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MATH 226 - 10.24.07

MATH 226 - 10.24.07 - Weibull Distribution o X = waiting...

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MATH 226 – October 24, 2007 Exponential Distribution o X = waiting time to the first event (of a Poisson Process) o f(x) = (1/α)e -x/α , x > 0, α > 0 F(x) = P(X ≤ x) = ∫ 0 x (1/α)e -t/α dt = 1 – e -x/α , x ≥ 0 o EX = α, VarX = α 2 Erlang Distribution o X = waiting time to the n th event o X ~ Erlang(n, α) o EX = nα
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Unformatted text preview: Weibull Distribution o X = waiting time to an event o f(x) = (β/α β )x β – 1 e-(x/α)^β F(x) = 1 - e-(x/α)^β o EX = αΓ(1+ (1/β)) o α is the scale parameter β is the shape parameter Comparison o Exponential geometric Erlang negative binomial o Memory less property...
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