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In this article, we suggested a generalized class of ratio type estimator to estimate the unknown population mean under Adaptive Cluster Sampling (ACS). The quantitative evaluation is executed to identify the best values of (p and q). The estimator’s Mean Squared Error has been estimated up to the first order of approximation and efficiency has been assessed through percentage relative efficiency

KEYWORDS: Adaptive Cluster Sampling; Ratio Type estimator; Rare Population; Auxiliary Variable; Mean Squared Error.

This research focuses on applying Markov modeling to the progression of type 2 diabetes mellitus. The study involves constructing a transition probability matrix that represents various stages in the advancement of type 2 diabetes. By utilising this matrix, the probability distributions for the consecutive occurrences of the same state, looking one and two days ahead. Furthermore, the investigation formulates explicit mathematical expressions for different statistical measures, utilizing Pearson’s coefficients. The developed model behaviour is examined through numerical examples and sensitivity analysis. The primary objective of this study is to create user-friendly tools, and developing appropriate software based on the derived mathematical formulations. The application of these findings can significantly enhance the management of type 2 diabetes in healthcare settings, potentially extending to decision support systems.

KEYWORDS: Type-2 Diabetes; Markov Model; Transition Probability Matrix; Disease Progression.

Sequencing problem is to select the order in which the vital tasks are to be done to minimize the total elapsed time taken for all the tasks. Generally, in job sequencing problems, the processing times are precisely valued. But in reality, it is observed that the processing times during the performance of the job are indefinite. For that reason, the conception of fuzzy job sequencing problem make available for use an effective outline which is useful for real-life situations with fuzzy processing times. Here, we suggest a new technique for solution of fuzzy sequencing problems involving Octagonal Fuzz Numbers (OFNs).

In this paper, we propose a simple approach for the solution of fuzzy sequencing problem under fuzzy environment where processing time taken as octagonal fuzzy numbers. It can be solved using robust ranking method and fuzzy sequencing problem can be converted into a crisp valued sequence problem and solved by Johnson’s algorithm which is illustrated through a numerical example.

KEYWORDS: Ranking, Fuzzy sequencing problem, Octagonal fuzzy numbers, Robust ranking technique.

The present paper is a generalization of the linear growth process by considering the probabilities that a birth is a single birth or a twin birth. Explicit expression for the probabilities Pn(t) was derived and expressions for mean and variance was obtained from the probability generating function of the process. Also, we have obtained the expression for mean and variance directly from the differential difference equation of the process. A simulation study was done to analyze the effects of birth in presence of single as well as twin births and deaths.

KEYWORDS:  Birth, Death, Immigration Process, Linear Growth Process, Single or Twin Birth

AMS Subject Classification: 62M99, 60J80, 60J27, 60G07

In this paper we explore the problem of estimation of finite population variance in simple random sampling without replacement by utilizing information of multiauxiliary variables.We propose an almost unbiased multivariate estimator that has a smaller mean squared error than the conventional biased multivariate estimators. In addition, we support these theoretical result with the aid of a numerical investigation and simulation study into the performance of the estimator has been made.

KEYWORDS: Auxiliary information, Bias, Mean Squared Error, Simple random sampling without replacement (SRSWOR), Relative efficiency, simulation technique.

In this paper we study estimation of unknown parameter in the subdiffusion model based on discrete observations. We obtain consistency and asymptotic distribution properties of the estimator. The limit distributions are shown to be different in sub-critical, critical and super-critical cases.

KEYWORDS: Subdiffusion, fractional Brownian motion; method of moments; fractional Langevin equation; nanoscale biophysics; COVID-19.