Hölder Means, Lehmer Means, andx−1logcoshx

Optimal estimations of some Sei¤ert type means by Lehmer means

Let us consider the logarithmic mean L; the identric mean I; the trigonometric means P and T de…ned by H. J. Sei¤ert, the hyperbolic mean M de…ned by E. Neuman and J. Sándor, and the Gini mean J . The optimal estimations of these means by power means Ap and also some of the optimal estimations by Lehmer means Lq are known. We prove two new optimal estimation by Lehmer means L0 < M < L1=6 and L1...

Invariance in the Class of Weighted Lehmer Means

We study invariance in the class of weighted Lehmer means. Thus we look at triples of weighted Lehmer means with the property that one is invariant with respect to the other two.

Generalized Steffensen Means

narative means

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Clustering with Intelligent Linexk-Means

The intelligent LINEX k-means clustering is a generalization of the k-means clustering so that the number of clusters and their related centroid can be determined while the LINEX loss function is considered as the dissimilarity measure. Therefore, the selection of the centers in each cluster is not randomly. Choosing the LINEX dissimilarity measure helps the researcher to overestimate or undere...