The Pareto distribution with parameter a > 0 has PDF f(x)= al xa+1 for x > 1 (and 0 otherwise). This distribution is often used in statistical modeling. (a) Find the CDF of a Pareto r.v. with...

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The Pareto distribution with parameter a > 0 has PDF f(x)= al xa+1 for x > 1 (and 0 otherwise). This distribution is often used in statistical modeling. (a) Find the CDF of a Pareto r.v. with parameter a; check that it is a valid CDF. (b) Suppose that for a simulation you want to run, you need to generate i.i.d. Pareto(a) r.v.s. You have a computer that knows how to generate i.i.d. Unif(0, 1) r.v.s but does not know how to generate Pareto r.v.s. Show how to do this.

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Answered Same DayDec 26, 2021

Answer To: The Pareto distribution with parameter a > 0 has PDF f(x)= al xa+1 for x > 1 (and 0 otherwise). This...

David answered on Dec 26 2021

131 Votes

Ans. 1
The PDF of given Pareto distribution,
1
( ) , 0, 1
a
a
f x a x
x 
  
(a)
Now, integrate the given CDF with respect to dummy variable ( )y , taking the limits as
1 toy x ,
( 1)
11 1
1
( )
( ) 1
y y
a
a
y
a a
a
f x ax dx
x
f x x y
 

 
 
     
...

SOLUTION.PDF

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The Pareto distribution with parameter a > 0 has PDF f(x)= al xa+1 for x > 1 (and 0 otherwise). This distribution is often used in statistical modeling. (a) Find the CDF of a Pareto r.v. with...

Answer To: The Pareto distribution with parameter a > 0 has PDF f(x)= al xa+1 for x > 1 (and 0 otherwise). This...

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