Notes On Paretian Distribution Theory
Notes On Paretian Distribution Theory
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10) are loss integrals linear in a -- which, as we would expect, have certain undesirable prop- erties if a 1 with probability 1. In order to proceed in this direction we will need to know the conditional expectations E(a|a - e) and E(a|a S e) for values of e between and + », We show that + CO for ^ €) ""o^ 0, ^1 rcixpx. '^"^ G . (e-l|i, l)j pr(r) "-' ^ + (£)1 for € > 1, o ' where 0^(e) = / y'^e'^dy, X « log^lt 'x^'') and p = G^^(e| r, t) .
Proof ; Formula (3, 10) follows directly from (1. 2).... Now suppose that a ~ f^^(a|r, t) =— ^ (\a) e, ^ > Then for e > 1, 00 E(i|e> 1) = !° J(-i^) f^^(z|r, t) dz e 00 ° ' (z-l)'^e"^^(\z)''d(\z) .
P^r(r), e Letting u = z-1, we may write the above as ^o^ / y"-^e"y [Xu +xf d(\u), P^r(r) e-1 or letting y = \u, as Since V_ f y'^e'y[ L (Oy^"""'] dy pr(r) J^^^ ""o^ 5 /^^r-i r i-1 -y €-1 00 V^"'"'''^ ~-Fa)I y^'^'^^dy, i>0, e-1 we may write -X.
What to read after Notes On Paretian Distribution Theory?
You can find similar books in the "Read Also" column, or choose other free books by G M Kaufman to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
10) are loss integrals linear in a -- which, as we would expect, have certain undesirable prop- erties if a 1 with probability 1. In order to proceed in this direction we will need to know the conditional expectations E(a|a - e) and E(a|a S e) for values of e between and + », We show that + CO for ^ €) ""o^ 0, ^1 rcixpx. '^"^ G . (e-l|i, l)j pr(r) "-' ^ + (£)1 for € > 1, o ' where 0^(e) = / y'^e'^dy, X « log^lt 'x^'') and p = G^^(e| r, t) .
Proof ; Formula (3, 10) follows directly from (1. 2).... Now suppose that a ~ f^^(a|r, t) =— ^ (\a) e, ^ > Then for e > 1, 00 E(i|e> 1) = !° J(-i^) f^^(z|r, t) dz e 00 ° ' (z-l)'^e"^^(\z)''d(\z) .
P^r(r), e Letting u = z-1, we may write the above as ^o^ / y"-^e"y [Xu +xf d(\u), P^r(r) e-1 or letting y = \u, as Since V_ f y'^e'y[ L (Oy^"""'] dy pr(r) J^^^ ""o^ 5 /^^r-i r i-1 -y €-1 00 V^"'"'''^ ~-Fa)I y^'^'^^dy, i>0, e-1 we may write -X.
What to read after Notes On Paretian Distribution Theory?
You can find similar books in the "Read Also" column, or choose other free books by G M Kaufman to read onlineMoreLess
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