Browsing by Author "Kumar, Anoop"

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    A next generation probabilistic approach to analyze cancer patients data with inference and applications
    (2025) Kumar, Anoop
    This study addresses the critical challenges faced in cancer care, particularly in predicting survival times for patients with lung cancer and acute myeloid leukemia. Despite recent advancements in medical science, existing models often fall short in accurately capturing disease progression, leading to less effective clinical decision making, and compromised patient outcomes. The need for advanced predictive models is urgent to improve survival time forecasts and enhance treatment strategies. In response to this, we introduce a novel probabilistic approach, the New Weibull (NEWE) model, which is part of a newly generated class designed to model cancer patient data more effectively. Our methodology includes using seven well-known estimation methods, each rigorously evaluated for consistency through Monte Carlo simulation studies focused on key metrics such as absolute bias, mean square error, and mean relative error. The datasets analyzed include survival times for twenty acute myeloid leukemia patients, 121 breast cancer patients from 1929 to 1938, 33 patients with acute myelogenous leukemia, data from eighteen individuals who died from causes unrelated to cancer, and survival times of advanced lung cancer patients undergoing standard chemotherapy. The NEWE model outperformed competing models, particularly in Anderson-Darling, Cramer-von Mises, and Kolmogorov-Smirnov tests, with significantly higher p-values. These findings highlight the NEWE model’s potential to transform predictive oncology by offering more precise survival time predictions, improving the quality of care and decision-making in cancer treatment.
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    Logarithmic imputation techniques for temporal surveys: a memory‑based approach explored through simulation and real‑life applications
    (2025) Kumar, Anoop
    This research introduces memory-based logarithmic imputation techniques and the result ing estimators to address missing data within the temporal surveys. The mean square error of the resulting memory type estimators is reported to the first order approximation and the efficiency conditions are obtained by comparing the properties of the proposed and adapted imputation methods. The study contains a comprehensive simulation study to evaluate the performance of the resulting estimators under various conditions, providing insights into their applicability. Furthermore, the proposed methods are also illustrated through some real-life applications. The findings of simulation and real data application demonstrate the effectiveness of the memory type logarithmic imputation methods, providing insights into its application across different survey contexts and highlighting its potential to enhance data completeness and reliability in temporal survey analysis.
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    Optimal classes of estimators for population mean using higher order moments
    (2025) Kumar, Anoop
    This paper considers some optimal classes of difference and ratio type estimators for the estimation of population mean using higher order moments viz variance of auxiliary variable with the aim of improvement over its entrants existing till date. The bias and mean square error of the considered estimators are derived using Taylor series method up to the first order of approximation. The theoretical results have been determined and appraised with a computational study using real and artificially generated data sets. The computational results are turned out to be rather advance providing better improvement over the contemporary estimators.
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    Optimal Imputation Methods under Stratified Ranked Set Sampling
    (2025) Kumar, Anoop
    It is long familiar that the stratified ranked set sampling (SRSS) is more efficient than ranked set sampling (RSS) and stratified random sampling (StRS). The existence of missing values may alter the final inference of any study. This paper is a fundamental effort to suggest some combined and separate imputation methods in the presence of missing data under SRSS. The proposed imputation methods become superior than the mean imputation method, ratio imputation method, Diana and Perri (2010) type imputation method, and Sohail et al. (2018) type imputation methods. A simulation study is administered over two hypothetically drawn asymmetric populations