briefnts5_funct

# briefnts5_funct - and This distribution is known as the...

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Brief Notes #5 Functions of Random Variables and Vectors 1

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Examples of Monotonic Transformations Consider an exponential variable X ~ ) ( EX λ with cumulative distribution function , . x X e 1 ) x ( F λ = 0 x Exponential, Power and Log Functions Exponential Functions Suppose , , . This is a monotonic increasing function, and . This distribution is known as the (strict) Pareto Distribution. X e Y = Y ln X = 0 y λ λ = = = y 1 e 1 )) y ( x ( F ) y ( F y ln X Y Power Functions Suppose α = 1 X Y , , . This is a monotonic increasing function,

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Unformatted text preview: and . This distribution is known as the Weibull (Extreme Type III) Distribution. > α ⇒ Y ln X = y ≥ α λ − − = = y X Y e 1 )) y ( x ( F ) y ( F Log Functions Suppose , , X ln Y − = ⇒ Y e X − = ∞ ≤ ≤ ∞ − y . This is a monotonic decreasing function, and . This distribution is known as the Gumbel (Extreme Type I) Distribution. y e X Y e )) y ( x ( F 1 ) y ( F − λ − = − = 4 5 6 7 8...
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## This note was uploaded on 02/27/2008 for the course PTE 461 taught by Professor Donhill during the Fall '07 term at USC.

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briefnts5_funct - and This distribution is known as the...

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