In Loss Model: from data to decison (2nd edition) ,Page 44.
quotes:
" F(x)=1-a(theta1/(theta1+x))^alpha-(1-a)(theta2/(theta2+x))^(alpha+2).
Note that the shape parameters in the two Pareto distributions differ by 2. The second distribution places more probability on smaller values. This might be a model for frequent, small claims while the first distribution covers large but infrequent claims."
My questions:
what is the relation between the so-called "shape parameter ---alpha" and the frequency,amount of claims? since (theta/theta+X) is always less than 1,and its square is always less than itself, then why the second distribution places more probabity on smaller values ?
looking forward for the replies!
besides,can any one explain the shape parameter and the scale parameter? better with some properties...i just can't find answers from my limited reference books
quotes:
" F(x)=1-a(theta1/(theta1+x))^alpha-(1-a)(theta2/(theta2+x))^(alpha+2).
Note that the shape parameters in the two Pareto distributions differ by 2. The second distribution places more probability on smaller values. This might be a model for frequent, small claims while the first distribution covers large but infrequent claims."
My questions:
what is the relation between the so-called "shape parameter ---alpha" and the frequency,amount of claims? since (theta/theta+X) is always less than 1,and its square is always less than itself, then why the second distribution places more probabity on smaller values ?
looking forward for the replies!
besides,can any one explain the shape parameter and the scale parameter? better with some properties...i just can't find answers from my limited reference books