Monotonicity of certain integrals involving gamma distributions and their applications in multiple comparisons |
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| Institution: | 1. Department of General, Vascular and Transplant Surgery, Medical University of Silesia, Katowice, Poland;2. Department of Nephrology, Transplantation and Internal Medicine, Medical University of Silesia, Katowice, Poland;3. The Polish Transplant Coordinating Centre Poltransplant, Warsaw, Poland;4. Department of Statistics, Department of Instrumental Analysis, Faculty of Pharmaceutical Sciences in Sosnowiec, Medical University of Silesia, Katowice, Poland;5. Department of Statistical Modelling, Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic;1. Department of Statistics, Sarsuna College, Kolkata, India;2. General Motors Tech Center India (GMTCI), Bengaluru, India;3. Department of Statistics, University of Calcutta, Kolkata, India;1. Department of Mathematics and Statistics, McMaster University, Hamilton, Canada;2. Department of Statistics, Zabol University, Sistan and Baluchestan, Iran;3. Department of Statistics, King Abdulaziz University, Jeddah, Saudi Arabia;1. Department of Statistics, Banaras Hindu University, Varanasi-221 005, India;2. DST Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi-221 005, India;1. LTCI, Télécom ParisTech, Université Paris-Saclay, 46, rue Barrault, 75013 Paris, France;2. Université catholique de Louvain, Institut de statistique, biostatistique et sciences actuarielles, Voie du Roman Pays 20, B-1348 Louvain-la-Neuve, Belgium |
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| Abstract: | Barlow and Gupta (1969) and Alam (1970) studied the monotonicity of two integrals, involving gamma distributions, that arise in certain ranking and selection problems. In this paper, we shall unify their results by studying the monotonicity of two generalized versions of integrals considered by them. We will also provide applications of derived results in study of certain multiple comparison procedures. |
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| Keywords: | Monotonicity Multiple comparisons Ranking and selection |
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