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International Journal of Mathematics and Statistics
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ISSN (Print) 0974-7117 - ISSN (Online) 0973-8347
Published by CESER Publications

[11 journals]

Estimation of Exponential Ratio-cum-Exponential dual to Ratio Imputation
Techniques in Sample Survey
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  Authors: Jyotishman Das, B. K. Singh
  Pages: 1 - 12
  Abstract: In most of the large-scale surveys, the problems of non-response occur. To deal with nonresponse, several techniques are available in use, one of the best among them is imputation method. In this paper, some exponential ratio-cum-exponential dual to ratio imputation techniques and their corresponding estimators are proposed for evaluating the population mean of the study variable. Also the bias, the mean square error and the percentage relative efficiency are evaluated to examine the adaptability of the proposed estimators.
  PubDate: 2024-04-13
  Issue No: Vol. 25 (2024)
A Difference Ratio-Regression Type Exponential Estimator of Population
Mean in Post-Stratification under Linear Transformation of Auxiliary
Variable
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  Authors: Nirupama Sahoo, Suman Dash
  Pages: 13 - 20
  Abstract: Following Grover and Kaur (2014) and Rao (1991), we have proposed an exponential ratio-type estimator of the population mean in post-stratification. It has been discovered that our suggested estimator is more efficient than practically every other estimator already in existence that has been defined for the identical scenarios. Moreover, our proposed estimator outperforms several other existing estimators under certain simple conditions. Theoretical results so obtained and the efficiency have been verified by the numerical illustrations. The performance of the suggested estimator is also the subject of a general study.
  PubDate: 2024-04-13
  Issue No: Vol. 25 (2024)
A control chart based on fuzzy hazard function
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  Authors: Afsaneh Rezaeifar, Bahram Sadeghpour Gildeh, G.R. Mohtashami Borzadaran
  Pages: 21 - 31
  Abstract: Monitoring medical outcomes is desirable so as to help quickly detect performance changes. Previous applications have mostly focused on binary outcomes, such as 30-day mortality after surgery. However, in many applications, survival time data is routinely collected. Survival analysis examines and models the time that it takes for an event to occur. Proportional hazard regression is the most popular tool for studying the dependency of survival time on predictor variables. By using the maximum partial likelihood method in this regression, the hazard function is approximated. In applications, real data are frequently not precise numbers or vectors but often more or less imprecise. On the other side, the hazard function is the rate of failure at any instant or the rate at which risk accumulated. So when the failure is a fuzzy number, it is better to use fuzzy approaches to estimate the fuzzy hazard function. In this paper, we propose a way to estimate the fuzzy hazard function, and based on that, a CUSUM control chart to monitor risk-adjusted survival times is introduced. By using real data, the chart is compared with the crisp hazard function, which is proposed by Biswas and Kalbfleisch.
  PubDate: 2024-04-13
  Issue No: Vol. 25 (2024)
Some New Regression Estimators for Incomplete Sampling Frames
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  Authors: Shilpa Yadav, Pankaj Nagar
  Pages: 32 - 48
  Abstract: A crucial element in any research or survey process, the sampling frame serves as the foundation upon which the entire structure of data collection is built. However, inherent imperfections can render these frameworks incomplete, potentially leading to a skewed representation of the target population. In the realm of statistics and social research, the concept of incomplete sampling frames poses a pertinent challenge, impacting the accuracy and reliability of findings. As such, comprehending the ramifications of incomplete sampling frames within the context of research methodologies is pivotal in discerning the extent of its influence on data quality and the subsequent implications for decision-making and policy formulation. The present study tackles with the problem of incompleteness in sampling frames using information on the unincluded units as well as some auxiliary information through regression estimators. Combined and separate regression estimators are developed using the concept of stratification in double sampling paradigm and their relative efficiencies are compared. Further, a simulation study is conducted to numerically illustrate the efficacy of the proposed estimators.
  PubDate: 2024-04-13
  Issue No: Vol. 25 (2024)
Estimation of Volume under ROC surface and Asymptotic Variance for
diagnostic classifier following Rayleigh distribution
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  Authors: T.S. Sahana, G. Kumarapandiyan
  Pages: 49 - 60
  Abstract: Clinical diagnosis emphasizes the importance of assessing biomarker performance for disease screening and diagnosis. The Receiver Operating Characteristic (ROC) Curve is a crucial tool for evaluating and interpreting biomarker performance. Various models and methods have been developed to evaluate biomarkers in binary classification (i.e., Non-Diseased and Diseased). This research article aims to extend the binary classification problem to a three-class scenario, including Diseased, Suspicious, and Non-Diseased classes for Rayleigh distribution. It introduces a three-class Rayleigh ROC model based on a Parametric approach, deriving metrics such as Volume Under the ROC Surface (VUS) and Asymptotic Variance, as well as an alternative Non-Parametric approach. The model was validated using simulated data generated for the underlying distribution, and the real-life dataset was used to fit the VUS and ROC curves.
  PubDate: 2024-04-13
  Issue No: Vol. 25 (2024)

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