This article addresses the issue of computing the constant required to implement a specific nonparametric subset selection procedure based on ranks of data arising in a statistical randomized block experimental design...This article addresses the issue of computing the constant required to implement a specific nonparametric subset selection procedure based on ranks of data arising in a statistical randomized block experimental design. A model of three populations and two blocks is used to compute the probability distribution of the relevant statistic, the maximum of the population rank sums minus the rank sum of the “best” population. Calculations are done for populations following a normal distribution, and for populations following a bi-uniform distribution. The least favorable configuration in these cases is shown to arise when all three populations follow identical distributions. The bi-uniform distribution leads to an asymptotic counterexample to the conjecture that the least favorable configuration, i.e., that configuration minimizing the probability of a correct selection, occurs when all populations are identically distributed. These results are consistent with other large-scale simulation studies. All relevant computational R-codes are provided in appendices.展开更多
In this article, we have pointed out that some propositions corresponding to the distance measure between the type-2 fuzzy sets （T2FSs） as provided by Singh （Frontiers of Computer Science, 2014, 8（5）, 741-752）, ...In this article, we have pointed out that some propositions corresponding to the distance measure between the type-2 fuzzy sets （T2FSs） as provided by Singh （Frontiers of Computer Science, 2014, 8（5）, 741-752）, are incorrect by a counterexample. Further, these propositions have been corrected in the present manuscript by giving a correct relation between the T2FSs and validating it with a numerical example.展开更多
In this paper, we give a counterexample to the article 'Globally asymptotic stability of a recurrence sequence', Ann. of Diff. Eqs., 17:1(2001), 82-85.
文摘This article addresses the issue of computing the constant required to implement a specific nonparametric subset selection procedure based on ranks of data arising in a statistical randomized block experimental design. A model of three populations and two blocks is used to compute the probability distribution of the relevant statistic, the maximum of the population rank sums minus the rank sum of the “best” population. Calculations are done for populations following a normal distribution, and for populations following a bi-uniform distribution. The least favorable configuration in these cases is shown to arise when all three populations follow identical distributions. The bi-uniform distribution leads to an asymptotic counterexample to the conjecture that the least favorable configuration, i.e., that configuration minimizing the probability of a correct selection, occurs when all populations are identically distributed. These results are consistent with other large-scale simulation studies. All relevant computational R-codes are provided in appendices.
文摘In this article, we have pointed out that some propositions corresponding to the distance measure between the type-2 fuzzy sets （T2FSs） as provided by Singh （Frontiers of Computer Science, 2014, 8（5）, 741-752）, are incorrect by a counterexample. Further, these propositions have been corrected in the present manuscript by giving a correct relation between the T2FSs and validating it with a numerical example.
基金Research supported by Distinguished Expert Science Foundation of Naval Aeronautical Engineering Institute.
文摘In this paper, we give a counterexample to the article 'Globally asymptotic stability of a recurrence sequence', Ann. of Diff. Eqs., 17:1(2001), 82-85.
