Under military war weapon support the economic bond level estimation using generalized Petersen graph with imputation

Several countries of the world are involved in mutual and collaborative business of military equipments, weapons in terms of their production, sales, technical maintenance, training and services. As a consequence, manufacturing of boms, rockets, missiles and other ammunitions have taken structured and smooth shape to help others where and when needed. Often the military support among countries remain open for information to the media, but sometime remain secret due to the national security and international political pressure. Such phenomenon (hidden or open support ) is a part of military supply chain and could be modeled like a Petersen graph considering vertices as countries and edges as economic bonds. For a large graphical structure, without sampling, it is difficult to find out average economic bonding (open & secret) between any pair of countries involved in the military business or support. This paper presents a sample based estimation methodology for estimating the mean economic bond value among countries involved in the military support or business. Motivation to the problem is derived from current Russia-Ukraine war situation and a kind of hidden support to war by NATO countries. A node sampling procedure is proposed whose bias, mean-squared error and other properties are derived. Results are supported with empirical studies. Findings are compared with particular cases and confidence intervals are used as a basic tool of comparison. Pattern imputation is used together with a new proposal of CIImputation method who has been proved useful for filling the missing value, specially when secret economic support data from involved countries found missing. The current undergoing war between Ukraine and Russia and secret weapon, economic support from NATO countries is an application of the proposed methodology contained in this paper. Key words: Graph, Petersen Graph, Estimator, Bias, Mean Squared Error (MSE), Optimum Choice, Confidence intervals (CI), Nodes (vertices), Pattern Imputation, CI-Imputation (LLimputation and UL-imputation), Economic Bonds, Military War, Weapon Support