Pareto Distribution

Hi All,

I'm looking at the inflation example in Chapter 4 involving the Pareto distribution. I don't understand the solution to parts i or ii. Are there some tricks to integrating the Pareto distribution? I understand setting y=kx and then substituting y/k into the distribution for x, but not how this then represents a Pareto (alpha,k*lambda) distribution.

Many Thanks

 

The trick is pareto has inverted linear R.V. apply formula "integration of x^(-n)=x^(-n+1)/(-n+1)"
& for inflatinary part, just put x=y/k(you know the reason) then replace dx=(1/k)*dy then simplify you'll get it.

 

I get it now! Thank you

 

if you're measuring probability from the PDF, then you can do it directly by basic integration.

But if you measure any expected value, then it may or may not be solved by integration by parts.
say,
for E(X^n) where n>0, you should choose u=x because you know it'll be going to vanish, and you can go on with v until u will be vanished.
for E(lnX), I can't think of solving it with integration by part with ease