Andrei Volodin

1. Complete convergence, complete moment convergence, complete integral convergence, and their relationship is investigated in this article. The definitions of these concepts will be reviewed below...

1. During the last two decades, numerous families of probability distributions have been developed to provide greater flexibility in statistical modeling. Many of these approaches are based on appl...

Two-parameter exponential distribution has been widely used in research involving lifetime data, survival analysis, medical research, and reliability assessment. Since variables following this distribution are continuous, the population mean is often regarded as a key parameter of interest. In this paper, confidence intervals for the mean of a two-parameter exponential population are developed based on the joint asymptotic normality of the method of moments estimators, derived using the Delta method. The proposed asymptotic confidence intervals are compared with Wald-type confidence intervals in terms of coverage probability and average interval width. The performance of the proposed intervals is evaluated using Monte Carlo simulation, where particular attention is given to their coverage probability and mean interval width. The performance is further illustrated through a real-data application using daily PM2.5 concentration data from Bangkok, Thailand. Simulation, and the theoretical results indicate that the performance of estimators in the two-parameter exponential distribution improves as the sample size increases. Small samples lead to biased and unstable estimates, with wider confidence intervals and lower coverage probabilities, whereas moderate and large samples yield more accurate and stable results. For large samples, bias becomes negligible, variances approach the corresponding theoretical values, and coverage probabilities and interval widths approach the nominal level, confirming consistency and asymptotic efficiency.

A class of distributions is determined within which the test based on the sum of the squares of the sample coefficients of skewness and kurtosis (so-called Jarque–Bera test) is the asymptotically most stringent invariant test. This class consists of Edgeworth expansions of infinitely divisible distributions. Based on the Jarque–Bera test, we propose a statistical procedure for the multiple testing of a hypothesis for normality over a large number of samples with d-risk restrictions (pFDR) of the first kind. The power properties of the d-guarantee multiple hypotheses testing are illustrated using statistical modeling data in comparison with the most commonly used Benjamini–Hochberg test. The procedure is also applied to testing the hypothesis of normality for real data arrays representing the results of observations of the expression of a gene in each member of a group of patients.

The cosine partially geometric distribution, a weighted probability model, is introduced for analyzing over-dispersed discrete data, exemplified by weekly counts of patients over 60 diagnosed with eye inflammation in Phitsanulok province in 2021. Its key properties, including the cumulative distribution function, moment generating function, first two raw moments, and maximum likelihood estimation, are derived, highlighting its practical applicability in real-world count data modeling.

This paper substitutes the six-deck card model with an effective and respondent-friendly three-deck randomized response paradigm. Although the six-deck randomized response technique is excellent in protecting respondents’ privacy in sensitive surveys, it makes the process much complicated for them. This work would propose preserving respondent secrecy while lowering response burden and enhancing cooperation through modification of the model to use only three decks of cards. The proposed three-deck model extends the work of [1] and reveals that, in opposition to the earlier models, the maximum likelihood estimator for population percentage remains objective with reduced variance. Empirical works show that the three-deck paradigm achieves considerable efficiency gains, particularly when the share of sensitive characteristics is high or rare. These results suggest that this three-deck model, offering simplicity and privacy without any loss of statistical accuracy, may be a competitive alternative to intricate multi-deck systems.