Although individuals may exhibit both gradual and abrupt changes in their dynamic properties as shaped by both slowly accumulating influences and acute events, existing statistical frameworks offer limited capacity for the simultaneous detection and representation of these distinct change patterns. We propose a Bayesian regime-switching (RS) modelling framework and an entropy measure adapted from the frequentist framework to facilitate simultaneous representation and testing of postulates of gradual and abrupt changes. Results from Monte Carlo simulation studies indicated that using a combination of entropy and information criterion measures such as the Bayesian information criterion was consistently most effective at facilitating the selection of the best-fitting model across varying magnitudes of abrupt changes. We found that slight lower entropy thresholds may be helpful in facilitating the selection of longitudinal models with RS properties as this class of models tended to yield lower entropy values than conventional thresholds for reliable classification in cross-sectional mixture models-even under satisfactory parameter recovery and classification results. We fitted the proposed models and other candidate models to the data collected from an intervention study on the psychological well-being (PWB) of college-attending early adults. Results suggested abrupt, regime-related transitions in the intra-individual variability levels of PWB dynamics among some participants following the intervention period. Practical usage of the entropy measure in conjunction with other model selection measures, and guidelines to enhance simultaneous detection of true abrupt and gradual changes are discussed.

Conventional imaging techniques such as SPECT and PET cannot directly identify the positions of individual decaying nuclei. As such, they heavily rely on statistical backprojection for image point reconstruction. Therefore, this study explores an alternative approach using non-collinear gamma-ray cascade emissions, which are emitted directly from the decay position and unaffected by positron movement. Detecting these cascades in coincidence allows precise localization of decay events, enabling direct image point reconstruction. To evaluate this concept, GATE Monte Carlo simulation was used to simulate the cascade emission from 111In-ion point sources and detection using collimated small animal PET scanner. Finally, a custom image reconstruction algorithm was developed to estimate the three-dimensional position of a decaying nucleus by calculating the midpoint of the shortest segment, or the intersection, between two collimator projections from a valid coincidence event. The results show that at the center of the field of view, image sensitivities of 22.2 cps/MBq in air and 20.0 cps/MBq in a PMMA phantom were achieved. Furthermore, a spatial resolution of 4.1 mm FWHM was obtained in the transaxial direction and 7.6 mm FWHM in the axial direction. The imaging system is capable of resolving two-point sources separated by 8.0 mm (transaxial) and 10.0 mm (axial). The results from this simulation study indicate that the proposed imager with its image reconstruction method surpasses conventional PET and SPECT in emission point localization accuracy.

The graded response model (GRM) is commonly used in psychometrics to analyze ordinal response data. Despite its growing application in scale development and validation, sample size recommendations-such as those provided by the COSMIN guidelines (e.g., n ≥ 1000)-are often based on expert consensus rather than empirical validation. Furthermore, the extent to which the number of items (J) and the number of response categories (K) contribute to parameter estimation accuracy remains insufficiently explored. We conducted a Monte Carlo simulation to examine how three design conditions-sample size (n = 500-1500), number of items (J = 5-50), and a number of response categories (K = 4-7)-influence the estimation accuracy of the latent trait parameter ([Formula: see text]) and the item discrimination parameter (a) under the GRM. For each condition, we generated a large population dataset based on predefined distributions for [Formula: see text], a, and b, and then randomly drew samples (n) for estimation. The GRM was fitted using the EM algorithm. Estimation accuracy was evaluated using root mean squared error (RMSE), FPC-corrected RMSE, and Pearson's correlation coefficient between true and estimated [Formula: see text] values. The RMSE of the discrimination parameter a decreased with increasing sample size (n) and number of items (J), while the effect of K was negligible. In contrast, the RMSE of [Formula: see text] was primarily influenced by J, with only minor effects from n and K. Notably, the Pearson correlation between true and estimated [Formula: see text] values consistently exceeded r = .98 across all conditions, suggesting high ordinal fidelity even with small samples. Increasing J beyond approximately 30 yielded diminishing returns in RMSE reduction. Our findings suggest that sample size recommendations for GRM should be flexibly tailored to the measurement goal. For accurate estimation of [Formula: see text], a sufficiently large number of items (e.g., J ≥ 30) can compensate for smaller sample sizes (n ≈ 500), whereas precise estimation of a requires larger samples (n ≥ 1000). The impact of increasing K was limited, indicating that additional response categories may not always enhance parameter recovery. These results provide empirically grounded guidance to support efficient and purpose-specific measurement designs in GRM applications.

We propose a new goodness of fit test for the Lomax distribution using the fixed-point characterization developed using Stein's type identity. The theory of U-statistics is used for deriving the test statistic. The proposed test statistic is modified to incorporate the right-censored data. The asymptotic distribution of the test statistics is obtained. Monte Carlo simulation studies are conducted to evaluate the finite-sample performance of the test statistic. To assess the practical applicability of the test statistic, we analyzed four real datasets.

This paper introduces a q-deformed extension of the Lindley distribution. This extension is obtained by replacing the classical exponential with the q-exponential function from Tsallis non-extensive statistical techniques. This transformation offers more control over the tail behavior of the distribution, providing a transition between exponential and power-law decay patterns. Such flexibility is particularly useful when modeling right-skewed data with excess kurtosis, where classical models may not adequately describe heavy-tailed and highly skewed data. We derive several key properties, including the quantile function, expressed by the Lambert–Tsallis function Wq, the raw and incomplete moments, the probability-weighted moments, and the Tsallis entropy. The distribution of order statistics is also investigated. For parameter estimation, we employ several frequentist methods and conduct extensive Monte Carlo simulation studies to assess and compare their performance. Finally, applications to real-world datasets show that the q-deformed Lindley model is practically superior and more flexible than the classical Lindley distribution and other well-known models.

Gamma radiation shielding characteristics of some nitrides: a Monte–Carlo simulation study

Theoretical and Monte Carlo simulation studies on the radiation shielding performance of lead-free TeO2-ZnO-CaO-B2O3 glass system.

Using Bayesian decision theory, we modify the perfect-information, differential-game-based guidance law (DGL1) to address the inevitable estimation error occurring when driving this guidance law with a separately designed state estimator. This yields a stochastic guidance law complying with the generalized separation theorem, as opposed to the common approach, that implicitly, but unjustifiably, assumes the validity of the regular separation theorem. The required posterior probability density function of the game’s state is derived from the available noisy measurements using an interacting multiple model particle filter. When the resulting optimal decision turns out to be nonunique, this feature is harnessed to appropriately shape the trajectory of the pursuer so as to enhance its estimator’s performance. In addition, certain properties of the particle-based computation of the Bayesian cost are exploited to render the algorithm amenable to real-time implementation. The performance of the entire estimation–decision–guidance scheme is demonstrated using an extensive Monte Carlo simulation study.

Meta-analytic structural equation modeling (MASEM) is a method to systematically synthesize results from primary studies, allowing the researchers to simultaneously examine multiple relations among variables by fitting a structural equation model to the pooled correlations. Incorporating dichotomous variables (e.g., having a specific disease or not) into MASEM poses challenges. While primary studies that investigate the relation between a dichotomous and continuous variable typically report standardized mean differences (e.g., Cohen'sd), in the specialized MASEM software it is not possible to directly include standardized mean differences. Instead, MASEM typically uses correlation matrices as input. A proposed solution is to convert the standardized mean differencesto point-biserial correlations. Here lies a complication because, in contrast to a standardized mean difference,the point-biserial correlation depends on the distribution of group membership. Through three Monte Carlo simulation studies, we investigated which conversion formula is suitable when one wants to include a dichotomous variable in MASEM. We varied the prevalence, sampling plan, within-study sample sizes, and the distribution of participants over two groups. Our results show that which conversion is suitable, and which is not depends on the aim of the meta-analyst. Moreover, if the group distribution in the sample does not reflect the prevalence in the population, it is necessary to adjust the correlation between the continuous variables in the model. We have extended our freely available web application (Effect Size Calculator and Converter; https://hdejonge.shinyapps.io/ESCACO/ ) to fill the existing gap and to assist the meta-analyst with both the conversions and the adjustment.

This study examines the estimation of the scale parameter of the Weibull-Power Function Distribution (WPFD) using both maximum likelihood and Bayesian approaches. Bayesian estimation is conducted under one informative Gamma prior with hyperparameters , as well as two non-informative priors: the uniform prior and Jeffreys’ prior. For each prior specification, Bayes estimators are derived under squared error, quadratic, and precautionary loss functions. Closed-form expressions for the posterior distributions and corresponding Bayes estimators are obtained. The finite-sample performance of the competing estimators is evaluated through a Monte Carlo simulation study based on 1000 replications. Estimator performance is assessed using mean squared error (MSE), bias, and coverage probability. The results indicate that all estimators are consistent, with bias and MSE decreasing as sample size increases. Across different prior specifications and parameter settings, the Bayesian estimator under the quadratic loss function consistently attains the lowest MSE, yielding reductions of approximately 10-20% relative to the maximum likelihood estimator in small and moderate samples. These findings suggest that Bayesian estimation under quadratic loss provides improved finite-sample efficiency for estimating the WPFD scale parameter, while maintaining asymptotic comparability with the maximum likelihood approach.

In this study, the gamma-ray shielding properties of polyester (PE)/ZrO2 polymer composites were evaluated over the energy range of 0.01–10 MeV using the Monte Carlo codes GEANT4 and MCNPX, as well as the software packages XCOM, Phy-X, EpiXS, and NGCal. In addition, experimental investigations were carried out at an energy of 662 keV using a 137Cs source (100 mCi). In this paper, parameters including the linear attenuation coefficient (LAC), mass attenuation coefficient (MAC), half-value layer (HVL), tenth-value layer (TVL), mean free path (MFP), effective atomic number (Zeff)and effective electron density (Neff) were calculated using the aforementioned software tools, The structural characteristics of the materials were also investigated using XRD and SEM techniques. The simulation results were compared with the experimental data, showing good agreement between them. Furthermore, the lead equivalent thickness (LET) was also investigated, and it was demonstrated that increasing the ZrO2 filler content leads to a gradual increase in the lead equivalent thickness. As observed from the figures and tables, the gamma-ray shielding performance of the PE/ZrO2 composites improves with increasing ZrO2 content, indicating their potential applicability in radiation shielding applications.

We introduce the one-parameter bounded p-exponential distribution on (0, p+1), which includes the uniform model as a special case and converges pointwise to the exponential law as p→∞. Closed-form expressions are derived for the CDF and PDF, the survival function, an explicit increasing-failure-rate hazard function, the quantile function (enabling inversion-based simulation), moments, and entropy, along with a constructive scaled beta or Kumaraswamy representation. We also establish stochastic ordering with respect to p in stop-loss and increasing convex order, formalizing how dispersion varies with the parameter while preserving the mean scale. Inference is discussed under parameter-dependent support, a non-regular setting, and we develop and compare several estimation procedures, including a likelihood-based boundary MLE, a variance-matching method-of-moments estimator, and Bayesian estimation under a gamma prior implemented via numerical quadrature or MCMC. Monte Carlo simulation studies evaluate finite-sample performance and interval behavior, and two real-world applications in survival and reliability analysis illustrate competitive goodness-of-fit relative to standard benchmark models.

This article introduces an inaccuracy measure of order α that quantifies the error between distributions of the ith order statistic and that of the underlying parent random variable. The proposed measure uniquely characterizes the parent distribution and exhibits invariance under scale transformations. Some analytical bounds for the measure have also been established. To estimate the proposed measure, non parametric procedures are developed, including kernel-based and empirical methods. A Monte Carlo simulation study is conducted to evaluate the performance of the estimator. The results demonstrate that the combination of the reflection method for probability density estimation with the empirical cumulative distribution function yields the most accurate estimates in various settings. Finally, the utility of the proposed approach is illustrated through an application to real-world failure time data.

The article proposes a step-up closed multiple testing procedure designed to evaluate the uniformity across all subsets of location parameters within k exponential distributions characterized by location and scale parameter. The proposed procedure (PP) ensures strong control of the family wise error rate. The computational approach for determining critical constants is detailed for k = 3 , while simulated critical constants are computed for specific configurations for population of size greater than 3 . A Monte Carlo simulation study evaluates the estimated power of the PP under various alternative hypothesis configurations. Additionally, a graphical comparison illustrates that the PP outperforms the existing procedures in terms of the computed estimated power. A numerical example is provided to demonstrate the practical application of the proposed method.

The categorical Gini covariance is a measure of dependence between a numerical variable and a categorical variable, quantifying the difference between conditional and unconditional distribution functions. The categorical Gini covariance equals zero if and only if the numerical variable and the categorical variable are independent. Inspired by this property, we propose a non-parametric test to assess the independence between a numerical and categorical variable using a modified version of the categorical Gini covariance. We used the theory of U-statistics to find the test statistics and study the properties. The proposed test has an asymptotic normal distribution under both the null and alternative hypotheses. Since implementing a normal-based test is difficult, we developed a jackknife empirical likelihood (JEL) ratio test for testing independence. Monte Carlo simulation studies are performed to validate the performance of the proposed JEL ratio test. We illustrate the test procedure using two real data sets.

We investigate rejection probabilities of statistical tests based on resampling procedures. Our general framework under consideration covers, in particular, bootstrap and permutation techniques. It turns out that specific properties of the p-value distribution play a key role, namely convexity or concavity, the Bernstein property and those of beta mixture models. We provide a detailed analysis and clarify how these properties relate to each other. We derive new bounds for the rejection probability. The results link the number of replications with size and power of the test. Numerical considerations demonstrate the quality of the bounds. An important application is the nested simulation estimator in Monte Carlo simulation studies. Our findings indicate that a moderate or even rather small number of replications is sufficient to obtain useful simulation results. This enables a substantial reduction of the computational effort in Monte Carlo simulation studies.

This study focuses on parameter estimation and reliability analysis for the two-parameter Rayleigh distribution under random censoring. It is shown that directly fitting the standard Rayleigh distribution can lead to substantial estimation errors, especially when the dataset contains a markedly high minimum value. To overcome the limitation of the conventional single-parameter Rayleigh distribution, which lacks a threshold parameter in practical applications, a two-parameter Rayleigh distribution model is proposed. The main research contents include the following: establishing a randomly censored data model; deriving classical inference methods based on maximum likelihood estimation along with several other classical estimation techniques; and constructing a Bayesian estimation framework. We also analyze several reliability and experimental characteristics by deriving their corresponding estimates. A Monte Carlo simulation study is carried out to assess the performance of the proposed estimators. Finally, the practicality and superiority of the two-parameter model are validated using real strength datasets. The results demonstrate that the two-parameter Rayleigh distribution can more accurately describe survival data with threshold characteristics and outperforms the single-parameter model in terms of model fit and reliability estimation.

We present a Monte Carlo simulation study of cooperative self-assembly of oppositely charged porphyrin-like molecules, with a focus on disentangling the roles of electrostatic attraction and π-π stacking in supramolecular nanowire formation. Electrostatic interactions were described by a screened Debye-Hückel potential, and the short-range cohesive interactions were introduced via a Lennard-Jones (LJ) potential acting on the neutral cores. Our simulations reveal that Coulombic interactions alone cannot sustain aggregation; a critical LJ strength between 1.5 and 2kBT triggers the transition from disordered clusters to ordered one-dimensional nanowires. This disorder-to-order transition was quantitatively supported by changes in radial distribution functions, cluster size distributions, and charge alternation indices. Increased ionic strength weakens long-range electrostatic attraction, thus delaying nanowire formation, although the short-range cohesive interactions alone can still drive aggregation under these conditions. These findings reveal the delicate balance between electrostatic screening and short-range forces in directing supramolecular organization in aqueous colloidal systems. These results provide design principles for tuning the morphology of porphyrin-based nanostructures with potential applications in colloidal engineering, interfacial science, and functional nanomaterials.

In this article, we propose non-parametric estimators for mean inactivity time function for complete and censored data. The asymptotic properties of the estimators are established using suitable regularity conditions. Monte Carlo simulation studies are used to study the efficiency of the estimators. Three real data sets are used to demonstrate the usefulness of the estimation procedure.

Liquid crystal mesophases of achiral molecules are normally achiral, yet in a few materials they spontaneously segregate and form right- and left-handed chiral domains. One mechanism that drives chiral segregation is molecular shape fluctuations between axial chiral conformations, where molecular interactions favor matching chirality and promote helical twist. Cooperative chiral ordering may also play a role in chirality amplification, as when a tiny fraction of chiral dopant drives a nematic phase to become cholesteric. We present a model of cooperative chiral ordering in liquid crystals using Maier-Saupe theory, and predict a phase diagram with a segregated cholesteric phase with alternating domains of left- and right-handed chiral twist, with opposite enantiomeric excess, in addition to racemic nematic and isotropic phases. Our model also demonstrates how chiral molecular fluctuations influence the helical twisting power of dopants in the nematic phase, which may be observed even in materials where the segregated cholesteric phase is preempted by a transition to another phase. We compare these results with Monte Carlo simulation studies of the switchable chiral Lebwohl-Lasher model, where each spin switches between right- and left-handed chiral states. Simulation results validate the predicted phase diagram, demonstrate chiral amplification in the racemic nematic phase, and reveal complex coarsening dynamics in the segregated cholesteric phase. These results suggest that molecular fluctuations between degenerate chiral configurations may be a common mechanism to produce cooperative chiral order in achiral liquid crystals.