Statistical Modeling and Applications on Real-Time Problems. Enhancing Understanding and Practical Implementation

Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
Acknowledgments
Contributors
About the editors
Chapter 1: Comparison between Ml, Bayes and E-Bayes estimates of γ(t) and ρ(t) for Lomax distribution under type II censoring scheme
	1.1 Introduction
	1.2 Definition and Preliminaries
	1.3 ML and Bayes under Type II Censoring Scheme
		1.3.1 Maximum likelihood estimator under type II censoring scheme
		1.3.2 Bayes estimators under type II censoring scheme
		1.3.3 Al-Bayyati loss function (ABLF), minimum expected loss function (MELF) and DeGroot loss function (DGLF)
			1.3.3.1 Parameter estimation under ABLF, MELF and DGLF
			1.3.3.2 Reliability estimation ρ(t) under ABLF, MELF and DGLF
	1.4 E-Bayesian Estimation under Type II Censoring Scheme
		1.4.1 Al-Bayyati loss function
		1.4.2 Minimum expected loss function
		1.4.3 DeGroot loss function
	1.5 Simulation Illustration
		1.5.1 Real data study
	1.6 Conclusion
	References
Chapter 2: Estimating population proportion using auxiliary character under non-response in stratified sampling
	2.1 Introduction
	2.2 Sampling Methodology and Proposed Classes
	2.3 Bias and MSE of the Proposed Estimators
	2.4 Members of the Proposed Class of Estimators
	2.5 Theoretical Comparison
	2.6 Empirical Study
	2.7 Simulation Study
	2.8 Conclusion
	References
Chapter 3: Estimation of ratio and product of two population means under pps sampling with and without measurement error
	3.1 Introduction
	3.2 Adopted Estimators
	3.3 Proposed Estimators
	3.4 Theoretical Comparisons
		3.4.1 For ratio of two means
		3.4.2 For product of two means
	3.5 Extension of Work in Presence of Measurement Error (ME)
	3.6 Empirical Study
		3.6.1 For ratio of two population means (ℛ)
		3.6.2 For product of two population means (P)
	3.7 Simulation Study
	3.8 Conclusions
	References
Chapter 4: An efficient estimator of population mean in successive sampling using auxiliary information
	4.1 Introduction
	4.2 Proposed Estimators
	4.3 Bias and MSE of Proposed Estimators
	4.4 Optimum Values
	4.5 Efficiency Comparisons
	4.6 Numerical Illustration
	Acknowledgement
	References
Chapter 5: A comparative study regarding prevalence of caesarean section in Indian female
	5.1 Introduction
	5.2 Data Collection and Methodology
		5.2.1 Socio-economic factors
		5.2.2 Statistical analyses
	5.3 Results and Discussion
		5.3.1 Socio-economic determinants of prevalence of caesarean section
		5.3.2 Discussion
	5.4 Conclusion
	Acknowledgement
	Notes
	References
Chapter 6: A review on estimation of ratio and product of two population means
	6.1 Introduction
	6.2 Estimation of Ratio and Product of Two Population Means under Complete Information
	6.3 Estimation of Ratio and Product of Two Population Means under Incomplete Information
	6.4 Conclusion
	References
Chapter 7: Statistical analysis of agriculture productivity cost for different zones of India
	7.1 Introduction
	7.2 Effect of Green Revolution on Agriculture
	7.3 Data Collection Process
		7.3.1 Data analysis
	7.4 Agriculture Domestic Product Cost Analysis
	7.5 Cost Analysis through Coefficient of Variation
	7.6 Conclusion
	References
Chapter 8: Comparative and performance analyses of unreliable server queues: An economic perspective
	8.1 Introduction
	8.2 Queueing System with Server Breakdown
		8.2.1 Notations
	8.3 Queueing System with Working Breakdown of the Server
		8.3.1 Notations
	8.4 Queueing System with WB, Service Pressure Condition, and Threshold-Based Recovery Policy
		8.4.1 Notations
	8.5 Special Cases
	8.6 Cost Analysis
		8.6.1 Steady-state analysis
		8.6.2 Cost function
		8.6.3 Quasi-Newton method
	8.7 Numerical Results and Discussion
	8.8 Conclusion
	References
Chapter 9: A single-server feedback queuing system with encouraged arrivals, customers' impatience, and catastrophe
	9.1 Introduction
	9.2 Assumptions of the Model
	9.3 Mathematical Formulation of the Model
	9.4 Steady-State Solution
	9.5 Measures of Performance
		9.5.1 Expected system size (Ls)
		9.5.2 Expected waiting time of the customer in the system
		9.5.3 Expected waiting time of a customer in the queue
		9.5.4 Expected queue length Lq=λWq
	9.6 Numerical Results
	9.7 Particular Cases
	9.8 Conclusion and Future Work
	References
Chapter 10: Solution of real life optimization problems
	10.1 Introduction
	10.2 Solving a Real Life Optimization Problem
	10.3 Mathematical Model of an Optimization Problem
	10.4 Solution of an Optimization Problem
		10.4.1 Goal programming
		10.4.2 Multi-objective optimization problems
		10.4.3 Optimization in a dynamic environment
	10.5 Conventional Solution Techniques
		10.5.1 Limitations of conventional theory-based techniques
	10.6 Heuristics and Meta Heuristics
	10.7 Optimization Algorithms
		10.7.1 Search for optimality
		10.7.2 Solution of constrained problems
			10.7.2.1 Converting the constrained problem to an unconstrained problem
			10.7.2.2 Penalty methods
			10.7.2.3 Feasibility rules and stochastic ranking approach
			10.7.2.4 Problem specific approach
		10.7.3 Multi-solution problems
		10.7.4 Multi-objective problems
		10.7.5 Problems in dynamic environments
	10.8 An Ideal Optimization Algorithm
	10.9 Random Search Based Optimization Techniques
	10.10 General Purpose Computer Based Nature Inspired Optimization Techniques
	10.11 A Layman's Approach to Solving an Optimization Problem
	About the Author
	References
Chapter 11: Role and importance of multi-criteria decision-making (MCDM) as an optimization technique
	11.1 Introduction
	11.2 Multi-Criteria Decision-Making (MCDM)
		11.2.1 Terminology of MCDM
		11.2.2 Categories of MCDM
			11.2.2.1 Outranking decision-making methods
			11.2.2.2 Compensatory decision-making
		11.2.3 Domain of MCDM
		11.2.4 Examples of MCMD
	11.3 Conclusion
	References
Index