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
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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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$\begingroup$ would you suggest another type of distribution? $\endgroup$– CharlesMCommented Oct 7, 2012 at 1:27
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2$\begingroup$ It would be better to know more about the data first. For instance is that buildup around 0 due to a whole lot of 0 values or just values that are near 0? $\endgroup$– DasonCommented Oct 7, 2012 at 1:28
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$\begingroup$ There is a lot of values = 0. It is basically the time between events....and a lot of events occur at the same time. $\endgroup$– CharlesMCommented Oct 7, 2012 at 1:35
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$\begingroup$ The it might be that a zero-inflated exponential distribution would be better. But that is just an option to try - I'm sure we could find plenty of other possible distributions as well. But given what you've said I would think you would probably want some sort of zero-inflated model. $\endgroup$– DasonCommented Oct 7, 2012 at 1:38
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1$\begingroup$ Can you discard the zeros in your data set and do the plot again? $\endgroup$– ZenCommented Oct 7, 2012 at 4:14