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BL
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| Record Number
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667650
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| Doc. No
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dltt
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| Main Entry
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Samaniego, Francisco J.
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| Title & Author
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Stochastic modeling and mathematical statistics : : a text for statisticians and quantitative scientists /\ Francisco J. Samaniego.
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| Series Statement
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Texts in statistical science.
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| Page. NO
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xx, 602 p. :: ill. ;; 26 cm.
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| ISBN
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9781466560468 (cloth : acid-free paper)
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: 1466560460 (cloth : acid-free paper)
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9781482226805 (ePub ebook)
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| Notes
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"A Chapman & Hall book."
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| Bibliographies/Indexes
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Includes bibliographical references (p. 593-596) and index.
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| Contents
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Machine generated contents note: 1.1.A Bit of Background -- 1.2.Approaches to Modeling Randomness -- 1.3.The Axioms of Probability -- 1.4.Conditional Probability -- 1.5.Bayes' Theorem -- 1.6.Independence -- 1.7.Counting -- 1.8.Chapter Problems -- 2.1.Random Variables -- 2.2.Mathematical Expectation -- 2.3.The Hypergeometric Model -- 2.4.A Brief Tutorial on Mathematical Induction (Optional) -- 2.5.The Binomial Model -- 2.6.The Geometric and Negative Binomial Models -- 2.7.The Poisson Model -- 2.8.Moment-Generating Functions -- 2.9.Chapter Problems -- 3.1.Continuous Random Variables -- 3.2.Mathematical Expectation for Continuous Random Variables -- 3.3.Cumulative Distribution Functions -- 3.4.The Gamma Model -- 3.5.The Normal Model -- 3.6.Other Continuous Models -- 3.6.1.The Beta Model -- 3.6.2.The Double Exponential Distribution -- 3.6.3.The Lognormal Model -- 3.6.4.The Pareto Distribution -- 3.6.5.The Weibull Distribution -- 3.6.6.The Cauchy Distribution --
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Contents note continued: 3.6.7.The Logistic Model -- 3.7.Chapter Problems -- 4.1.Bivariate Distributions -- 4.2.More on Mathematical Expectation -- 4.3.Independence -- 4.4.The Multinomial Distribution (Optional) -- 4.5.The Multivariate Normal Distribution -- 4.6.Transformation Theory -- 4.6.1.The Method of Moment-Generating Functions -- 4.6.2.The Method of Distribution Functions -- 4.6.3.The Change-of-Variable Technique -- 4.7.Order Statistics -- 4.8.Chapter Problems -- 5.1.Chebyshev's Inequality and Its Applications -- 5.2.Convergence of Distribution Functions -- 5.3.The Central Limit Theorem -- 5.4.The Delta Method Theorem -- 5.5.Chapter Problems -- 6.1.Basic Principles -- 6.2.Further Insights into Unbiasedness -- 6.3.Fisher Information, the Cramer-Rao Inequality, and Best Unbiased Estimators -- 6.4.Sufficiency, Completeness, and Related Ideas -- 6.5.Optimality within the Class of Linear Unbiased Estimators -- 6.6.Beyond Unbiasedness -- 6.7.Chapter Problems --
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Contents note continued: 7.1.Basic Principles -- 7.2.The Method of Moments -- 7.3.Maximum Likelihood Estimation -- 7.4.A Featured Example: Maximum Likelihood Estimation of the Risk of Disease Based on Data from a Prospective Study of Disease -- 7.5.The Newton-Raphson Algorithm -- 7.6.A Featured Example: Maximum Likelihood Estimation from Incomplete Data via the EM Algorithm -- 7.7.Chapter Problems -- 8.1.Exact Confidence Intervals -- 8.2.Approximate Confidence Intervals -- 8.3.Sample Size Calculations -- 8.4.Tolerance Intervals (Optional) -- 8.5.Chapter Problems -- 9.1.The Bayesian Paradigm -- 9.2.Deriving Bayes Estimators -- 9.3.Exploring the Relative Performance of Bayes and Frequentist Estimators -- 9.4.A Theoretical Framework for Comparing Bayes vs. Frequentist Estimators -- 9.5.Bayesian Interval Estimation -- 9.6.Chapter Problems -- 10.1.Basic Principles -- 10.2.Standard Tests for Means and Proportions -- 10.3.Sample Size Requirements for Achieving Pre-specified Power --
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Contents note continued: 10.4.Optimal Tests: The Neyman-Pearson Lemma -- 10.5.Likelihood Ratio Tests -- 10.6.Testing the Goodness of Fit of a Probability Model -- 10.7.Fatherly Advice about the Perils of Hypothesis Testing (Optional) -- 10.8.Chapter Problems -- 11.1.Simple Linear Regression -- 11.2.Some Distribution Theory for Simple Linear Regression -- 11.3.Theoretical Properties of Estimators and Tests under the SLR Model -- 11.4.One-Way Analysis of Variance -- 11.5.The Likelihood Ratio Test in One-Way ANOVA -- 11.6.Chapter Problems -- 12.1.Nonparametric Estimation -- 12.2.The Nonparametric Bootstrap -- 12.3.The Sign Test -- 12.4.The Runs Test -- 12.5.The Rank Sum Test -- 12.6.Chapter Problems.
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| Subject
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Mathematical statistics.
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| Subject
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Stochastic models.
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| LC Classification
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QA276.S26 2014
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