Inference about the difference between two normal mean vectors when the covariance matrices are unknown and arbitrary is considered. Assuming that the incomplete data are of monotone pattern, a pivotal quantity, similar to the Hotelling T 2 statistic, is proposed. A satisfactory moment approximation to the distribution of the pivotal quantity is derived. Hypothesis testing and confidence estima...

The generalized Pauli group and its normalizer, the Clifford group, have a rich mathematical structure which is relevant to the problem of constructing symmetric informationally complete POVMs (SIC-POVMs). To date, almost every known SIC-POVM fiducial vector is an eigenstate of a “canonical” unitary in the Clifford group. I show that every canonical unitary in prime dimensions p > 3 lies in the...

In this paper we approach the construction of the both upper and lower tolerance limit in a two-way nested model with mixed effects in balanced data. In order to do so we proceed as Fonseca et al [1] did in order to derive the upper tolerance limit in a two-way nested model with mixed effects in unbalanced data, by using the generalized confidence interval idea earlier used by Krishnamoorthy an...

Analytical and geometrical properties of generalized power-law (GPL) density profiles are reviewed, and special effort is devoted to the special cases where GPL density profiles reduce to (i) a double power-law (DPL), and (ii) a single power-law (SPL). Then GPL density profiles are compared with simulated dark haloes (SDH) density profiles, and nonlinear least-squares fits are prescribed, invol...

In this paper, the Cramér-Rao lower bound (CRLB) of image registration error using an isotropic fiducial mark is derived. The derived CRLB is a function of the intensity profile of the fiducial mark. Following the development of the CRLB, a new method for designing an isotropic fiducial mark, suitable for digital image registration, is presented. A parameterization method of the fiducial intens...

Abstract Zero-inflated and hurdle models are widely applied to count data possessing excess zeros, where they can simultaneously model the process from how zeros were generated potentially help mitigate effects of overdispersion relative assumed distribution. Which use depends on generated: zero-inflated add an additional probability mass zero, while two-part comprised a degenerate distribution...

In diagnostic test studies, one crucial task is to evaluate the diagnostic accuracy of a test. Currently, most studies focus on the Receiver Operating Characteristics Curve and the Area Under the Curve. On the other hand, the Youden index, widely applied in practice, is another comprehensive measurement for the performance of a diagnostic test. For a continuous-scale test classifying diseased a...