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: ...
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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 ...
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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, ...
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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 ...
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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 ...
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Weighted harmonic mean of rates expressed as decimals

Wikipedia defines the weighted harmonic mean of a set of rates as follows: $$H=\frac{\sum\limits_{i=1}^n w_i}{\sum\limits_{i=1}^n\frac{w_i}{x_i}}=\left(\frac{\sum\limits_{i=1}^n w_ix_i^{-1}}{\sum\...
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Most "statistically sound" method for finding the average of multiple different metrics [duplicate]

If I have 3 different metrics and I wanted to find an "average" (not necessarily arithmetic mean) of the 3 metrics so that observations can be ranked, what would be the most "statistically sound" ...
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Median versus Harmonic Mean As Log Normal Data Summary

I have a set of data that follows a lognormal distribution (it is fixed-distance, variable-speed situation https://stats.stackexchange.com/a/23130/55305). I am trying to summarize the data in a single ...
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Isn't HM a better way of averaging k fold cross validation scores than AM?

When calculating fscore we use the harmonic mean of precision and recall since hm penalizes situations when either of the two metrics is low while the other is large unlike the arithmetic mean. So ...
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How to estimate harmonic mean?

Is there a way to estimate harmonic mean given other statistics such as arithmetic mean, variance, min, max, ... . The goal is to estimate the mean incrementally as we get new data using a few ...
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What does it mean to say the harmonic mean is a non-Lagrangian average?

A paper by Grabisch et al (2011) states that the arithmetic and geometric means are Lagrangian means whereas the harmonic mean is not Lagrangian. What does this mean? What properties does a ...
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Why we don't use weighted arithmetic mean instead of harmonic mean?

I wonder what is an intrinsic value of using harmonic mean (for instance to calculate F-measures), as opposed to weighted arithmetic mean in combining precision and recall? I am thinking that weighted ...
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The Harmonic Mean of the Likelihood, n sample normal-normal case

This is very related to Radford Neal's awesome blogpost, but his example uses a single data point x, and I want to know how to replicate the results using $n$ data points. This is essentially what my ...
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Why is F-score called "F-score"?

All other algorithm scores have names that make sense, but the F-score is just "F". Was the letter chosen at random?
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How to measure a mean frequence of fft transform

I have this time series (utilization of app by day of an user) And this fourier transform of the above time series How can I extract one number that express the mean frequency of this time series? ...
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What is the proper method for calculating the Coefficient of Variation of a rate?

I have been asked to evaluate the variation between movement rates of fish within different systems (rates are in km/day). I have between 25-100 samples in each system. I understand that when ...
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Harmonic mean of random variables

Is there an analytic solution/approximation to the PDF/CDF and mean of an harmonic mean of random variables? I'm wondering about beta distributions ($\beta$) or truncated exponential distributions ($E$...
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Change of support or inverse problem where block data is not the arithmetic mean

The change of support problem or inverse problem in geostatistics is concerned with inferences about the values of variables at points or block different from those at which it has been observed. ...
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Harmonic mean minimizes sum of squared relative errors

I am looking for a reference where it is proven that the harmonic mean $$\bar{x}^h = \frac{n}{\sum_{i=1}^n \frac{1}{x_i}}$$ minimizes ( in $z$) the sum of squared relative errors $$\sum_{i=1}^n \...
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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? [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 ...
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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 $1/0=\infty$?
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In calculating the F-measure with precision and recall, why is the harmonic mean used?

The article for F-measure in Wikipedia says: The traditional F-measure or balanced F-score (F1 score) is the harmonic mean of precision and recall: $F_1=2\times\frac{precision \times recall}{...
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Can the standard deviation be calculated for harmonic mean?

Can the standard deviation be calculated for the harmonic mean? I understand that the standard deviation can be calculated for arithmetic mean, but if you have harmonic mean, how do you calculate the ...
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