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Suppose we have two independent random Gaussian-distributed variables X and Y. X and Y represent thresholds for activation and deactivation, respectively. I'm interested in ensemble averaging over many iterations of X and Y and getting that distribution. I need this distribution to have a maximum but I'm not sure how to get this. A convolution of a CDF (for X) and survival function (for Y) will still be monotonically increasing.

Any ideas?

Jeremy
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  • It's not clear what distribution you are looking for. Please, be more precise. As a general suggestion, please also add precise details about what you did in order to solve your problem. – the_candyman May 26 '15 at 17:46
  • I have individual units whose values are 0 if the external input is less than X and greater than Y and 1 if the input is greater than X but less than Y. I want to find the distribution of values for these units because X and Y are noisy. It should be Gaussian. I'd like to rigorously set this problem up and don't know which statistical distributions to use. – Jeremy May 26 '15 at 17:56

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