# Questions tagged [harmonic-mean]

The harmonic mean is a kind of mean (or average) for positive scalar data. The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals. See https://en.wikipedia.org/wiki/Harmonic_mean

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### convergence in probability of harmonic mean

I have $X_1,...,X_n$ iid as gamma($\alpha,\beta$). Defined also is the harmonic mean $Y_n=\frac{n}{\sum{x_i^{-1}}}$. I'm trying to figure out if $Y_n$ converges in probability to some constant $c$. ...
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### convergence of geometric mean/harmonic mean

Does any one know papers regarding the convergence of geometric mean or harmonic mean in probability, parallel to central limit theorem?
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### Harmonic mean for averaging predictions?

I have 14 different predictions about each observation in my dataset and I want to compute an overall prediction for each observation based on these. Would it be better to use the harmonic mean ...
345 views

### Is the harmonic mean the maximum likelihood estimator for some common continous distribution's parameter?

If $y$ is a vector of continuous data the arithmetic mean is the maximum likelihood estimator for $\mu$ when assuming $y \sim \text{Normal}(\mu,\sigma)$ (not uniquely, of course). The geometric mean ...
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### Finite variance of harmonic mean estimator when samples are bounded

Harmonic mean estimator is notorious for the possibility of having infinite variance. Now I want to show that it has finite variance when samples are bounded. I am wondering whether my following ...
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### What is the difference between 'Laplace approximation' and 'Modified harmonic mean'?

this question is about Bayesian and computational statistics. I am learning them right now, I have two very common output from my software, one is Laplace approximation and the other is Modified ...
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### Harmonic mean with zero value

How does harmonic mean handle zero values? what would the harmonic mean of {3, 4, 5, 0} be since $1/0=\infty$?