.1007/BF02923644 [12] Koutrcuvelis I.A., Commun. Statist. Theor. Meth. 10 (2) pp 189– (1981) · Zbl 0461.62029 · doi:10.1080/03610928108828029 [13] Kubat P., Technometrics 12 pp 345– (1980) [14] Mosteller F., Ann. Math. Statist. 17 pp 377– (1946) · Zbl 0063.04123 · doi:10.1214/aoms/1177730881 [15] Ogawa J., Osaka Math. Journal 3 pp 175– (1951) [16] Ehsanes Saleh A.K. Md., Metrika (1984) [17] Ehsanes Saleh A.K. Md., J. Statist. Plann. Infer 8 pp 75– (1983) · Zbl 0533.62042 · doi:10.1016/0378-3758(83)90063-0 [18] Ehsanes Saleh A. K. Md., Statistics and Related Topics pp 279– (1981) [19] Sarhan A.E., Contributions to order statistics (1962) · Zbl 0102.35204 [20] Sarndal C.E., Information from censored samples (1962) [21] Umbach D., Aligarh J. Statist. 1 (2) pp 113– (1981) [22] Umbach D., Commun. Statist. – Theor. Meth. 10 (19) pp 1933– (1981) · doi:10.1080/03610928108828162 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.