# Finding mode using mean and skewness (and higher moments)?

I have a pdf that doesn't yield trivial derivatives, so I cannot differentiate it and find the root to determine where its max exactly occurs. However, I have a general formula to express all its moments (mean, var, skew, kurtosis, etc).

The mean doesn't coincide with the mode because the function is not symmetrical. Is there a way to use the mean and the skewness (and/or higher moments) to characterize the mode?

• The position of the maximum probability density (if such exists and is unique) is called the mode. Dec 21, 2017 at 13:11
• Thanks Nick, apologies i'm not familiar with statistics terminology. I'll correct it. Dec 21, 2017 at 13:12
• The accepted answer does not address the recently-edited version of this question (not the answerer's fault, of course).
– mkt
Dec 21, 2017 at 13:19
• @mkt Stephan answered that moments cannot determine the max's location (in the comments) Dec 21, 2017 at 13:22
• In a reply at stats.stackexchange.com/questions/25010/… I show, with plots of the PDFs, a family of distributions that all share the same (infinitely many) moments, yet clearly have different modes.
– whuber
Dec 21, 2017 at 14:29