Is it possible to use MLE to estimate the parameters of a (very strange) exponential distribution? As you can see from the picture below, there is not much variation in the data. I wish to estimate the parameters that generate that form of exponential distribution
Of course you can. And depending on the parameterization you use the MLE is either the sample mean or one over the sample mean. However it looks to me like you don't actually have something that would be adequately fit by an exponential distribution.
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