Density Functions

**janvdl** · July 26th 2008, 08:33 AM

Let F(x) = 1 - e^{- \alpha x^{\beta}} for $x \geq 0$ ; $\alpha > 0$ ; \beta > 0 ; and $F(x) = 0$ for $x < 0$ .

Show F is a cdf and find the corresponding density.

**CaptainBlack** · July 26th 2008, 10:31 AM

Originally Posted by janvdl

Let F(x) = 1 - e^{- \alpha x^{\beta}} for $x \geq 0$ ; $\alpha > 0$ ; \beta > 0 ; and $F(x) = 0$ for $x < 0$ .

Show F is a cdf and find the corresponding density.

To show its a cdf you need to show that it is increasing, non-negative with a supremum of 1.

Then since F is continuous and differentiable, the density is the derivative of F.

RonL

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