Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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

0
votes
0answers
3 views

Aggregate Sentiment and Behaviour Index

I have data of sentiment and behavior based signals for certain stocks. They are based on positive, negative words in a document. How can I aggregate(like an index) those individual signals to ...
1
vote
0answers
24 views

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" ...
0
votes
0answers
20 views

Which mean to use to find the average of measurements given in the form of “per period”

Let's say I made several measurements on my gas consumption. 2m^3 per day 1m^3 per day 1.5m^2 per day 2m^3 per day What is the average daily consumption of gas? I can take arithmetic mean and it ...
2
votes
0answers
23 views

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 ...
1
vote
0answers
30 views

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 ...
0
votes
0answers
51 views

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 ...
0
votes
1answer
78 views

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 ...
10
votes
2answers
2k views

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 ...
3
votes
1answer
57 views

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 ...
2
votes
2answers
3k views

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?
1
vote
0answers
46 views

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? ...
3
votes
0answers
79 views

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 ...
4
votes
1answer
874 views

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 ($E$...
1
vote
0answers
17 views

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. ...
13
votes
2answers
997 views

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 \...
2
votes
0answers
149 views

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 $c$. ...
3
votes
1answer
511 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?
2
votes
1answer
148 views

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 ...
7
votes
1answer
324 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 ...
0
votes
0answers
131 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 ...
7
votes
1answer
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 ...
9
votes
2answers
6k 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 $1/0=\infty$?
7
votes
1answer
5k views

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}{...
11
votes
5answers
6k views

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 ...