The title pretty much says it all. I have data that consists of 80 samples but there are always at least four samples that have exactly the same value. I want to assess, whether the data is unimodal. Now the plot of the kernel density estimate shows clearly that the data has two "hooks":

density estimate However this data would have never been obtained by any continuous probability distribution, so I am not sure whether it is appropriate to use a kernel density estimate at all?

  • 2
    $\begingroup$ If the duplicates are due to rounding or similar forms of discretization, ties in the data apparently cause issues in bandwidth selection using cross validation and there seem to be posts about k.d.e. with uncertainties in the data. Apart from these, I'd guess that the error imposed by ties is largely dependant on the context - understandably, using wide bandwidths, k.d.e. of rounded data looks similar to k.d.e. not-rounded data. $\endgroup$
    – adityar
    Commented Nov 6, 2018 at 13:48
  • $\begingroup$ One idea in the second link is to use wider wider kernels on points with ties. $\endgroup$
    – adityar
    Commented Nov 6, 2018 at 13:53
  • $\begingroup$ Could you provide a definition of a "mode" for such a mixed distribution? $\endgroup$
    – whuber
    Commented Nov 25, 2023 at 18:33

1 Answer 1


if these duplicates are drawn from same random variable then yes (experiment can yield same observation sometimes and it is normal) - although it would be better to give answer in terms of probability of RV unimodality under some conditions (kernel variance used for K.D.E.) maybe function of probability of unimodality under variance value


I think it is better solution

you can compare your data to some unimodal distribution and apply rank-test


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.