Belbachir, Hacène Determining the mode for convolution powers of discrete uniform distribution. (English) Zbl 1241.60007 Probab. Eng. Inf. Sci. 25, No. 4, 469-475 (2011). Summary: We specify the smallest mode of the ordinary multinomials leading to the expression of the maximal probability of convolution powers of the discrete uniform distribution. The generating function for an extension of the maximal probability is given. Cited in 1 ReviewCited in 5 Documents MSC: 60E05 Probability distributions: general theory 60E10 Characteristic functions; other transforms Keywords:convolution powers; discrete uniform distribution; generating function; maximal probability PDFBibTeX XMLCite \textit{H. Belbachir}, Probab. Eng. Inf. Sci. 25, No. 4, 469--475 (2011; Zbl 1241.60007) Full Text: DOI References: [1] DOI: 10.1214/aop/1176993082 · Zbl 0561.60021 · doi:10.1214/aop/1176993082 [2] DOI: 10.1016/j.spl.2008.05.005 · Zbl 1152.60310 · doi:10.1016/j.spl.2008.05.005 [3] de Moivre, Miscellanca analytica de scrichus et quadraturis (1731) [4] de Moivre, The doctrine of chances (1967) · Zbl 0153.30801 [5] DOI: 10.1016/j.aim.2006.03.009 · Zbl 1108.60041 · doi:10.1016/j.aim.2006.03.009 [6] DOI: 10.1016/0167-7152(84)90032-4 · Zbl 0541.62006 · doi:10.1016/0167-7152(84)90032-4 [7] Belbachir, Annales de Mathematicae et Informaticae 35 pp 21– (2008) [8] Wintner, Asymptotic distributions and infinite convolutions (1938) [9] Stanley, In graph theory and its applications: East and West pp 500– (1989) [10] Dharmadhikari, Unimodality, convexity and applications (1988) 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.