Ch6 - Choice of Distribution 1. Theoretical Basis e.g. CLT,...

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1 Choice of Distribution Choice of Distribution 1. Theoretical Basis e.g. CLT, Extreme value 1. Simplify calculations e.g. Normal or Log Normal 1. Based on data: - Histogram - Probability paper
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2 (a) Arrange the data in ascending order (b) Let (c) Plot VS (d) See if follows a straight line N m x x x x ,... ,..., , 2 1 1 + = N m P m m x m P Use of Probability Paper Use of Probability Paper
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3 Arithmetic Plot Probability Paper 1 0 x ) ( x F x Probability Scale x ) ( x F x Concept of Probability Paper Concept of Probability Paper
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4 Example Example Data: 2.9, 3.5, 4, 2.5, 3.1 N=5 1 m m m m 1 2.5 1/6= 0.1667 2 2.9 2/6= 0.3333 3 3.1 3/6= 0.5000 4 3.5 4/6= 0.6667 5 4 5/6= 0.8333 m x 1 / + = N m P m
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5 Normal Probability paper 75 . 0 2 . 3 95 . 3 ˆ 2 . 3 ˆ 5 . 0 84 . 0 5 . 0 = - = - = = = x x x σ μ 50% 84% 4 3 2 1 3.2 3.95
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6 Shear strength of concrete Shear strength of concrete m h Shear strength s h m/N+1 h h lnS h m h Shear strength s h m/N+1 h h lnS 1 0.35 0.0714 -1.05 h 8 0.58 0.5714 -0.54 2 0.40
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Ch6 - Choice of Distribution 1. Theoretical Basis e.g. CLT,...

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