Introduction While product review systems that collect and disseminate opinions about products from recent buyers (Table 1) are valuable forms of word-of-mouth communication, evidence suggests that they are overwhelmingly positive. Kadet notes that most products receive almost five stars. Chevalier and Mayzlin also show that book reviews on Amazon and Barnes & Noble are overwhelmingly positive. Is this because all products are simply outstanding? However, a graphical representation of product reviews reveals a J-shaped distribution (Figure 1) with mostly 5-star ratings, some 1-star ratings, and hardly any ratings in between. What explains this J-shaped distribution? If products are indeed outstanding, why do we also see many 1-star ratings? Why aren't there any product ratings in between? Is it because there are no "average" products? Or, is it because there are biases in product review systems? If so, how can we overcome them? The J-shaped distribution also creates some fundamental statistical problems. Conventional wisdom assumes that the average of the product ratings is a sufficient proxy of product quality and product sales. Many studies used the average of product ratings to predict sales. However, these studies showed inconsistent results: some found product reviews to influence product sales, while others did not. The average is statistically meaningful only when it is based on a unimodal distribution, or when it is based on a symmetric bimodal distribution. However, since product review systems have an asymmetric bimodal (J-shaped) distribution, the average is a poor proxy of product quality. This report aims to first demonstrate the existence of a J-shaped distribution, second to identify the sources of bias that cause the J-shaped distribution, third to propose ways to overcome these biases, and finally to show that overcoming these biases helps product review systems better predict future product sales. We tested the distribution of product ratings for three product categories (books, DVDs, videos) with data from Amazon collected between February--July 2005: 78%, 73%, and 72% of the product ratings for books, DVDs, and videos are greater or equal to four stars (Figure 1), confirming our proposition that product reviews are overwhelmingly positive. Figure 1 (left graph) shows a J-shaped distribution of all products. This contradicts the law of "large numbers" that would imply a normal distribution. Figure 1 (middle graph) shows the distribution of three randomly-selected products in each category with over 2,000 reviews. The results show that these reviews still have a J-shaped distribution, implying that the J-shaped distribution is not due to a "small number" problem. Figure 1 (right graph) shows that even products with a median average review (around 3-stars) follow the same pattern.

This paper presents a new method to accurately characterize and predict the annual variation of wind conditions. Estimation of the distribution of wind conditions is necessary (i) to quantify the available energy (power density) at a site, and (ii) to design optimal wind farm configurations. We develop a smooth multivariate wind distribution model that captures the coupled variation of wind speed, wind direction, and air density. The wind distribution model developed in this paper also avoids the limiting assumption of unimodality of the distribution. This method, which we call the Multivariate and Multimodal Wind distribution (MMWD) model, is an evolution from existing wind distribution modeling techniques. Multivariate kernel density estimation, a standard non-parametric approach to estimate the probability density function of random variables, is adopted for this purpose. The MMWD technique is successfully applied to model (i) the distribution of wind speed (univariate); (ii) the distribution of wind speed and wind direction (bivariate); and (iii) the distribution of wind speed, wind direction, and air density (multivariate). The latter is a novel contribution of this paper, while the former offers opportunities for validation. Ten-year recorded wind data, obtained from the North Dakota Agricultural Weather Network (NDAWN), is used in this paper. We found the coupled distribution to be multimodal. A strong correlation among the wind condition parameters was also observed.

There were continuous positive Arctic Oscillation index (AOI) and large-scale weather and climate anomalies in the Northern Hemisphere in the winter and spring of 2019/2020, and the relationship between these anomalies is an important issue for subseasonal to seasonal (S2S) predictability. This study shows that an AOI event with splitting characteristics occurred in the Northern Hemisphere and that there was a gap between the periods in event, which has not been observed in any of the 12 previous positive AOI events. The 3 stages of upward propagating planetary wave (UPPW) variation caused the gap between the periods. First, in early November, the westerly flow from the troposphere to the stratosphere weakened, resulting in persistent weak UPPWs that allowed a strong polar vortex to form. Then, the two strong UPPWs in January and early February caused the original westerlies to decelerate and induced warming in the lower stratosphere. However, the UPPWs caused only moderate changes in the geopotential height and temperature due to the strong polar vortex that had formed in the previous stage. This moderate AOI decline resulted in the conditions that divided the positive event into two periods. Finally, the low-level westerlies became stronger and strengthened the UPPWs into the stable stratosphere, which ended the second positive AOI period in late March. The role of zonal circulation anomalies (ZCA) in the upper stratosphere as metrics of and intermediates in UPPW-AO interactions is revealed in this study. The typical ZCA development mode was identified by statistical analysis and a composite treatment based on eight historical positive AOI events. In this mode, when strong UPPWs occur and lead to the consequent propagation of the ZCA from the stratosphere to the troposphere, the geopotential height field in the lower troposphere changes away from a typical AO mode; eventually, the AOI becomes abnormal. The temperature anomaly and ZCA produced in the two positive AOI periods during the winter and spring of 2019/2020 led to increasing precipitation in the eastern polar region, northern Asia, and areas along 60°N latitude.

Recently, the assortative mixing of complex networks has received much attention partly because of its significance in various social networks. In this paper, a new scheme to generate an assortative growth network with given degree distribution is presented using a Monte Carlo sampling method. Since the degrees of a great number of real-life networks obey either power-law or Poisson distribution, we employ these two distributions to grow our models. The models generated by this method exhibit interesting characteristics such as high average path length, high clustering coefficient and strong rich-club effects.