A contribution to multivariate L-moments: L-comoment matrices

Spatial based drought assessment: Where are we heading? A review on the current status and future

Droughts are the most spatially complex natural hazards that exert global impacts and are further aggravated by climate change. The investigation of drought events is challenging as it involves numerous factors ranging from detection and assessment to modelling, management and mitigation. The analysis of these factors and their quantitative assessments have significantly evolved in recent times. In this paper, we review recent methods used to examine and model droughts from a spatial viewpoint. Our analysis was conducted at three spatial scales (point-wise, regional and global) and we evaluated how recent spatial methods have advanced our understanding of drought through case study examples. Further, we also examine and provide a broad overview of relevant case studies related to future drought occurrences under climate change. This study is a comprehensive synthesis of the various quantitative techniques used to assess the spatial characteristics of droughts at different spatial scales, and not an exhaustive review of all drought aspects. However, this serves as a basis for understanding the key milestones and advances accomplished through new spatial concepts relative to the traditional approaches to study drought. This work also aims to address the gaps in knowledge that are in need of further attention and provides recommendations to improve our understanding of droughts.

Simulating Univariate and Multivariate Nonnormal Distributions through the Method of Percentiles

This article derives a standard normal-based power method polynomial transformation for Monte Carlo simulation studies, approximating distributions, and fitting distributions to data based on the method of percentiles. The proposed method is used primarily when (1) conventional (or L) moment-based estimators such as skew (or L-skew) and kurtosis (or L -kurtosis) are unknown or (2) data are unavailable but percentiles are known (e.g., standardized test score reports). The proposed transformation also has the advantage that solutions to polynomial coefficients are available in simple closed form and thus obviates numerical equation solving. A procedure is also described for simulating power method distributions with specified medians, inter-decile ranges, left-right tail-weight ratios (skew function), tail-weight factors (kurtosis function), and Spearman correlations. The Monte Carlo results presented in this study indicate that the estimators based on the method of percentiles are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias. It is also shown that the percentile power method can be modified for generating nonnormal distributions with specified Pearson correlations. An illustration shows the applicability of the percentile power method technique to publicly available statistics from the Idaho state educational assessment.