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위험도 관리 및 의사결정론

위험도 관리 및 의사결정론. 한양대학교 건설관리학과. Frequency and Probability Distributions. 1. Cost Estimate Example. 1. Cost Estimate Example. - 50 professionals estimate Project Cost. - The collected values → $26.7 mil. ~$76.0 mil. Frequency Histogram Procedure ① Divide the range of

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위험도 관리 및 의사결정론

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  1. 위험도 관리 및 의사결정론 한양대학교 건설관리학과

  2. Frequency and Probability Distributions

  3. 1. Cost Estimate Example

  4. 1. Cost Estimate Example - 50 professionals estimate Project Cost. - The collected values → $26.7 mil. ~$76.0 mil. • Frequency Histogram • Procedure ① Divide the range of values (5~50 intervals) ② Count the number of values occurring within each interval. ③ Draw a bar graph • One bar per interval • Bar heights → the number(or frequency) of occurrences ※ (Option) Label the y-axis with Numbers of values or Percents of the total

  5. 1. Cost Estimate Example • Suppose that we have 500 data points • More data and smaller value segment partitions provide the additional detail shown in Fig. 1.4 • If we obtain a great many data points and use smaller intervals → Probability Density Function (p.d.f) or simply, Probability Distribution

  6. 1. Cost Estimate Example • Probability Distribution • Relative likelihood of estimate values along the x-axis • The p.d.f represents a judgment about uncertainty. → Unlike a frequency distribution, the p.d.f is not representing data. Y-axis is scaled so that the area under the curve equals 1.

  7. 2. Popular Central Measures

  8. 2. Popular Central Measures • Two statistics annotated in Fig. 1.5 • Most likely value ($40 mil.) - This peak is also called mode - Useful in describing a distribution’s shape • Expected value ($45 mil.) • Probability-weighted average • Mean value = Greek letter μ • Best single measure of value under uncertainty

  9. 3. Cumulative Probability Density Curve

  10. 3. Cumulative Probability Density Curve • The p.d.f (Fig.1.5) can be converted into a cumulative (probability) density function (c.d.f) curve. • Integration of p.d.f • Median • centermost value, at 50% probability • another central measure • used with demographics to indicate “average” values, such as house price or salaries

  11. 3. Cumulative Probability Density Curve • Confidence Limit • About 74% of the Project Cost estimates: below $50 mil. ☞74% (less-than) confidence limit(or level) is $50 mil. • Confidence Interval • About 80% of the Project Cost estimates: $33 mil. ~ $57 mil. ☞80% confidence interval is $33 mil. ~ $57 mil. range

  12. 4. Expected Value

  13. 4. Expected Value • Expected Value • Range $2.2 mil. ~ $2.7 mil. Most likely value $2.3 mil. • Low, Most likely, and High values ▷ Triangle Distribution • The best single-point estimate is expected value(EV) • Performing many similar projects → average $2.4 mil. • Over the long run, estimate error will approach zero subjective objective (unbiased)

  14. 4. Expected Value • Calculating Expected Value • Distribution expressed as a mathematical formulaintegral equation: Where is the value of the variable and is the p.d.f of • EV is the sum of the outcome values times their probabilities: Where are the outcome values, and are the probabilities of these outcomes.

  15. 4. Expected Value • Measurement of Dispersion • Probability Distribution: Better for estimating Risks • Standard Deviation • = Outcome • = Expected Value • = Probabilities • Coefficient of Variation(변동계수) • Expected Income: 1억 Standard Deviation: 100만원 • Expected Income: 100만원 Standard Deviation: 50만원 → C.O.V =

  16. Thank You ! 위험도 관리 및 의사결정론

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