# Which summary statistics are always nonnegative? [just for fun] [closed]

Which summary statistics are always nonnegative?

So far, the only ones I can think of are range and standard deviation/variance (which are positive except in trivial cases).

• Adding to @Kurtosis' list (+1): coefficient of determination; coefficient of variation; estimate of a probability / proportion; standard error; various indexes of similarity; sample mean, median, mode of distribution with non-negative support (binomial, Poisson, geometric, hypergeometric; exponential, gamma, beta, Rayleigh, Weibull, Pareto, etc.). Commented Jul 28, 2020 at 7:18
• The exponential of any summary statistic is a non-negative summary statistic. If we stipulate $\log(0)=-\infty$ and allow $-\infty$ as a possible value, then the log of any non-negative summary statistic is a summary statistic. Thus, your question is tantamount to asking for an enumeration of all summary statistics. That's beyond the capacity of this site.
– whuber
Commented Jul 28, 2020 at 14:12