Statistical Modeling and Applications on Real-Time Problems. Unraveling Insights through Advanced Analytical Techniques

Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
Acknowledgments
Contributors
About the editors
Chapter 1: Goodness of fit based and variable selection in non-parametric measurement error model
	1.1 Introduction
	1.2 Model Description and Preliminary Concepts
		1.2.1 Multiple non-parametric measurement error model
		1.2.2 Goodness of fit in parametric regression models
		1.2.3 Goodness of fit in non-parametric measurement error model
	1.3 Large Sample Statistical Properties of Rn2
	1.4 Finite Sample Study and Real Data Analysis
		1.4.1 Finite sample study
			1.4.1.1 Addressing (iii) mentioned in Section 1.1
			1.4.1.2 Addressing (ii) mentioned in Section 1.1
			1.4.1.3 Addressing (i) mentioned in Section 1.1
			1.4.1.4 Covariates not having measurement errors
		1.4.2 Real data analysis
			1.4.2.1 Pig data
			1.4.2.2 Tourism data
	1.5 Concluding Remarks
	Acknowledgement
	References
	Appendix
Chapter 2: Bayesian statistics with applications in cosmology
	2.1 Elements of Bayesian Statistics
		2.1.1 Bayes' theorem
		2.1.2 Bayesian model selection
	2.2 Monte Carlo Markov Chain Method
	2.3 Cosmological Model with Interacting Dark Sector
	2.4 Data and Likelihoods
		2.4.1 H(z)
		2.4.2 Baryon acoustic oscillations (BAO)
		2.4.3 Cosmic microwave background
		2.4.4 Methodology
	2.5 Results and Discussion
	2.6 Conclusion
	References
Chapter 3: An improved sufficient bootstrapping
	3.1 Introduction
	3.2 Conventional Bootstrapping
	3.3 Sufficient Bootstrapping
	3.4 Improved Sufficient Bootstrapping
	3.5 Theoretical Developments of Three Types of Bootstrapping
		3.5.1 Conventional bootstrapping
		3.5.2 Sufficient bootstrapping
		3.5.3 Improved sufficient bootstrapping
	3.6 Analytical Comparison
	3.7 Simulation Study
	3.8 Conclusion
	3.9 Remarks
	Acknowledgements
	References
Chapter 4: A new measure of empirical mode
	4.1 Introduction
	4.2 Naive Estimator
	4.3 Ratio Type Estimator
	4.4 Regression Type Estimator
	4.5 Empirical Evidence: Simulation
	References
	Appendix A
	A.1 ‚Notations and Expected Values
	A.2 ‚SAS Codes Used in the Simulation Study
Chapter 5: On the distribution of a busy period for the single server queue with balking, catastrophes and repairs
	5.1 Introduction
	5.2 Model Description and Busy Period Analysis
		5.2.1 Evaluation for Pk(t)
		5.2.2 Evaluation for the busy density function
	5.3 Numerical Illustrations
	5.4 Conclusion
	References
	Appendix I
	Appendix II
Chapter 6: Studying the impact of feature importance and weighted aggregation in tackling process fairness
	6.1 Introduction
	6.2 Related Work
		6.2.1 Assessing fairness
		6.2.2 Explanations to assess fairness
			6.2.2.1 LIME
			6.2.2.2 SHAP
		6.2.3 The tension between fairness and classification performance
	6.3 FixOut
	6.4 Experiments
		6.4.1 Datasets and experimental setup
		6.4.2 Classification performance assessment
		6.4.3 Process fairness assessment
		6.4.4 Fairness metrics assessment
	6.5 Extensions of FixOut
		6.5.1 Automating the choice of k: the algorithm Find-K
		6.5.2 FixOut's extension for textual data
	6.6 Discussion and Conclusion
	Acknowledgments
	Notes
	References
Chapter 7: Gaussian mixture model with modified hard EM algorithm in clustering problems
	7.1 Introduction
	7.2 Methodology
	7.3 Comparison on Benchmark Data Sets
	7.4 Real Data Application
		7.4.1 Breast cancer data
		7.4.2 Yeast cell cycle data
	7.5 Conclusion
	References
Chapter 8: Impatient customers on an M/M/1 queueing system subjected to differentiated vacations
	8.1 Introduction
	8.2 Model Description
	8.3 Transient Probabilities
		8.3.1 Evaluation of P1,n(t) and P2,n(t)
		8.3.2 Evaluation of P0,n(t)
		8.3.3 Evaluation of P2,0(t)
		8.3.4 Evaluation of P1,0(t)
	8.4 Time Dependent Mean and Variance
		8.4.1 Mean
		8.4.2 Variance
	8.5 Special Case
	8.6 Numerical Illustrations
	8.7 Conclusions
	References
	Appendix A Expression for ϕn(t) and ψn(t)
	B  Confluent hyper-geometric function
Chapter 9: Application of Error Correction Model (ECM) in stabilizing/adjusting fiscal burden post COVID situation
	9.1 Introduction
	9.2 Literature Review
	9.3 Methodology
		9.3.1 Description of variables
			9.3.1.1 Dependent variable
			9.3.1.2 Independent/explanatory variables
	9.4 Estimation Procedure
		9.4.1 Test for stationarity
		9.4.2 Co-integration test
	9.5 Estimated Model
	9.6 Data Analysis and Interpretation
	9.7 ARDL Co-Integration Relationship
	9.8 Estimated Results of ARDL Error Correction Model
	9.9 Diagnostic Tests
	9.10 Normality Test
	9.11 Granger Causality Test
	9.12 Summary and Conclusion
	References
Chapter 10: An inventory model with preserving environment for perishable items under learning effect
	10.1 Introduction
	10.2 Assumptions and Notations
		10.2.1 Assumptions
		10.2.2 Notations
	10.3 Mathematical Formulation
	10.4 Solution Process
		10.4.1 Numerical example
	10.5 Sensitivity Analysis
	10.6 Conclusions
	References
Index