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Direct Transformation for normal and lognormal
Beta distribution (from gamma distribution) 14 Direct Transformation [Special Properties] Approach for normal(0,1):
Consider two standard normal random variables, Z1 and Z2,
plotted as a point in the plane:
In polar coordinates:
Z1 = B cos
Z2 = B sin B2 = Z21 + Z22 ~ chi-square distribution with 2 degrees of freedom
= Exp( = 2). Hence, B = ( 2 ln R )1/ 2
The radius B and angle are mutually independent.
Z1 = ( 2 ln R)1/ 2 cos(2 R2 )
Z 2 = ( 2 ln R)1/ 2 sin( 2 R2 ) 15 Direc...
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This document was uploaded on 02/16/2014.
- Spring '14