International Journal of Statistics and Probability, Issue: Vol.14, No.4

The Extended H Theorem and the Extended Entropy

Tue, 16 Dec 2025 18:25:06 +0000

This article introduces an extension of the H theorem to an arbitrary order d ≥1 . The extended H theorem defines the extended entropy Hd for a given distribution and identifies the distribution function f_d(v) that maximizes entropy H_d . When d=1, H_1 corresponds to the original entropy defined by Boltzmann, and the distribution that maximizes it is the Boltzmann distribution. For d=2 , the maximizing distribution is the Rayleigh distribution. For d=3 , the maximizing distribution is the Maxwell distribution. Therefore, in the three-dimensional physical world, the correct speed distribution of gas particles is the Maxwell distribution, which maximizes the extended entropy H_3 rather than the original entropy H_1 . The result distribution f_d(v) that maximizes the extended entropy H_d for any d≥1 is derived and applied to gases that include rotational and strain energy in addition to translational energy. Numerical validation supporting these findings is also presented.

Testing for the Eigenvector Based on the Multiple Correlation Coefficient

Mon, 30 Mar 2026 23:49:53 +0000

This article has been corrected. See: https://ccsenet.org/journal/index.php/ijsp/article/view/0/53036

Real-time Application of Optimal Experimental Design to Study Factors Related to Doubles Pickleball Match Outcome

Tue, 16 Dec 2025 17:18:57 +0000

In kinesiology and exercise science, researchers want to identify factors associated with players’ performance. In racquet sports, matches are played in a tournament format, and researchers often find observational data for their studies rather than collecting experimental data. Even when an experiment is conducted, which is very rare in literature, a randomized design has been considered to produce unbiased results. Given a small number of participants and limited time, in theory, an optimal experimental design can produce more statistical information about parameters of interest than a completely randomized design. This article includes simulations and a real application of an optimal experimental design to racquet sports research. In our research plan, there were some logistical considerations (e.g., no replicated matches, computation time), and simulations demonstrated that the c- and D-optimal designs result in higher statistical power for single- and multiple-parameter hypothesis testing, respectively, than the completely randomized design. For our research, the D-optimal design was applied to a doubles pickleball tournament with 16 subjects and one half of a day. Participants’ fitness and skill levels were measured in the morning, the doubles tournament was designed in real time on site using a pre-written algorithm, and the tournament design was executed on the same day. To make this computation accessible, an interactive applet is provided in the Appendix of this article with instructions.

A Modified Normalizing Transformation Statistic Based on Kurtosis Testing Multivariate Normality

Mon, 02 Mar 2026 17:54:33 +0000

In this paper, we consider a testing problem of multivariate normality (MVN). We deal with the kurtosis test statistic based on Mardia's multivariate kurtosis as an MVN test and propose a modified normalizing transformation (NT) statistic. The accuracy of the normal approximation of the proposed test statistic through a Monte Carlo simulation is investigated. The results of empirical power of a modified NT statistic are presented. Alternative distributions are chosen to represent different types of departure from multivariate normality. Moreover, to compare the empirical power of the modified NT statistic, we target a NT statistic, the improved Mardia's test statistic, and the Henzer-Zirkler test statistic. Finally, an example is provided.

Time-Frequency Segmentation of Northern Fur Seal Diving Behavior Using Autoregressive Spectral Analysis

Thu, 01 Jan 2026 01:28:46 +0000

Analyzing marine animal movement data is essential for understanding at-sea behavior. This study introduces an autoregressive spectral analysis framework for assessing time-varying movement dynamics in northern fur seals. A time segmentation approach, based on an AR(3) model with Yule-Walker estimation, is employed to estimate movement parameters and characterize behavioral variability over time. The method captures temporal changes in movement persistence and oscillatory patterns, enabling the segmentation of behavioral states such as resting, exploratory diving, and active foraging. Using high-resolution vertical velocity data from eight northern fur seals tagged at the Pribilof Islands, Alaska, the analysis shows that a 26-minute window with 50% overlap achieves stationarity while preserving behavioral transitions. Spectral analysis identifies mid-frequency oscillations associated with active diving, low-frequency signals corresponding to exploratory diving, and spectral shifts indicative of behavioral transitions. Comparisons with non-parametric methods highlight the advantages of AR(3)-based spectral estimation in producing smooth and interpretable frequency-based insights. The framework provides new perspectives on fur seal foraging strategies and behavioral adaptations to environmental conditions. It also offers a computationally efficient alternative to state-space models, with potential for broader application in studying movement patterns of marine predators to support ecological and conservation research.

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 14, No. 4

Thu, 01 Jan 2026 01:32:24 +0000

Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 14, No. 4