Convolution random number generator: Difference between revisions

Revision as of 18:21, 3 May 2007

Revision as of 20:58, 7 July 2008

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== Example ==

Consider the random variable <math>X\ \sim Erlang(k, \theta)</math>, defined as the sum of '''''k''''' random variables each with distribution '''<math>exp(k \theta)</math>'''.

Notice that :

:<math>E[X] = \frac{1}{k \theta} + \frac{1}{k \theta} + ... + \frac{1}{k \theta} = \frac{1}{\theta}</math>

WeOne can now generate '''<math>Erlang(k, \theta)</math>''' samples using the sampler for the exponential distribution:

if <math>X_i\ \sim exp(k \theta)</math> then <math>X=\sum_{i=1}^k X_i \sim Erlang(k,\theta)</math>