Amiri, Mehdi; Jamalizadeh, Ahad Stochastic ordering of medians in samples from normal distributions. (English) Zbl 07539721 Commun. Stat., Theory Methods 48, No. 13, 3413-3420 (2019). Summary: In this paper, we discuss some stochastic comparisons for the sample median in a random sample from a normal distribution. Specifically, we establish that the sample median is stochastically farther than the sample mean to the population mean. To verify the result of comparison, we derive an upper bound for some distributional characteristics of the distance between the sample median and the population mean. The stochastic ordering considered here is the likelihood ratio order. MSC: 60E15 Inequalities; stochastic orderings Keywords:likelihood ratio order; median; normal distribution; stochastic ordering PDFBibTeX XMLCite \textit{M. Amiri} and \textit{A. Jamalizadeh}, Commun. Stat., Theory Methods 48, No. 13, 3413--3420 (2019; Zbl 07539721) Full Text: DOI References: [1] Ahmadi, J.; Arghami, N. R., Some univariate stochastic orders on record values, Communications in Statistics-Theory and Methods, 30, 1, 69-74 (2001) · Zbl 0997.60007 [2] Arnold, B. C.; Balakrishnan, N.; Nagaraja, H. N., A first course in order statistic (2008), Philadelphia: SIAM, Philadelphia · Zbl 1172.62017 [3] Balakrishnan, N.; Zhao, P., Ordering properties of order statistics from heterogeneous populations: a review with an emphasis on some recent developments, Probability in the Engineering and Informational Sciences, 27, 4, 403-69 (2013) · Zbl 1288.60023 [4] Belzunce, F.; Lillo, R.; Ruiz, J. M.; Shaked, M., Recent developments in ordered random variables, Stochastic ordering of record and inter-record values, 119-37 (2007), New York: Nova Scientific Publishing, New York [5] Belzunce, F.; Mercader, J. A.; Ruiz, J. M., Stochastic comparisons of generalized order statistics, Probability in the Engineering and Informational Sciences, 19, 1, 99-120 (2005) · Zbl 1067.62050 [6] Berrendero, J. R.; Cárcamo, J., Tests for stochastic orders and mean order statistics, Communications in Statistics-Theory and Methods, 41, 8, 1497-509 (2012) · Zbl 1319.60032 [7] Boland, P. J.; Hu, T.; Shaked, M.; Shanthikumar, J. G.; Dror, M.; L’Ecuyer, P.; Szidarovszky, F., Modelling uncertainty: an examination of stochastic theory, methods and applications, Stochastic ordering of order statistics II, 607-23 (2002), Boston, MA: Kluwer, Boston, MA · Zbl 0979.00016 [8] Boland, P. J.; Shaked, M.; Shanthikumar, J. G.; Balakrishnan, N.; Rao, C. R., Handbook of statistics, 16, Stochastic ordering of order statistics, 89-103 (1998), Amsterdam: Elsevier, Amsterdam · Zbl 0906.62046 [9] Jamalizadeh, A.; Madadi, M.; Amiri, M.; Balakrishnan, N., Stochastic ordering of medians in exchangeable trivariate normal vectors., Applied Mathematics-A Journal of Chinese Universities, 31, 148-156 (2016) · Zbl 1363.62048 [10] Malinovsky, Y.; Rinott, Y., On stochastic orders of absolute value of order statistics in symmetric distributions, Statistics & Probability Letters, 79, 19, 2086-91 (2009) · Zbl 1171.62032 [11] Müller, A., Stochastic ordering of multivariate normal distributions, Annals of the Institute of Statistical Mathematics, 53, 3, 567-75 (2001) · Zbl 0989.62031 [12] Müller, A.; Stoyan, D., Comparison methods for stochastic models and risks (2002), New York: JohnWiley & Sons, New York · Zbl 0999.60002 [13] Shaked, M.; Shanthikumar, J., Stochastic orders (2007), New York: Springer, New York · Zbl 1111.62016 [14] Zhao, P.; Balakrishnan, N., A stochastic inequality for the largest order statistics from heterogeneous gamma samples, Journal of Multivariate Analysis, 129, 145-50 (2014) · Zbl 1293.60027 [15] Zhao, P.; Wang, L.; Zhang, Y., On extreme order statistics from heterogeneous beta distributions with applications, Communications in Statistics-Theory and Methods, 46, 14, 7020-38 (2017) · Zbl 1369.90062 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.