Cubic transmuted (CT) distributions were introduced recently by Granzotto, Louzada and Balakrishnan (Journal of Statistical Computation and Simulation 87 (2017) 2760–2778). In this article, we derive Shannon entropy, Gini’s mean difference and Fisher information (matrix) for CT distributions and establish some of their theoretical properties. In addition, we propose cubic transmuted Shannon entropy and cubic transmuted Gini’s mean difference. The CT Shannon entropy is expressed in terms of Kullback-Leibler divergences, while the CT Gini’s mean difference is shown to be connected with energy distances. We show that the Kullback-Leibler and Chi-square divergences are free of the underlying parent distribution. Finally, we carry out some simulation studies for the proposed information measures from an inferential viewpoint.

Predicting future values of a time series is often insufficient; understanding the complete uncertainty surrounding these predictions is crucial. This necessity has led to the use of conditional density estimators (CDEs). However, many existing CDEs for time series either impose rigid parametric assumptions or exhibit scalability issues when dealing with a high number of covariates. Concurrently, a substantial body of literature has developed around regression methods that offer single-point predictions. In this paper, we introduce a novel approach called FlexCodeTS, which harnesses the power of regression methods to provide enhanced estimates of conditional densities. Through extensive experiments, we demonstrate that FlexCodeTS exhibits strong performance across both real-world and simulated datasets. Furthermore, we establish convergence rates and illustrate how FlexCodeTS can attain rapid convergence by adopting a regression technique that best aligns with the underlying data structure. Finally, we show that FlexCodeTSprovides a straightforward yet accurate measure of variable importance assessment for time series data.

Classical estimators often suffer from inefficiency when data is contaminated with outliers, leading to skewed results. To overcome this issue, we propose robust estimators for estimating the population mean in various ranked set sampling scenarios. Our research introduces an innovative technique that enhances Zaman estimators under simple random sampling (SRS) and extends these advancements to ranked set sampling (RSS) and median-ranked set sampling (MRSS) designs. Real and simulated datasets, incorporating outliers, are employed to compare the performance of the proposed robust estimator using robust regression methods, that is, LAD, LMS, LTS, Huber-M, Hampel-M, Turkey-M, and Huber-MM, against classical and Zaman estimators. The results demonstrate the superior performance of our robust regression-type estimator in effectively handling outliers.

Originally suggested for the blood testing problem by Dorfman in 1943, an idea of Group Testing (GT) has found many applications in other fields as well. Among many (binomial) GT procedures introduced since then, in 1990, Yao and Hwang proposed the Pairwise Testing Algorithm (PTA) and demonstrated that PTA is the unique optimal nested GT procedure provided the probability of contamination lies in $\left(1-\frac{\sqrt{2}}{2},\frac{3-\sqrt{5}}{2}\right)$. Despite the fundamental nature of the result, PTA did not receive considerable attention in the literature. In particular, even its basic probabilistic properties remained unexplored. In this paper, we fill the gap. This is achieved through derivation of an explicit form of the moment generating function (MGF) for the total number of tests ${\mathit{T}}_{\mathit{n}}$ required by the PTA procedure. By making use of MGF, we obtain first moments of ${\mathit{T}}_{\mathit{n}}$ and characterize its asymptotic behaviour by establishing Law of Large Numbers, Central Limit Theorem and Large Deviation Principle.

Exponential chart is widely used to monitor the high-yield processes, i.e., where the failure rate is too low. The exponential chart with runs and scans rules (RSR) scheme has been suggested in the literature for improved performance, especially, for small to moderate shifts. A single sample is used in such a control chart to determine whether the process is in-control (IC) or out-of-control (OOC). However, real-world scenarios may not always permit such conclusive decisions with a single sample. Repetitive sampling can be considered an alternative to single sampling when there is a dispute about the process based on a single sample. In this article, we proposed the exponential chart with the RSR scheme using repetitive sampling and evaluated its performance in terms of average run length $(\mathrm{ARL})$. It is found that the proposed chart is $\mathrm{ARL}$-biased. Therefore, we present a method for designing an $\mathrm{ARL}$-unbiased exponential chart with the RSR scheme using repetitive sampling. The OOC $\mathrm{ARL}$ for various shift levels has been computed in order to assess the proposed chart’s efficiency. The advantages of the suggested monitoring scheme have been examined and compared with both the existing $\mathrm{ARL}$-unbiased exponential chart using repetitive sampling and the RSR scheme using single sampling. Further, the proposed chart has been compared with the existing control chart using single sampling with roughly matched sample size to the IC average sample size $({\mathrm{ASS}}_0)$ of repetitive sampling and found to be the control chart using repetitive sampling is efficient with smaller $\mathrm{ASS}$ values. Finally, in order to illustrate the designed chart an example has been given.

Andrei Toom, who died in September 2022, contributed some of the most fundamental results on probabilistic cellular automata. We want to acquaint the reader with these and will also try to give the reader a look at the environment in which they were born. Toom was an original and strong personality, and other aspects of his life (education, literature) will also deserve mention.

Motivated by a chronic kidney disease dataset, we propose a Bayesian model for clustered semicompeting risks data based on Archimedean copulas, allowing for treatment switching. We consider the modeling of both independent and clustered observations. For clustered data, random effects are included to consider the dependence among observations in the same group. For the Clayton copula, we provide theoretical results for the posterior distribution when improper priors are used. A simulation study was conducted to evaluate the performance of the proposed model. Finally, the results of the analysis of chronic kidney disease data are discussed.

In this paper, we investigate the functional central limit theorem and the Marcinkiewicz strong law of large numbers for U-statistics having absolutely regular data and taking value in a separable Hilbert space. The novelty of our approach consists in using coupling in order to formulate a deviation inequality for original U-statistic, where the upper bound involves the mixing coefficient and the tail of several U-statistics of i.i.d. data. The presented results improve the known results in several directions: the case of metric space valued data is considered as well as that of Hilbert space valued kernels, and the mixing rates are less restrictive in a wide range of settings.