6 chapter8 Random Variate

09 and i i 1 2 13 special properties based on features

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Unformatted text preview: particular family of probability distributions For example: Direct Transformation for normal and lognormal distributions Convolution 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.

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