# 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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### average of geometric and harmonic means

I have a stochastic simulation model in which three types of mean (arithmetic mean, geometric mean, and harmonic mean) are calculated for three different variables. I run the simulation 1000 times so ...
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### Need suggestion on average method to perform on ratios (harmonic, geometric, weighted)

Im looking at different cities which all have different population counts. For each of these cities im calculating the proportions of smokers. For example: ...
23 views

### Recovering Sum of Observations Given Harmonic Mean

I think I know the answer to this, but just wanted to confirm. If we are given the number of observations in a dataset (n) and the arithmetic mean (m), we can easily solve for the total sum of all ...
38 views

### How can I perform a hypothesis test for this harmonic mean?

Abstract I have a software process that I try to measure with a calculation I call the EHD. The EHD value is computed this way: I perform searches for a "best fit" number in a search space, ...
80 views

### Estimating $1/a$ for following pdf using method of moments estimation

A random sample of size $n$ is being drawn from a population with pdf as: $$f(x) = \begin{cases} (a + 1)x^a & \text{for }0<x<1, \\ 0 & \text{otherwise.} \end{cases}$$ Can we express the ...
1 vote
118 views

### Sample of rates: mean, standard deviation, coefficient of variation

A performance test of a software application measures the maximum rate (operations per second), which this application can handle. The test is repeated multiple times each iteration yielding the ...
1 vote
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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 $c$. ...
2k views

### 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?
194 views

### Harmonic mean for averaging predictions? [closed]

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 ...
543 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 ...
182 views

### 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 ...
2k views

### 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 ...
10k views

### Harmonic mean with zero value

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