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Coverage-based NHPP SRGMs have been introduced in order to incorporate the coverage growth behavior into the NHPP SRGMs. The coverage growth function representing the coverage growth behavior during testing is an essential factor of the coverage-based NHPP SRGMs. This paper proposes a class of continuous-time coverage growth functions and shows its equivalence to the class of discrete-time coverage growth functions in [Park, J.-Y., Lee, G., & Park, J. H. (2007). A class of discrete time coverage growth functions for software reliability engineering. The Korean Communications in Statistics, 14,[497][498][499][500][501][502][503][504][505][506]. For the examination of usability of the proposed class, three coverage growth functions belonging to the class are applied to real data sets and compared.

High-throughput genomic technologies are leading to a paradigm shift in research of computational biology. Computational analysis with high-dimensional data and its interpretation are essential for the understanding of complex biological systems. Most biological data (e.g., gene expression and DNA sequence data) are high-dimensional, but consist of much fewer samples than predictors. Such high-dimension, low sample size (HDLSS) data often cause computational challenges in biological data analysis. A number of least absolute shrinkage and selection operator (LASSO) methods have been widely used for identifying biomarkers or prognostic factors in the field of bioinformatics. The LASSO solution has been improved through the development of the LASSO derivatives, including elastic-net, adaptive LASSO, relaxed LASSO, VISA, random LASSO, and recursive LASSO. However, there are several known limitations of the existing LASSO solutions: multicollinearity (particularly with different signs), subset size limitation, and the lack of the statistical test of significance. We propose a high-dimensional LASSO (Hi-LASSO) that theoretically improves a LASSO model providing better performance of both prediction and feature selection on extremely high-dimensional data. The Hi-LASSO alleviates bias introduced from bootstrapping, refines importance scores, improves the performance taking advantage of global oracle property, provides a statistical strategy to determine the number of bootstrapping, and allows tests of significance for feature selection with appropriate distribution. The performance of Hi-LASSO was assessed by comparing the existing state-of-the-art LASSO methods in extensive simulation experiments with multiple data settings. The Hi-LASSO was also applied for survival analysis with GBM gene expression data.

This paper proposes a new framework for measuring income inequality. The framework is based on the unequally distributed (UD) incomes that are obtained by removing the equally distributed parts from incomes. We then derive the normalized norm indexes from the cumulative distribution function and the unscaled Lorenz curve of the UD incomes. The relation between the normalized norm indexes and the popular Gini coefficient and coefficient of variation (CV) shows that the Gini coefficient and CV represent only parts of income inequality. We analyze example income distributions and the Luxembourg Income Study datasets to show that the normalized norm indexes evaluate income inequality appropriately and solve the negative income problem. Keywords Coefficient of variation • Gini coefficient • Income inequality • 1 Norm • 2 Norm • Normalized norm index • Rawlsian index • Unequally distributed income JEL Classification C43 • D31 • D63 B Joongyang Park

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