Statistics Review

# Statistics Review - CEE 597 Risk Analysis &amp; Management...

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CEE 597 Statistics Review Veronica W. Griffis February 20, 2006

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2 Statistics Review Provide motivation for use of probability theory and statistical estimation Review hypothesis testing Review use of standard normal tables and Student’s t-distribution Provide examples Introduce binomial distribution
3 Introduction to Statistical Estimation What is statistical estimation and why do we need it? To perform risk management, we need to understand what the major risks are We want to be able to prioritize risks and decide where to focus efforts and spend money To identify major risks, we need to quantify various risks use probability theory and statistical estimation

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4 Introduction to Statistical Estimation Probability Theory: Given sample space (set of all possible outcomes) and sampling procedure (experiment), determine likelihood of different “events” Based on characteristics of population, events are observed with some unknown probability Probabilities may be described by various distributions -- geometric, binomial, Poisson, gamma, normal, lognormal, Gumbel, and Weibull Population Characteristics Probabilities of Events
5 Introduction to Statistical Estimation Need to estimate probabilities to assess risk Don’t know characteristics of true population, can only estimate them Statistical Theory: Method of inferring characteristics of the real world based upon observed events Attempt to determine distributions used by nature from observations so we can estimate probabilities Observed Sample Characteristics of Population μ , σ , x x s

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6 Sample Statistical Estimation ˆ ˆ ˆ ( , , ) μ σ λ Population , σ , λ29 Observe sample with some unknown probability Use statistical estimation to infer characteristics of population from observed sample
7 Common Statistical Notation Random Variables: Upper case letters X, Y, Z, X 1 , Y k Observed Values (Sample Data): Lower case letters x, y, z, x 1 , y k True Parameters of Distributions: Greek letters μ , σ , α , β , λ Parameter Estimators: Greek letters with hats Or, moment estimators ˆ ˆ ˆ ˆ ˆ , , , , μ σ α β λ , x x s

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8 Hypothesis Testing Statistical hypothesis - a claim about the value of
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## This note was uploaded on 09/28/2008 for the course CEE 5970 taught by Professor Stedinger during the Spring '07 term at Cornell University (Engineering School).

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Statistics Review - CEE 597 Risk Analysis &amp; Management...

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