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Climate change includes the change of the long-term average values and the change of the tails of probability density functions, where the extreme events are located. However, obtaining average values are more straightforward than the high temporal resolution information necessary to catch the extreme events on those tails. Such information is difficult to get in areas lacking sufficient rain stations. Thanks to the development of Satellite Precipitation Estimates with a daily resolution, this problem has been overcome, so Extreme Precipitation Indices (EPI) can be calculated for the entire Colombian territory. However, Colombia is strongly affected by the ENSO (El Niño—Southern Oscillation) phenomenon. Therefore, it is pertinent to ask if the EPI’s long-term change due to climate change is more critical than the anomalies due to climate variability induced by the warm and cold phases of ENSO (El Niño and La Niña, respectively). In this work, we built EPI annual time series at each grid-point of the selected Satellite Precipitation Estimate (CHIRPSv2) over Colombia to answer the previous question. Then, the Mann-Whitney-Wilcoxon test was used to compare the samples drawn in each case (i.e., change tests due to both long-term and climatic variability). After performing the analyses, we realized that the importance of the change depends on the region analyzed and the considered EPI. However, some general conclusions became evident: during El Niño years (La Niña), EPI’s anomaly follows the general trend of reduction -drier conditions- (increase; -wetter conditions-) observed in Colombian annual precipitation amount, but only on the Pacific, the Caribbean, and the Andean region. In the Eastern plains of Colombia (Orinoquía and Amazonian region), EPI show a certain insensitivity to change due to climatic variability. On the other hand, EPI’s long-term changes in the Pacific, the Caribbean, and the Andean region are spatially scattered. Still, long-term changes in the eastern plains have a moderate spatial consistency with statistical significance.

The well-known Mann–Whitney–Wilcoxon (MWW) statistic is based on empirical distribution estimates. However, the data are often drawn from smooth populations. Therefore, the smoothness characteristic is not preserved. In addition, several authors have pointed out that empirical distribution is often an inadmissible estimate. Thus, in this work, we develop smooth versions of the MWW statistic based on smooth distribution function estimates. This approach preserves the data characteristics and allows the efficiency of the procedure to improve. In addition, our procedure is shown to be robust against a large class of dependent observations. Hence, by choosing a rectangular array of known distribution functions, our procedure allows the test to be a lot more reflective of the real data.

This paper is intended to provide the reader with an introduction to ranked set sampling, a statistical technique for data collection that generally leads to more efficient estimators than competitors based on simple random samples. Methods for obtaining ranked set samples are described, and the structural differences between ranked set samples and simple random samples are discussed. Properties of the sample mean associated with a balanced ranked set sample are developed. A nonparametric ranked set sample estimator of the distribution function is discussed and properties of a ranked set sample analog of the Mann-Whitney-Wilcoxon statistic are presented.

McGraw and Wong (1992) described an appealing index of effect size, called CL, which measures the difference between two populations in terms of the probability that a score sampled at random from the first population will be greater than a score sampled at random from the second. McGraw and Wong introduced this \"common language effect size statistic\" for normal distributions and then proposed an approximate estimation for any continuous distribution. In addition, they generalized CL to the n-group case, the correlated samples case, and the discrete values case. In the current paper a different generalization of CL, called the A measure of stochastic superiority, is proposed, which may be directly applied for any discrete or continuous variable that is at least ordinally scaled. Exact methods for point and interval estimation as well as the significance tests of the A = .5 hypothesis are provided. New generalizations ofCL are provided for the multi-group and correlated samples cases.

Animals that live in nests often face challenges like harsh environmental conditions, increased competition and severe predatory pressure super(1). In response to these stresses they relocate into new nests super(2). This movement is particularly complex in the case of ants as hundreds of colony members, immature young and stored resources need to be transferred. The dynamics of ant emigration remains to be thoroughly explored. However, it is understood that the route to the new site is indicated by pheromone trails in several species, whereas a few species use carrying or tandem running to transfer their nestmates to the new nest. Tandem running was first described by Adlerz super(3), and is the behaviour in which one ant follows another while maintaining physical contact. This behaviour is used in the context of relocation and recruitment of colony members for nest defence, raiding and foraging super(2).

As a popular real-time service on the Internet, Voice over Internet Protocol (VoIP) communication attracts more and more attention from the researchers in the information security field. In this study, we proposed a VoIP steganographic algorithm with variable embedding capacities, incorporating AES and key distribution, to realize a real-time covert VoIP communication. The covert communication system was implemented by embedding a secret message encrypted with symmetric cryptography AES-128 into audio signals encoded by PCM codec. At the beginning of each VoIP call, a symmetric session key (SK) was assigned to the receiver with a session initiation protocol-based authentication method. The secret message was encrypted and then embedded into audio packets with different embedding algorithms before sending them, so as to meet the realtime requirements of VoIP communications. For each audio packet, the embedding capacity was calculated according to the specific embedding algorithm used. The encryption and embedding processes were almost synchronized. The time cost of encryption was so short that it could be ignored. As a result of AES-based steganography, observers could not detect the hidden message using simple statistical analysis. At the receiving end, the corresponding algorithm along with the SK was employed to retrieve the original secret message from the audio signals. Performance evaluation with state-of-the-art network equipment and security tests conducted using the Mann-Whitney-Wilcoxon method indicated that the proposed steganographic algorithm is secure, effective, and robust.

In functional issues, due to lack of precise information and hypotheses and enough assumptions about distribution or the population parameters, the fuzzy nonparametric tests are used. Regarding the fact that the nonparametric tests are based upon ranking observations, it is important to rank the fuzzy observations in order to do nonparametric tests. In this article, a method of ranking fuzzy data is offered based on the D p,q —distance between two fuzzy numbers and the results of this method are evaluated and compared with other methods. When the data and hypotheses are not precise, the presented method is used to do nonparametric tests related to the median in one or two populations. Finally, some applied examples in management, psychology, and lifetime testing are provided to illustrate the efficiency of proposed approaches. Moreover, the proposed methods are examined to compare with some other existing methods and their effectiveness will be cleared via some numerical examples and some comparison studies.

Traditionally, the application of Bayesian testing procedures to classical nonparametric settings has been restricted by difficulties associated with prior specification, prohibitively expensive computation, and the absence of sampling densities for data. To overcome these difficulties, we model the sampling distributions of nonparametric test statistics—rather than the sampling distributions of original data—to obtain the Bayes factors required for Bayesian hypothesis tests. We apply this methodology to construct Bayes factors from a wide class of nonparametric test statistics having limiting normal distributions and illustrate these methods with data. Finally, we consider the extension of our methodology to nonparametric test statistics having limiting χ2 distributions.

Ranked-set samples have been shown to lead to improved methods of estimation in parametric settings under specific distributional forms when actual measurement of the sample observations is difficult but ranking them is relatively easy. The earliest work with ranked-set data concentrated on estimating a population mean or variance. More recently, a ranked-set sample estimator of a cumulative distribution function was developed and used to obtain a simultaneous confidence interval for the function. In this article, we take the next logical step and use this ranked-set empirical distribution function to construct distribution-free competitors to the standard Mann-Whitney-Wilcoxon estimation and testing procedures. The appropriate null distribution tables for the associated test are presented for the case of perfect ranking. Asymptotic relative efficiency comparisons between the simple random sample Mann-Whitney-Wilcoxon procedures and their ranked-set analogues are discussed, and the results of a small-sample Monte Carlo simulation study of the same are presented.