# What is the notation for calculating the mode?

### Question:

What is appropriate notation for calculating the mode of a function? In this case, I use the mode of a Gamma(a,b) distribution in a cost-function.

I am looking for something analogous to $\bar{x}$ or $\tilde{x}$ notation that is commonly used for the mean and medians, respectively, if something like $\bar{\text{G}(a,b)}$ would make sense.

### What I have tried:

1. Google results are confounded by mode $\simeq$ model and results for latex's 'math mode'

• For 1: tried this? – J. M. isn't a mathematician May 6 '11 at 15:53
• @J.M. that gives the analytical form of the mode, but that is not what I want. I have changed my question to focus on notation for mode rather than calculation of the mode of the gamma. – David LeBauer May 6 '11 at 16:04
• I was addressing the "Google results are confounded by" portion in #1; that is, use quote marks to tell Google that you meant what you said. – J. M. isn't a mathematician May 6 '11 at 16:06
• @J.M. Thanks for the hint. But I am still unsuccessful. – David LeBauer May 6 '11 at 16:14

One possibility for the notation for a mode is $$\underset{x}{\operatorname{arg\,max}} f(x)$$ but I thought that was ugly, so here I used a hat $$\hat{X}$$ to indicate the peak in the probability density or mass function, even though this can also be used for other meanings.
• Note: This can also be written simply as $\operatorname{argmax} f$. – user76284 Oct 28 '19 at 1:20
• thanks ... right now I am using mode(G(a,b)); perhaps I could use $u()$ but I didn't want to reinvent the wheel – David LeBauer May 6 '11 at 16:21