Measures of Variability for Qualitative Variables Using the R Software

Although there are many measures of variability for qualitative variables, they are little used in social research, nor are they included in statistical software. The aim of this article is to present six measures of variation for qualitative variables of simple calculation, as well as to facilitate their use by means of the R software. The measures considered are, on the one hand, Freemans variation ratio, Morals universal variation ratio, Kvalseths standard deviation from the mode, and Wilcoxs variation ratio which are most affected by proximity to a constant random variable, where the measures of variability for qualitative variables reach their minimum value of 0. On the other hand, the Gibbs-Poston index of qualitative variation and Shannons relative entropy are included, which are more affected by the proximity to a uniform distribution, where the measures of variability for qualitative variables reach their maximum value of 1. Point and interval estimation are addressed. Bootstrap by the percentile and bias-corrected and accelerated percentile methods are used to obtain confidence intervals. Two calculation situations are presented: with a sample mode and with two or more modes. The standard deviation from the mode among the six considered measures, and the universal variation ratio among the three variation ratios, are particularly recommended for use.

Diagnosis of Seasonal Variations of Tropical Cyclogenesis over the South China Sea Using a Genesis Potential Index

This study examines the seasonal variations of tropical cyclogenesis over the South China Sea (SCS) using a genesis potential (GP) index developed by Emanuel and Nolan. How different environmental factors (including low-level vorticity, mid-level relative humidity, vertical wind shear, and potential intensity) contribute to these variations is investigated. Composite anomalies of the GP index are produced for the summer and winter monsoons separately. These composites replicate the observed seasonal variations of the observed frequency and location of tropical cyclogenesis over the SCS. The degree of contribution by each factor in different regions is determined quantitatively by producing composites of modified indices in which only one of the contributing factors varies, with the others set to climatology. Over the northern SCS, potential intensity makes the largest contributions to the seasonal variations in tropical cyclogenesis. Over the southern SCS, the low-level relative vorticity plays the primary role in the seasonal modulation of tropical cyclone (TC) genesis frequency, and the vertical wind shear plays the secondary role. Thermodynamic factors play more important roles for the seasonal variations in tropical cyclogenesis over the northern SCS, while dynamic factors are more important in the seasonal modulation of TC genesis frequency over the southern SCS.

A variation pixels identification method based on kernel spatial attraction model and local entropy for robust endmember extraction

A variation pixels identification method was proposed aiming at depressing the effect of variation pixels, which dilates the theoretical hyperspectral data simplex and misguides volume evaluation of the simplex. With integration of both spatial and spectral information, this method quantitatively defines a variation index for every pixel. The variation index is proportional to pixels local entropy but inversely proportional to pixels kernel spatial attraction. The number of pixels removed was modulated by an artificial threshold factor α. Two real hyperspectral data sets were employed to examine the endmember extraction results. The reconstruction errors of preprocessing data as opposed to the result of original data were compared. The experimental results show that the number of distinct endmembers extracted has increased and the reconstruction error is greatly reduced. 100% is an optional value for the threshold factor α when dealing with no prior knowledge hyperspectral data.

Study on quality evaluation model in multi-station assembly processes

Based on features of dimension variation propagation in multi-station assembly processes,a new quality evaluation model of assembly processes is established. Firstly,the error source of multi-station assembly system is analyzed,the relationship of dimension variation propagation in multi-station assembly processes is studied and the state equation for variation propagation is constructed too. Then,the feature parameters which influence variation propagation and accumulation in multi-station assembly processes are found to evaluate quality characteristic of the assembly system. Through the derivation of equation on dimension variation propagation,station coefficient matrices which are combined and conversed to determine the max eigenvalue are educed. The max eigenvalue is multiplied by the weight coefficient to establish the quality evaluation model in multi-station assembly processes. Furthermore,assembly variation indexes are proposed to judge of the assembly technology process. Finally,through the practical example,the application of the model and assembly variation indexes are presented.

Definition of Arctic and Antarctic Sea Ice Variation Index

It is well known that varying of the sea ice not only in the Antarctic but also in the Arctic has an active influence on the globe atmosphere and ocean. In order to understand the sea ice variation in detail, for the first time, an objective index of the Arctic and Antarctic sea ice variation is defined by projecting the monthly sea ice concentration anomalies poleward of 20°N or 20°S onto the EOF (empirical orthogonal function)-1 spatial pattern. Comparing with some work in former studies of polar sea ice, the index has the potential for clarifying the variability of sea ice in northern and southern high latitudes.

Thermal stability of permafrost under U-shaped crushed rock embankment of the Qinghai-Tibet Railway

The U-shaped crushed rock embankment(UCRE),of which widely utilized in the permafrost regions along the Qinghai-Tibet Railway,has the capability to rapidly reduce the ground temperature of the underlying permafrost.However,there remains uncertainty regarding the adaptation of UCRE to climate change and its long-term cooling trend.This study focuses on nine UCRE monitoring sites along the Qinghai-Tibet Railway to analyze the dynamic variations of the ground temperature underlying permafrost from 2006 to 2020.The efficiency of UCRE in stabilizing permafrost temperature in different permafrost zones is evaluated by considering the permafrost table,ground temperature,and MAGT,as well as the temperature difference between the top and bottom of the crushed rock layer and the ground temperature variation index(GTVI).The results show that UCRE is suitable for application in extremely unstable warm permafrost regions where the MAGT is higher than-0.5℃.Moreover,UCRE effectively diminishes the disparity in permafrost thermal stability between the sunny and shaded shoulders of the embankment.The short-term and long-term effect of cooling permafrost is experiencing a change related with permafrost stability.Notably,in stable cold permafrost regions with MAGT lower than-1.5℃,the long-term cooling effect of UCRE on permafrost seems to gradually di-minishes,but UCRE continues to fulfill the role of stabilizing the underlying permafrost thermal state over the long-term.These results show that UCRE can quickly restore and stabilize the thermal state of permafrost in the early stages of construction,and adapt to the influence of future climate change.The findings provide important guidance for understanding the variations of permafrost thermal stability beneath the embankment in permafrost regions,as well as for improving the embankment stability and operational safety of the Qinghai-Tibet Railway.

Extraction of lacunarity variation index for revealing the slope pattern in the Loess Plateau of China

Lacunarity analysis is frequently used in multiscale and spatial pattern studies.However,the explanation for the lacunarity analysis results is limited mainly at a qualitative description level.In other words,this approach can be used to judge whether the spatial pattern of the objective is regular,random or aggregated in space.The lacunarity analysis,however,cannot afford many quantitative information.Therefore,this study proposed the lacunarity variation index(LVI)to reflect the rates of variation of lacunarity with the resolution.In comparison with lacunarity analysis,the simulated experiments show that the LVI analysis can distinguish the basic spatial pattern of the geography objects more clearly and detect the scale of aggregated data.The experiment showed that different slope types in the Loess Plateau display aggregated patterns,and the characteristic scales of these patterns were detected using the slope pattern in the Loess Plateau as the research data.This study can improve the spatial pattern analysis and scale detecting methods,as well as provide a new method for landscape and vegetation community pattern analyses.Lacunarity analysis is frequently used in multiscale and spatial pattern studies.However,the explanation for the lacunarity analysis results is limited mainly at a qualitative description level.In other words,this approach can be used to judge whether the spatial pattern of the objective is regular,random or aggregated in space.The lacunarity analysis,however,cannot afford many quantitative information.Therefore,this study proposed the lacunarity variation index(LVI)to reflect the rates of variation of lacunarity with the resolution.In comparison with lacunarity analysis,the simulated experiments show that the LVI analysis can distinguish the basic spatial pattern of the geography objects more clearly and detect the scale of aggregated data.The experiment showed that different slope types in the Loess Plateau display aggregated patterns,and the characteristic scales of these patterns were detected using the slope pattern in the Loess Plateau as the research data.This study can improve the spatial pattern analysis and scale detecting methods,as well as provide a new method for landscape and vegetation community pattern analyses.