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In this paper, we propose fiducial simultaneous generalized confidence intervals based on fiducial generalized pivotal quantities for the comparison of the successive differences of ordered location parameters of the Inverse Gaussian populations. The constructed intervals are shown to attain the correct coverage probabilities asymptotically. The simulation study indicates that the Type-I error probabilities are close to the nominal level. The illustration of the proposed procedure is done  using real datasets.

Keywords: Inverse Gaussian, Fiducial generalized pivotal quantities, Type-I error, Simultaneous fiducial generalized confidence interval.

For estimating the finite population mean, we have proposed a new difference estimator as a weighted estimator of the customary difference estimator and the difference estimator due to “Sahoo et. al. (2007)” when the preassigned constants used therein are the corresponding population regression coefficients. The proposed difference estimator is unbiased. Employing predictive approach advocated by “Basu (1971)”, the estimator is found to be endowed with the predictive character. Using the hierarchic estimation technique due to “Agrawal and Sthapit (1997)”, a sequence of estimators is generated from the proposed estimator. The estimator of order k, when k is optimum, is found to be more efficient than its competing estimators under conditions that hold good in practice. While simulation study reveals supremacy of the proposed difference estimator over existing difference estimators from the standpoint of efficiency, empirical investigation based on three real populations has been carried out to demonstrate the gain in efficiency of the suggested estimator over the competing estimators.

KEYWORDS: Hierarchic estimation; Predictive estimation; Weighted difference estimator; Simulation study

Here we introduce generalized discrete Pareto distribution as a flexible model to analyse count data, and includes as special cases: the discrete Burr, discrete Pareto, discrete generalized Pareto and alternative discrete Pareto distributions. We obtain limiting behaviour of parameters, infinite divisibility, moments and their bounds, hazard rates, stochastic orderings and aging intensity properties. The method of maximum likelihood estimation is used herein to estimate model parameters. Simulation study is carried out to examine the bias, mean square error, average absolute bias and mean relative error of maximum likelihood estimators. Finally, the paper illustrates the flexibility of the proposed distribution using medical dataset, demonstrating its superior fit compared to other models.

KEYWORDS: Characterizations; Count data modelling; Hazard rate; Infinite divisibility; Limiting behaviour.

Estimating stress-strength reliability of the form P(Y < X < Z) is a pivotal concern in reliability analysis, particularly when systems are subjected to both lower and upper stress limits. This paper investigates the reliability measure under the assumption that the stress variables Y and Z, as well as the strength variable X, follow exponential distributions. The analysis is conducted using both complete samples and right-censored samples to reflect realistic data collection scenarios. To improve estimation efficiency, we propose several shrinkage estimators based on distinct strategies: a constant shrinkage weight factor, a modified Thompson-type shrinkage weight, and the formulation introduced by Mehta and Srinivasan (1971). The performance of these estimators is evaluated via extensive Monte Carlo simulations and compared against the conventional maximum likelihood estimator, demonstrating the relative merits and limitations of each approach.

KEYWORDS: Exponential distribution, Shrinkage estimation, Stress Strength reliability.

In this paper, we introduce a three parameter distribution called the Marshall-Olkin New Two-Parameter Sujatha Distribution. It is a Marshall - Olkin extension of the New two-parameter Sujatha distribution. Several important statistical properties including the hazard rate function, reversed hazard rate function and order statistics are derived. The application of this new distribution in the modeling of lifetime data is demonstrated using real-life data sets. A comparison of this new distribution with some of the existing distributions has also been shown.

KEYWORDS: Lifetime Distributions, Sujatha Distribution, Two Parameter Sujatha Distribution, Marshall - Olkin Transformation.

This study presents a comparative analysis of various machine learning models applied to a classification problem, both before and after hyperparameter tuning. Models including Logistic Regression, Support Vector Machine, K-Nearest Neighbors, Decision Tree, Random Forest, Gradient Boosting, and XGBoost were evaluated.Performance metrics such as accuracy, precision, recall, and F1-score were used to assess each model. The results indicate that hyperparameter tuning significantly enhances the performance of certain models, particularly Decision Tree, Random Forest, and Gradient Boosting. Gradient Boosting outperformed all other models post-tuning with an accuracy of 0.80 and F1-score of 0.75.Models like KNN and SVM exhibited minimal improvements after tuning. Ensemble methods generally achieved better results compared to individual models. The study highlights the importance of fine-tuning model parameters to optimize results. Accuracy and F1-score suggest a consistent performance boost for tuned ensemble algorithms. These findings provide valuable insights for selecting and optimizing models in machine learning tasks.

KEYWORDS: Diabetes Prediction, Machine Learning Models, Performance Metrics, Grid Search Optimization, Hyperparameter Tuning.

In this paper, a stochastic framework is developed for modeling the operation of a photometric–counting (PC) analyzer used for the detection of mechanical impurities in liquid media. The measurement process is modeled using probabilistic tools, where particle arrivals follow a Poisson flow and the corresponding photometric signals are subject to random distortions, Gaussian noise, and overlapping effects. A mathematical model of the information formation process is formulated, and a simulation-based model is proposed to approximate complex analytical expressions and to evaluate error probabilities. Statistical criteria are introduced for the optimization of analyzer parameters, with the objective of minimizing measurement error and improving the reliability of impurity detection. Discussions carried out demonstrated the performance of the proposed approach under various noise and signal conditions, and illustrated its potential advantages over purely deterministic models. The study highlights how probabilistic modeling and simulation methods can be used to enhance the accuracy and reliability of particle measurement systems.

KEYWORDS: Particles analyzer; mechanical impurity; particles size; photometric-counting method; dispersed system.
JEL CLASSIFICATION: 62P30.