Progressively Type-II right censored order statistics from discrete distributions

Progressively Type-II right censored order statistics from continuous distributions have been studied rather extensively in the literature; see Balakrishnan and Aggarwala [2000. Progressive Censoring: Theory, Methods and Applications. Birkhäuser, Boston]. In this paper, we derive the joint and marginal distributions of progressively Type-II right censored order statistics from discrete distributions. We then use these distributions to show the non-Markovian property as well as to discuss some properties in the special case of the geometric distribution.     

Comparison of elementary price indices

Abstract

Most countries use the Dutot, Jevons or Carli index for the calculation of their Consumer Price Index (CPI) at the lowest (elementary) level of aggregation. The choice of the elementary formula for inflation measurement does matter and the effect of the change of the index formula was estimated by the Bureau of Labor Statistics. It has been shown that difference between elementary indices can be explained in terms of changes in price dispersion. In this article, we extend these results comparing both population and sample elementary indices. We assume that prices from two compared time moments are log-normally distributed and correlated. Under the above-mentioned assumption, we provide formulas for biases and mean-squared errors of main elementary indices.     

On prediction of population and subpopulation characteristics for future periods

The estimation or prediction of population characteristics based on the sample information is the key issue in survey sampling. If the sample sizes in subpopulations (domains) are large enough, similar methods as used for the whole population can be used to estimate or to predict subpopulations characteristics as well. To estimate or to predict characteristics of domains with small or even zero sample sizes, small area estimation methods “borrowing strength” from other subpopulations or time periods are widely used. We extend this problem and study methods of prediction of future population and subpopulations’ characteristics based on the longitudinal data.     

Remarks on the L1 distance in statistical data analysis

We propose the L₁ distance between the distribution of a binned data sample and a probability distribution from which it is hypothetically drawn as a statistic for testing agreement between the data and a model. We study the distribution of this distance for N-element samples drawn from k bins of equal probability and derive asymptotic formulae for the mean and dispersion of L₁ in the large-N limit. We argue that the L₁ distance is asymptotically normally distributed, with the mean and dispersion being accurately reproduced by asymptotic formulae even for moderately large values of N and k.     

An eigenproblem approach to optimal equal-precision sample allocation in subpopulations

Allocation of samples in stratified and/or multistage sampling is one of the central issues of sampling theory. In a survey of a population often the constraints for precision of estimators of subpopulations parameters have to be taken care of during the allocation of the sample. Such issues are often solved with mathematical programming procedures. In many situations it is desirable to allocate the sample, in a way which forces the precision of estimates at the subpopulations level to be both: optimal and identical, while the constraints of the total (expected) size of the sample (or samples, in two-stage sampling) are imposed. Here our main concern is related to two-stage sampling schemes. We show that such problem in a wide class of sampling plans has an elegant mathematical and computational solution. This is done due to a suitable definition of the optimization problem, which enables to solve it through a linear algebra setting involving eigenvalues and eigenvectors of matrices defined in terms of some population quantities. As a final result, we obtain a very simple and relatively universal method for calculating the subpopulation optimal and equal-precision allocation which is based on one of the most standard algorithms of linear algebra (available, e.g., in R software). Theoretical solutions are illustrated through a numerical example based on the Labour Force Survey. Finally, we would like to stress that the method we describe allows to accommodate quite automatically for different levels of precision priority for subpopulations.     

Patterns of plant invasions at small spatial scale correspond with that at the whole country scale

Urban Ecosystems - Invasions were studied at different spatial scales, however these scales were rarely compared. The aim of this study is to compare the rate of expansion of eight alien plant...     

Three dimensions of the public sphere on Facebook

The article provides an empirical analysis of the online public sphere in the three dimensions introduced by Dahlgren (2005): structural, representational and interactional. The main subject of analysis is the largest social networking site – Facebook – and Polish users’ activity on the Facebook Pages of political parties and politicians. The researchers analysed data about all users active on those Pages during two 4-month periods in 2013 and 2015. The results of the study show that only a small fraction of Facebook users are active in public political discussions that take place on political Facebook Pages (structural dimension). However, the level of engagement depends on the current political events taking place within the public sphere offline, and users are more active during electoral campaigns. Moreover, Facebook does not provide an alternative public sphere for political actors that are less present in mainstream media. Parties and politicians that are visible in traditional media are also attracting active fans in social media (representational dimension). Nonetheless, non-parliamentary groups have more active fans than would result only from their popularity in mainstream media. Finally, the online public on Facebook is fragmented and clustered into homogenous political groups (interactional dimension), thus supporting the hypothesis on ‘echo chambers’ presented by Sunstein (2001). The divisions are smaller when there are significantly more users involved. However, most of these cross-cutting links are the result of the electoral campaign.     

An ‘ordinary man’s’ protest: self-immolation as a radical political message in Eastern Europe today and in the past

The article describes the tradition of self-immolation in Eastern Europe as a form of radical protest during periods of structural crisis. The authors describe cases of self-immolation (Ryszard Siwiec, Jan Palach, Evzen Plocek, Musa Mamut) which took place in the communist period, particularly in the 1960s and 1970s. In the context of Eastern European tradition, they also describe the last case of self-immolation, when Piotr Szcz?sny set himself on fire in Warsaw in October 2017 to protest against the authoritarian rule of the Law and Justice (PiS) party in Poland. After this incident, Piotr Szcz?sny and his memory have become an element of the ‘culture of protest’ in Poland. Quotes from his manifesto began to appear on walls and during anti-government demonstrations. Piotr Szcz?sny has also become a protagonist of protest songs.