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I have a unimodal continuous distribution which is skewed and I would like to estimate the mode using the modeest package in R. However, the package offers a relatively large number of methods to do so. What makes the situation more complicated is that some of these methods have even more options for different ways of estimating the mode within the particular method. Since I'm a relative newbie to statistics in general, I'm a little overwhelmed.

How can I choose the right method here?

Is it a valid approach to just plot the distribution and use the method which returns a value that seems reasonable given the graphic information?

kjetil b halvorsen
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Gerome Bochmann
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    The right method (a) matches your ideas of what you are estimating and (b) works well with your data to the extent allowed. (Not all samples have well-defined modes; no white magic will extract a worthwhile estimate in those cases.) That may seem a worthless answer, but you haven't given enough information to allow guidance. Why do different methods exist, any way? You might try various methods, see if they agree, relating results to various different graphs of your data and your scientific understanding. In this context, there is no such thing as "just plot[ting] the distribution"! – Nick Cox Dec 10 '13 at 15:06
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    This is a very helpful answer, since I now know that things arent't as simple as I thought. I was already wondering why different methods do exist. Can you recommend any paper or literature where you got that information from? Most introductory literature on statistics I have basically says: Well, this is the mode, here's how you do it and now good luck. – Gerome Bochmann Dec 10 '13 at 15:13
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    The mode is *sometimes* well-defined for discrete data. Otherwise there are numerous different ways to get at it. Even if you focus on kernel density estimation (which is only one method among several), there is always a choice of kernel type and width before you can get the position of the maximum density. So, I'd this follows from any survey of density estimation alone, without needing a wider context. Modes tend not to be discussed seriously in introductory texts or courses. – Nick Cox Dec 10 '13 at 15:21

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Partially answered in comments: The right method (a) matches your ideas of what you are estimating and (b) works well with your data to the extent allowed. (Not all samples have well-defined modes; no white magic will extract a worthwhile estimate in those cases.) That may seem a worthless answer, but you haven't given enough information to allow guidance. Why do different methods exist, any way? You might try various methods, see if they agree, relating results to various different graphs of your data and your scientific understanding. In this context, there is no such thing as "just plot[ting] the distribution"! – Nick Cox

The mode is sometimes well-defined for discrete data. Otherwise there are numerous different ways to get at it. Even if you focus on kernel density estimation (which is only one method among several), there is always a choice of kernel type and width before you can get the position of the maximum density. So, I'd this follows from any survey of density estimation alone, without needing a wider context. Modes tend not to be discussed seriously in introductory texts or courses. – Nick Cox

Since mode is not always welldefined/uniquely defined, mode is often a not very helpful concept. That is probably a reason why it is little discussed in texts, little formal statistical analysis is based on modes.

kjetil b halvorsen
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    I naturally agree with my own comments. I would just add, a little more positively, that the mode is of some descriptive interest as the position of the peak of unimodal skewed distributions with left and right tails. Also, much more at https://stats.stackexchange.com/questions/176112/how-to-find-the-mode-of-a-probability-density-function – Nick Cox Aug 08 '18 at 10:16