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Therefore <math>\hat{\tau_i} \sim F_{\hat{\tau}}\;</math>, where :<math>F_{\hat{\tau}} = 1 - e^{\left( \sum_{j\ne i} -h(x_j) \right) t}\;</math>.
Loury (1979) - Market Structure And Innovation (view source)
Revision as of 21:47, 16 November 2010
, 21:47, 16 November 2010→Basic Setup and Assumptions
Assuming iid tau's (no externalities in innovation!), then we can use a [http://en.wikipedia.org/wiki/Exponential_distribution#Distribution_of_the_minimum_of_exponential_random_variables nice feature of the exponential distribution] which is that if <math>X_1,\ldots,X_N\;</math> are iid exponential with rates <math>\lambda_1,\ldots,\lambda_N\;</math>, then <math>\min(X_1,\ldots,X_N)\;</math> is distributed exponential with rate <math>\sum_1^N \lambda_i\;</math>.
Therefore <math>\hat{\tau_i} \sim F_{\hat{\tau}}\;</math>, where
For convenience we denote :<math>a_i= \sum_{j\ne i} -h(x_j)\; </math>
