EDGE ESTIMATION IN POPULATION OF PLANER GRAPHS USING SAMPLING

  • D. Shukla Deptt. of Mathematics and Statistics, University of Sagar, Sagar, M.P., India
  • Yashwant Singh Rajput Deptt. of Mathematics and Statistics, University of Sagar, Sagar, M.P., India
  • Narendra Singh Thakur Deptt. of Mathematics and Statistics, University of Sagar, Sagar, M.P., India
Keywords: Graph, Planer Graph, Edge, Vertices(nodes), Simple Random Sampling without replacement (SRSWOR), Class, Estimator, Bias, Mean Squared Error (MSE), Optimum Choice, Confidence intervals

Abstract

Consider a population which contains graphical relationship between two variables. There are two graphs of vertices and edges, each edge contains a length value and linked with two vertices (nodes). Mean length of all edges is unknown which is a problem to explore. This paper takes into account two planer graphs in particular, one of them is under main interest and other is an auxiliary graph. A sample of some nodes is drawn by simple random sampling (SRSWOR) along with a laid down node-sampling procedure and a class of estimators is proposed to estimate the mean length of an edge of planer graph using the structure of other planer graph as an auxiliary source of information. Optimal properties of estimators are derived and results are numerically supported with the calculation of length estimates and confidence intervals.

 

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Published
2010-09-01
Section
Articles