Meeker W., Hahn G., Escobar L. Statistical Intervals: A Guide for Practitioners and Researchers

2nd Edition. — Wiley, 2017. — 631 p. — (Wiley Series in Probability and Statistics). — ISBN: 978-0-471-68717-7.Describes statistical intervals to quantify sampling uncertainty,focusing on key application needs and recently developed methodology in an easy-to-apply format.Statistical intervals provide invaluable tools for quantifying sampling uncertainty. The widely hailed first edition, published in 1991, described the use and construction of the most important statistical intervals. Particular emphasis was given to intervals—such as prediction intervals, tolerance intervals and confidence intervals on distribution quantiles—frequently needed in practice, but often neglected in introductory courses.Vastly improved computer capabilities over the past 25 years have resulted in an explosion of the tools readily available to analysts. This second edition—more than double the size of the first—adds these new methods in an easy-to-apply format. In addition to extensive updating of the original chapters, the second edition includes new chapters on:Likelihood-based statistical intervals
Nonparametric bootstrap intervals
Parametric bootstrap and other simulation-based intervals
An introduction to Bayesian intervals
Bayesian intervals for the popular binomial, Poisson and normal distributions
Statistical intervals for Bayesian hierarchical models
Advanced case studies, further illustrating the use of the newly described methodsNew technical appendices provide justification of the methods and pathways to extensions and further applications. A webpage directs readers to current readily accessible computer software and other useful information.This book is an up-to-date working guide and reference for all who analyze data, allowing them to quantify the uncertainty in their results using statistical intervals.Preface to Second Edition
Preface to First EditionAbout the Companion WebsiteIntroduction, Basic Concepts, and Assumptions
Statistical Inference
Different Types of Statistical Intervals: An Overview
The Assumption of Sample Data
The Central Role of Practical Assumptions Concerning Representative Data
Enumerative versus Analytic Studies
Differentiating between Enumerative and Analytic Studies
Statistical Inference for Analytic Studies
Inferential versus Predictive Analyses
Basic Assumptions for Inferences from Enumerative Studies
Deinition of the Target Population and Frame
The Assumption of a Random Sample
More Complicated Random Sampling Schemes
Considerations in the Conduct of Analytic Studies
Analytic Studies
The Concept of Statistical Control
Other Analytic Studies
How to Proceed
Planning and Conducting an Analytic Study
Convenience and Judgment Samples
Sampling People
Ininite Population Assumptions
Practical Assumptions: Overview
Practical Assumptions: Further Example
Planning the Study
The Role of Statistical Distributions
The Interpretation of Statistical Intervals
Statistical Intervals and Big Data
Comment Concerning Subsequent DiscussionOverview of Different Types of Statistical Intervals
Choice of a Statistical Interval
Purpose of the Interval
Characteristic of Interest
Conidence Intervals
Conidence Interval for a Distribution Parameter
Conidence Interval for a Distribution Quantile
Conidence Interval for the Probability of Meeting Speciications
One-Sided Conidence Bounds
Interpretations of Conidence Intervals and Bounds
Prediction Intervals
Prediction Interval to Contain a Single Future Observation
Prediction Interval to Contain All of m Future Observations
Prediction Interval to Contain at Least k out of m Future
Prediction Interval to Contain the Sample Mean or Sample Standard Deviation of a Future Sample
One-Sided Prediction Bounds
Interpretation of Prediction Intervals and Bounds
Statistical Tolerance Intervals
Tolerance Interval to Contain a Proportion of a Distribution
One-Sided Tolerance Bounds
Interpretation of -Content Tolerance Intervals
Expectation Tolerance Intervals
Which Statistical Interval Do I Use?
Choosing a Conidence Level
Further Elaboration
Problem Considerations
Sample Size Considerations
A Practical Consideration
Further Remarks
Two-Sided Statistical Intervals versus One-Sided Statistical Bounds
The Advantage of Using Conidence Intervals Instead of Signiicance Tests
Simultaneous Statistical IntervalsConstructing Statistical Intervals Assuming a Normal Distribution Using Simple
TabulationsThe Normal Distribution
Using the Simple Factors
Circuit Pack Voltage Output Example
Two-Sided Statistical Intervals
Simple Tabulations for Two-Sided Statistical Intervals
Two-Sided Interval Examples
Comparison of Two-Sided Statistical Intervals
One-Sided Statistical Bounds
Simple Tabulations for One-Sided Statistical Bounds
One-Sided Statistical Bound Examples
Comparison of One-Sided Statistical BoundsMethods for Calculating Statistical Intervals for a Normal Distribution
Notation
Conidence Interval for the Mean of a Normal Distribution
Conidence Interval for the Standard Deviation of a Normal Distribution
Conidence Interval for a Normal Distribution Quantile
Conidence Interval for the Distribution Proportion Less (Greater) than a Speciied Value
Statistical Tolerance Intervals
Two-Sided Tolerance Interval to Control the Center of a Distribution
Two-Sided Tolerance Interval to Control Both Tails of a Distribution
One-Sided Tolerance Bounds
Prediction Interval to Contain a Single Future Observation or the Mean of m Future Observations
Prediction Interval to Contain at Least k of m Future Observations
Two-Sided Prediction Interval
One-Sided Prediction Bounds
Prediction Interval to Contain the Standard Deviation of m Future Observations
The Assumption of a Normal Distribution
Assessing Distribution Normality and Dealing with Nonnormality
Probability Plots and Q–Q Plots
Interpreting Probability Plots and Q–Q Plots
Dealing with Nonnormal Data
Data Transformations and Inferences from Transformed Data
Power Transformations
Computing Statistical Intervals from Transformed Data
Comparison of Inferences Using Different Transformations
Box–Cox Transformations
Statistical Intervals for Linear Regression Analysis
Conidence Intervals for Linear Regression Analysis
Tolerance Intervals for Linear Regression Analysis
Prediction Intervals for Regression Analysis
Statistical Intervals for Comparing Populations and ProcessesDistribution-Free Statistical IntervalsMotivation
Notation
Distribution-Free Conidence Intervals and One-Sided Conidence Bounds for a Quantile
Coverage Probabilities for Distribution-Free Conidence Intervals or One-Sided Conidence Bounds for a Quantile
Using Interpolation to Obtain Approximate Distribution-Free Conidence Bounds or Conidence Intervals for a Quantile
Distribution-Free One-Sided Upper Conidence Bounds for a QuantileDistribution-Free One-Sided Lower Conidence Bounds for a Quantile
Distribution-Free Two-Sided Conidence Interval for a Quantile
Distribution-Free Tolerance Intervals and Bounds to Contain a Speciied Proportion of a Distribution
Distribution-Free Two-Sided Tolerance Intervals
Distribution-Free One-Sided Tolerance Bounds
Minimum Sample Size Required for Constructing a Distribution-Free Two-Sided Tolerance Interval
Prediction Intervals and Bounds to Contain a Speciied Ordered Observation in a Future Sample
Coverage Probabilities for Distribution-Free Prediction Intervals and One-Sided Prediction Bounds for a Particular Ordered
Distribution-Free One-Sided Upper Prediction Bound for Y(j )
Distribution-Free One-Sided Lower Prediction Bound for Y(j )
Distribution-Free Two-Sided Prediction Interval for Y(j )
Distribution-Free Prediction Intervals and Bounds to Contain at Least k of m Future Observations
Distribution-Free Two-Sided Prediction Intervals to Contain at Least k of m Future Observations
Distribution-Free One-Sided Prediction Bounds to Exceed or Be Exceeded by at Least k of m Future ObservationsStatistical Intervals for a Binomial DistributionThe Binomial Distribution
Other Distributions and Related Notation
Notation for Data and Inference
Binomial Distribution Statistical Interval Properties
Two Examples, Motivation, and a Caution
Conidence Intervals for the Actual Proportion Nonconforming in the Sampled Distribution
Preliminaries
The Conservative Method
The Wald (Normal Theory) Approximate Method
The Agresti–Coull Adjusted Wald-Approximation Method
The Jeffreys Approximate Method
Comparisons and Recommendations
Conidence Interval for the Proportion of Nonconforming Units in a Finite Population
The Conservative Method
Large-Population Approximate Method
Conidence Intervals for the Probability that the Number of Nonconforming Units in a Sample is Less than or Equal to (or Greater than) a Speciied Number
Conidence Intervals for the Quantile of the Distribution of the Number of Nonconforming Units
Two-Sided Conidence Interval for yp
One-Sided Conidence Bounds for yp
Tolerance Intervals and One-Sided Tolerance Bounds for the Distribution of the Number of Nonconforming Units
One-Sided Lower Tolerance Bound for a Binomial Distribution
One-Sided Upper Tolerance Bound for a Binomial Distribution
Two-Sided Tolerance Interval for a Binomial Distribution
Calibrating Tolerance Intervals
Prediction Intervals for the Number Nonconforming in a Future Sample
The Conservative Method
The Normal Distribution Approximation Method
The Joint-Sample Approximate Method
The Jeffreys Method
Comparisons and RecommendationsStatistical Intervals for a Poisson DistributionThe Poisson Distribution
Poisson Distribution Statistical Interval Properties
Conidence Intervals for the Event-Occurrence Rate of a Poisson Distribution
Preliminaries
The Conservative Method
The Wald (Normal Theory) Approximate Method
The Score Approximate Method
The Jeffreys Approximate Method
Comparisons and Recommendations
Comparison of Results from Applying Different Methods
Conidence Intervals for the Probability that the Number of Events in a Speciied Amount of Exposure is Less than or Equal to (or Greater than) A Speciied Number
Conidence Intervals for the Quantile of the Distribution of the Number of Events in a Speciied Amount of Exposure
Two-Sided Conidence Interval for yp
One-Sided Conidence Bounds for yp
Tolerance Intervals and One-Sided Tolerance Bounds for the Distribution of
the Number of Events in a Speciied Amount of Exposure
One-Sided Lower Tolerance Bound for a Poisson Distribution
One-Sided Upper Tolerance Bound for a Poisson Distribution
Two-Sided Tolerance Interval for a Poisson Distribution
Calibrating Tolerance Intervals
Prediction Intervals for the Number of Events in a Future Amount of Exposure
The Conservative Method
The Normal Distribution Approximation Method
The Joint-Sample Approximate Method
The Jeffreys Method
Comparisons and RecommendationsSample Size Requirements for Conidence Intervals on Distribution Parameters
Basic Requirements for Sample Size Determination
The Objectives of the Investigation
Statement of Needed Precision
Assumed Statistical Distribution and Parameter Planning Values
Sample Size for a Conidence Interval for a Normal Distribution MeanTabulations and a Simple Formula for the Case when is Assumed to Be Known
Tabulations for the Case when is Unknown
Iterative Formula for the Case when is Unknown
Using an Upper Prediction Bound from a Previous Sample when is Unknown
A Two-Stage Sampling Method
Sample Size to Estimate a Normal Distribution Standard DeviationComputational Method
Graphical Method
Tabular Method
Sample Size to Estimate a Normal Distribution Quantile
Sample Size to Estimate a Binomial ProportionGraphical Method
A Simple Computational Procedure
Sample Size to Estimate a Poisson Occurrence RateGraphical Method
A Simple Approximate Computational ProcedureSample Size Requirements for Tolerance Intervals, Tolerance Bounds, and Related Demonstration Tests
Sample Size for Normal Distribution Tolerance Intervals and One-Sided Tolerance Bounds
Criterion for the Precision of a Tolerance Interval
Tabulations for Tolerance Interval/Bound Sample Sizes
Sample Size to Pass a One-Sided Demonstration Test Based on Normally Distributed MeasurementsGraphical Method
Tabular Method
Computational Method
Minimum Sample Size for Distribution-Free Two-Sided Tolerance Intervals and One-Sided Tolerance Bounds
Minimum Sample Size for Two-Sided Tolerance Intervals
Minimum Sample Size for One-Sided Tolerance Bounds
Sample Size for Controlling the Precision of Two-Sided Distribution-Free Tolerance Intervals and One-Sided Distribution-Free Tolerance Bounds
Sample Size to Demonstrate that a Binomial Proportion Exceeds (Is Exceeded By) a Speciied Value
Graphical Method
Tabular Method
Computational MethodSample Size Requirements for Prediction Intervals
Prediction Interval Width: The Basic Idea
Sample Size for a Normal Distribution Prediction IntervalRelative Width of the Prediction Interval
Figures for Two-Sided Prediction Intervals
One-Sided Prediction Bounds for a Future Sample Mean
Other Prediction Intervals
Sample Size for Distribution-Free Prediction Intervals for at least k of m Future Observations
Tabular Method for Two-Sided Prediction Intervals
Tabular Method for One-Sided Prediction Bounds
Basic Case Studies
Demonstration that the Operating Temperature of Most Manufactured Devices will not Exceed a Speciied Value
Problem Statement
Some Basic Assumptions
Statistical Problem
Results from a Preliminary Experiment
Nonparametric One-Sided Lower Conidence Bound on the Proportion Conforming
One-Sided Lower Conidence Bound for the Proportion Conforming Assuming a Normal Distribution
An Alternative Approach: Conidence Interval for a Normal Distribution Quantile for Device Temperatures
Sample Size Requirements
Forecasting Future Demand for Spare Parts
Background and Available Data
Assumptions
Prediction and a One-Sided Upper Prediction Bound for Future Total Demand
An Alternative One-Sided Upper Prediction Bound Assuming a Poisson Distribution for Demand
Estimating the Probability of Passing an Environmental Emissions Test
Background
Basic Assumptions
Nonparametric Approach
Normal Distribution Approach
Finding a One-Sided Upper Prediction Bound on the Emission Level
Planning a Demonstration Test to Verify that a Radar System has a Satisfactory Probability of Detection
Background and Assumptions
Choosing the Sample Size
Estimating the Probability of Exceeding a Regulatory Limit
Background and Assumptions
Preliminary Graphical Analysis
Formal Tests for Periodicity and Autocorrelation
Formal Test for Trend
Nonparametric Binomial Model
Lognormal Distribution Model
Estimating the Reliability of a Circuit Board
Background and Assumptions
Estimate of the Proportion of Defective Chips
Estimating the Probability that an Assembled Circuit Board Will Be Defective
Estimating System Reliability
Using Sample Results to Estimate the Probability that a Demonstration Test Will Be Successful
Nonparametric Binomial Model Approach
Normal Distribution Approach
Testing Sensitivity of the Conclusions to Changes in the Extreme Observation(s)
Estimating the Proportion within Speciications for a Two-Variable Problem
Problem Description
Nonparametric Approach
Determining the Minimum Sample Size for a Demonstration Test
Problem Description
Solution
Further Comments
Likelihood-Based Statistical Intervals
Introduction to Likelihood-Based Inference
Motivation for Likelihood-Based Inference
Model Selection
Likelihood Function and Maximum Likelihood Estimation
Probability of the Data
The Likelihood Function and its Maximum
Likelihood-Based Conidence Intervals for Single-Parameter Distributions
Conidence Intervals for the Exponential Distribution Mean
Conidence Intervals for a Monotone Function of the Exponential Distribution Mean
Conidence Intervals for F(t; )
Effect of Sample Size on the Likelihood and Conidence Interval Width
Likelihood-Based Estimation Methods for Location-Scale and
Log-Location-Scale Distributions
Background on Location-Scale and Log-Location-Scale Distributions
Likelihood Function for Location-Scale Distributions
Likelihood Function for the Lognormal, Weibull, and Other Log-Location-Scale Distributions
Maximum Likelihood Estimation and Relative Likelihood for Log-Location-Scale Distributions
Likelihood-Based Conidence Intervals for Parameters and Scalar Functions of Parameters
Relative Likelihood Contour Plots and Likelihood-Based Joint Conidence Regions for ? and
The Proile Likelihood and Likelihood-Based Conidence Intervals for ? and exp(?)
Likelihood-Based Conidence Intervals for
Likelihood-Based Conidence Intervals for Scalar Functions of ? and
Wald-Approximation Conidence Intervals
Parameter Variance-Covariance Matrix
Wald-Approximation Conidence Intervals for ? and exp(?)
Wald-Approximation Conidence Intervals for
Wald-Approximation Conidence Intervals for Functions of ? and
Using the Wald Approximation to Compute a Conidence Interval for a Correlation Coeficient
Some Other Likelihood-Based Statistical Intervals
Likelihood-Based and Wald-Approximation Conidence Intervals for Other Distributions
Likelihood-Based One-Sided Tolerance Bounds and Two-Sided Tolerance Intervals
Likelihood-Based Prediction IntervalsNonparametric Bootstrap Statistical IntervalsBasic Concepts
Motivating Example
Nonparametric Methods for Generating Bootstrap Samples and Obtaining
Bootstrap Estimates
Nonparametric Bootstrap Resampling
Nonparametric Random-Weight Bootstrap Sampling
Bootstrap Operational Considerations
Choosing the Number of Bootstrap Samples
Saving Bootstrap Results
Calculation of Quantiles of a Bootstrap Distribution
Nonparametric Bootstrap Conidence Interval Methods
Methods for Computing Nonparametric Bootstrap Conidence Intervals from the Bootstrap Samples
The Simple Percentile Method
The BCa Percentile Method
The BC Percentile Method
The Nonparametric Basic Bootstrap Method
The Nonparametric Bootstrap-t Method
Nonparametric Bootstrap Conidence Intervals for a Correlation Coeficient
Cautions on the Use of Nonparametric Bootstrap Conidence Interval Methods
Parametric Bootstrap and Other Simulation-Based Statistical IntervalsBasic Concepts
Motivating Examples
Parametric Bootstrap Samples and Bootstrap Estimates
Bootstrap Conidence Intervals Based on Pivotal QuantitiesConidence Intervals for the Location Parameter of a Location-Scale Distribution or the Scale Parameter of a Log-Location-Scale Distribution
Conidence Intervals for the Scale Parameter of a Location-Scale Distribution or the Shape Parameter of a Log-Location-Scale Distribution
Conidence Intervals for the p Quantile of a Location-Scale or a Log Location-Scale Distribution
Generalized Pivotal Quantities
Generalized Pivotal Quantities for ? and of a Location-Scale Distribution and for Functions of ? and
Conidence Intervals for Tail Probabilities for Location-Scale and Log-Location-Scale Distributions
Conidence Intervals for the Mean of a Log-Location-Scale Distribution
Simpliied Simulation and Conidence Interval Computation with PQs and GPQs
Simulation-Based Tolerance Intervals for Location-Scale or Log-Location-Scale Distributions
Two-Sided Tolerance Intervals to Control the Center of a Distribution
Two-Sided Tolerance Intervals to Control Both Tails of a Distribution
One-Sided Tolerance Bounds
Simulation-Based Prediction Intervals and One-Sided Prediction Bounds for at least k of m Future Observations from Location-Scale or Log-Location-Scale Distributions
Simultaneous Two-Sided Prediction Intervals to Contain at Least k of m Future Observations
Simultaneous One-Sided Prediction Bounds for k of m Future Observations
Other Simulation and Bootstrap Methods and Application to Other Distributions and Models
Resampling for Parametric Bootstrap Conidence Intervals
Random-Weight Bootstrap Sampling for Parametric Bootstrap Conidence Intervals
Bootstrap Methods with Other Distributions and Models
Bootstrapping with Complicated CensoringIntroduction to Bayesian Statistical Intervals
Bayesian Inference: Overview
Motivation
Bayesian Inference versus Non-Bayesian Likelihood Inference
Bayes’ Theorem and Bayesian Data Analysis
The Need for Prior Information
Parameterization
Bayesian Inference: An Illustrative Example
Example Using Weibull Distribution ML Analysis
Speciication of Prior Information
Characterizing the Joint Posterior Distribution via Simulation
Comparison of Joint Posterior Distributions Based on Diffuse and Informative Prior Information on the Weibull Shape Parameter
Generating Sample Draws with Simple Simulation
Using the Sample Draws to Construct Bayesian Credible Intervals
More About Speciication of a Prior Distribution
Diffuse versus Informative Prior Distributions
Whose Prior Distribution Should We Use?
Sources of Prior Information
Implementing Bayesian Analyses Using Conjugate Distributions
Some Further Considerations in the Speciication of Prior Distributions
Implementing Bayesian Analyses using Markov Chain Monte Carlo Simulation
Basic Ideas of MCMC Simulation
Risks of Misuse and Diagnostics
MCMC Summary
Software for MCMC
Bayesian Tolerance and Prediction Intervals
One-Sided Bayesian Tolerance Bounds
Two-Sided Bayesian Tolerance Intervals to Control the Center of a Distribution
Two-Sided Bayesian Tolerance Intervals to Control Both Tails of a Distribution
Bayesian Simultaneous Prediction Intervals to Contain at Least k out of m Future Observations
An Alternative Method of Computing Bayesian Prediction IntervalsBayesian Statistical Intervals for the Binomial, Poisson, and Normal Distributions
Bayesian Intervals for the Binomial Distribution
Binomial Distribution Conjugate Prior Distribution
Credible Interval for the Binomial Distribution Parameter
Credible Intervals for Functions of the Binomial Distribution Parameter
Tolerance Intervals for the Binomial Distribution
Prediction Intervals for the Binomial Distribution
Bayesian Intervals for the Poisson Distribution
Poisson Distribution Conjugate Prior Distribution
Credible Interval for the Poisson Event-Occurrence Rate
Other Credible Intervals for the Poisson Distribution
Tolerance Intervals for the Poisson Distribution
Prediction Intervals for the Poisson Distribution
Bayesian Intervals for the Normal Distribution
Normal Distribution Conjugate Prior Distribution
MCMC Method
Credible Intervals for the Normal Distribution Parameters
Other Credible Intervals for the Normal Distribution
Tolerance Intervals for the Normal Distribution
Prediction Intervals for the Normal DistributionStatistical Intervals for Bayesian Hierarchical Models
Bayesian Hierarchical Models and Random Effects
Normal Distribution Hierarchical Models
Binomial Distribution Hierarchical Models
Poisson Distribution Hierarchical Models
Longitudinal Repeated Measures ModelsAdvanced Case Studies
Conidence Interval for the Proportion of Defective Integrated Circuits
The Limited Failure Population Model
Estimates and Conidence Intervals for the Proportion of Defective
Conidence Intervals for Components of Variance in a Measurement Process
Two-Way Random-Effects Model
Bootstrap (GPQ) Method
Bayesian Method
Comparison of Results Using GPQ and Bayesian Methods and Recommendations
Tolerance Interval to Characterize the Distribution of Process Output in the Presence of Measurement Error
Bootstrap (GPQ) Method
Bayesian Method
Conidence Interval for the Proportion of Product Conforming to a Two-Sided Speciication
Bootstrap Simulation (GPQ) Method
Bayesian Method
Conidence Interval for the Treatment Effect in a Marketing Campaign
Background
Bootstrap (Simulation) Method
Bayesian Method
Conidence Interval for the Probability of Detection with Limited Hit/Miss Data
Logistic Regression Model
Likelihood Method
Bayesian Method
Using Prior Information to Estimate the Service-Life Distribution of a Rocket Motor
Rocket Motor Example Revisited
Rocket Motor Prior Information
Rocket Motor Bayesian Estimation Results
Credible Interval for the Proportion of Healthy Rocket Motors after or Years in the StockpileEpilogue
A Notation and Acronyms
B Generic Deinition of Statistical Intervals and Formulas for Computing Coverage
ProbabilitiesB Introduction
B Two-Sided Conidence Intervals and One-Sided Conidence Bounds for Distribution Parameters or a Function of Parameters
B Two-Sided Conidence Interval Deinition
B One-Sided Conidence Bound Deinition
B A General Expression for Computing the Coverage Probability of a Conidence Interval Procedure
B Computing the Coverage Probability for a Conidence Interval Procedure When Sampling from a Discrete Probability Distribution
B Computing the Coverage Probability for a Conidence Interval Procedure When Sampling from a Continuous Probability Distribution
B Two-Sided Control-the-Center Tolerance Intervals to Contain at Least a Speciied Proportion of a Distribution
B Control-the-Center Tolerance Interval Deinition
B A General Expression for Computing the Coverage Probability of a Control-the-Center Tolerance Interval Procedure
B Computing the Coverage Probability for a Control-the-Center Tolerance Interval Procedure When Sampling from a Discrete Distribution
B Computing the Coverage Probability for a Control-the-Center Tolerance Interval Procedure When Sampling from a Continuous Probability Distribution
B Two-Sided Tolerance Intervals to Control Both Tails of a Distribution
B Control-Both-Tails Tolerance Interval Deinition
B A General Expression for Computing the Coverage Probability of a Control-Both-Tails Tolerance Interval Procedure
B Computing the Coverage Probability for a Control-Both-Tails Tolerance Interval Procedure When Sampling from a Discrete Probability Distribution
B Computing the Coverage Probability for a Control-Both-Tails Tolerance Interval Procedure When Sampling from a Continuous Probability Distribution
B One-Sided Tolerance Bounds
B Two-Sided Prediction Intervals and One-Sided Prediction Bounds for Future Observations
B Prediction Interval Deinition
B One-Sided Prediction Bound Deinition
B A General Expression for Computing the Coverage Probability of a Prediction Interval Procedure
B Computing the Coverage Probability for a Prediction Interval Procedure When Sampling from a Discrete Probability Distribution
B Computing the Coverage Probability for a Prediction Interval Procedure When Sampling from a Continuous Probability Distribution
B Two-Sided Simultaneous Prediction Intervals and One-Sided Simultaneous Prediction Bounds
B Calibration of Statistical IntervalsC Useful Probability Distributions
C Probability Distributions and R Computations
C Important Characteristics of Random Variables
C Density and Probability Mass Functions
C Cumulative Distribution Function
C Quantile Function
C Continuous Distributions
C Location-Scale and Log-Location-Scale Distributions
C Examples of Location-Scale and Log-Location-Scale Distributions
C Beta Distribution
C Log-Uniform Distribution
C Gamma Distribution
C Chi-Square Distribution
C Exponential Distribution
C Generalized Gamma Distribution
C Noncentral t-Distribution
C Student’s t-Distribution
C Snedecor’s F-Distribution
C Scale Half-Cauchy Distribution
C Discrete Distributions
C Binomial Distribution
C Beta-Binomial Distribution
C Negative Binomial Distribution
C Poisson Distribution
C Hypergeometric Distribution
C Negative Hypergeometric DistributionD General Results from Statistical Theory and Some Methods Used to Construct Statistical Intervals
D The cdfs and pdfs of Functions of Random Variables
D Transformation of Continuous Random Variables
D Transformation of Discrete Random Variables
D Statistical Error Propagation—The Delta Method
D Likelihood and Fisher Information Matrices
D Information Matrices
D Fisher Information for a One-to-One Transformation of
D Convergence in Distribution
D Outline of General Maximum Likelihood Theory
D Asymptotic Distribution of ML Estimators
D Asymptotic Distribution of Functions of ML Estimators via the Delta Method
D Estimating the Variance-Covariance Matrix of ML Estimates
D Likelihood Ratios and Proile Likelihoods
D Approximate Likelihood-Ratio-Based Conidence Regions or Conidence Intervals for the Model Parameters
D Approximate Wald-Based Conidence Regions or Conidence Intervals for the Model Parameters
D Approximate Score-Based Conidence Regions or Conidence Intervals for Model Parameters
D The cdf Pivotal Method for Obtaining Conidence Intervals
D Continuous Distributions
D Discrete Distributions
D Coverage Probability of the Intervals Derived from the cdf Pivotal Method
D Bonferroni Approximate Statistical Intervals
D The Bonferroni Inequality
D Bonferroni Conservative Approach for Simultaneous Statistical Intervals
D Bonferroni Conservative Approach for Tolerance Intervals
D Alternative Approximate Tolerance Interval Method
D Two-Sided Prediction Intervals Based on Two One-Sided Prediction Bounds and a Bonferroni ApproximationE Pivotal Methods for Constructing Parametric Statistical Intervals
E General Deinition and Examples of Pivotal Quantities
E Pivotal Quantities for the Normal Distribution
E Pivotal Quantities from a Single Normal Distribution Sample
E Pivotal Quantities Involving Data from Two Normal Distribution Samples
E Conidence Intervals for a Normal Distribution Based on Pivotal Quantities
E Conidence Interval for the Mean of a Normal Distribution
E Conidence Interval for the Standard Deviation of a Normal Distribution
E Conidence Interval for the Quantile of a Normal Distribution
E Conidence Intervals for Tail Probabilities of a Normal Distribution
E Conidence Intervals for Two Normal Distributions Based on Pivotal Quantities
E Conidence Interval to Compare Two Sample Variances
E Conidence Interval for the Difference between Two Normal Distribution Means
E Tolerance Intervals for a Normal Distribution Based on Pivotal Quantities
E Tolerance Intervals to Control the Center
E Tolerance Intervals to Control Both Tails
E Normal Distribution Prediction Intervals Based on Pivotal Quantities
E Prediction Interval to Contain the Mean of m Future Observations from a Previously Sampled Normal Distribution
E Prediction Interval for the Sample Standard Deviation from a Sample of m Future Observations from a Previously Sampled Normal Distribution
E One-Sided Prediction Bound to Exceed (be Exceeded by) at Least k Out of m Future Observations from a Previously Sampled Normal Distribution
E Simultaneous Prediction Interval to Contain at Least k Out of m Future Observations from a Previously Sampled Normal Distribution
E Pivotal Quantities for Log-Location-Scale Distributions
E Pivotal Quantities Involving Data from a Location-Scale Distribution
E Conidence Interval for a Location Parameter
E Conidence Interval for a Scale Parameter
E Conidence Interval for a Distribution Quantile
E One-Sided Simultaneous Prediction Bound to Exceed (be Exceeded by) at Least k Out of m Future Observations from a Previously Sampled (Log-)Location-Scale Distribution
E Two-Sided Simultaneous Prediction Interval to Contain at Least k Out of m Future Observations from a Previously Sampled (Log-)Location-Scale Distribution
E Pivotal Quantities Involving Data from Two Similar (Log-)Location-Scale DistributionsF Generalized Pivotal Quantities
F Deinition of a Generalized Pivotal Quantity
F A Substitution Method to Obtain Generalized Pivotal Quantities
F Examples of Generalized Pivotal Quantities for Functions of Location-Scale Distribution Parameters
F GPQ Function for?
F GPQ Function for
F GPQ Function for a Tail Probability F(x; ?, )
F GPQ Function for Probability Content of an Interval
F Conditions for Exact Conidence Intervals Derived from Generalized Pivotal Quantities
F A Necessary and Suficient Condition for an Exact GPQ Conidence Interval Procedure
F A Suficient Condition for an Exact GPQ Conidence Interval ProcedureG Distribution-Free Intervals Based on Order Statistics
G Basic Statistical Results Used in this Appendix
G Distribution-Free Conidence Intervals and Bounds for a Distribution Quantile
G Distribution-Free Conidence Intervals for Quantiles
G Distribution-Free One-Sided Conidence Bounds for Quantiles
G Distribution-Free Tolerance Intervals to Contain a Given Proportion of a Distribution
G Distribution-Free Tolerance Intervals
G Distribution-Free Prediction Interval to Contain a Speciied Ordered Observation From a Future Sample
G Distribution-Free Prediction Interval for Y(j ) in a Future Sample
G Distribution-Free One-Sided Prediction Bounds for Y(j ) in a Future Sample
G Prediction Interval to Contain a Speciied Ordered Observation Y(j ) in a Future Sample (Technical Details)
G Distribution-Free Prediction Intervals and Bounds to Contain at Least k of m Future Observations From a Future Sample
G Prediction Intervals to Contain at Least k of m Future Observations
G One-Sided Prediction Bounds to Exceed (or Be Exceeded by) at Least k of m Future Observations
G Special Cases, Limiting Behavior, and Relationship to Predicting a Future Ordered Observation
G Distribution-Free Prediction Intervals and Bounds to Contain at Least k of m Future Observations: Coverage Probabilities (Technical Details)H Basic Results from Bayesian Inference Models
H Basic Results Used in this Appendix
H Bayes’ Theorem
H Conjugate Prior Distributions
H Conjugate Prior Distribution for the Binomial Distribution
H Conjugate Prior Distribution for the Poisson Distribution
H Conjugate Prior Distribution for the Normal Distribution
H Jeffreys Prior Distributions
H Jeffreys Prior Distribution for the Binomial Distribution
H Jeffreys Prior Distribution for the Poisson Distribution
H Jeffreys Prior Distribution for the Normal Distribution
H Posterior Predictive Distributions
H General Results
H Posterior Predictive Distribution for the Binomial Distribution Based on a Conjugate Prior Distribution
H Posterior Predictive Distribution for the Poisson Distribution Based on a Conjugate Prior Distribution
H Posterior Predictive Distribution for the Normal Distribution Based on a Conjugate Prior Distribution
H Posterior Predictive Distributions Based on Jeffreys Prior Distributions
H Posterior Predictive Distribution for the Binomial Distribution Based on Jeffreys Prior Distribution
H Posterior Predictive Distribution for the Poisson Distribution Based on Jeffreys Prior Distribution
H Posterior Predictive Distribution for the Normal Distribution Based on the Modiied Jeffreys Prior DistributionI Probability of Successful Demonstration
I Demonstration Tests Based on a Normal Distribution Assumption
I Probability of Successful Demonstration Based on a Normal Distribution One-Sided Conidence Bound on a Quantile
I Probability of Successful Demonstration Based on a One-Sided Conidence Bound on a Normal Distribution Probability
I Sample Size to Achieve a pdem for a Demonstration Based on a Normal Distribution One-Sided Conidence Bound on a Quantile
I Distribution-Free Demonstration Tests
I Probability of Successful Demonstration Based on a Distribution-Free One-Sided Conidence Bound on a Quantile
I Probability of Successful Demonstration Based on a One-Sided Conidence Bound on a Binomial Distribution Probability
I Sample Size to Achieve a pdem for a Demonstration Based on a One-Sided Conidence Bound on a ProbabilityJ Tables

Index