Questions tagged [geometric-mean]

A measure of central tendency that represents the typical value of a set of numbers when those numbers are thought of as multiplicative in nature.

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24
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3answers
2k views

What can one conclude about the data when arithmetic mean is very close to geometric mean?

Is there anything significant about a geometric mean and arithmetic mean that fall very close to one another, say ~0.1%? What conjectures can be made about such a data set? I've been working on ...
20
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1answer
374 views

How can we simulate from a geometric mixture?

If $f_1,\ldots,f_k$ are known densities from which I can simulate, i.e., for which an algorithm is available. and if the product $$\prod_{i=1}^k f_i(x)^{\alpha_i}\qquad \alpha_1,\ldots,\alpha_k>0$$ ...
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2answers
2k views

The geometric mean is an unbiased estimator of the mean of which continuous distribution?

Is there any continuous distribution expressible in closed form, whose mean is such that the geometric mean of the samples is an unbiased estimator for that mean? Update: I just realized that my ...
10
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2answers
151 views

$X_n$ $\,{\buildrel a.s. \over \rightarrow}\,$ $X$, then $(\prod_{i=1}^{n}X_i)^{1/n}$ $\,{\buildrel a.s. \over \rightarrow}\,$ $X$?

Prove or provide a counterexample: If $X_n$ $\,{\buildrel a.s. \over \rightarrow}\,$ $X$, then $(\prod_{i=1}^{n}X_i)^{1/n}$ $\,{\buildrel a.s. \over \rightarrow}\,$ $X$ My attempt: FALSE: Suppose $...
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2answers
5k views

How to calculate confidence interval for a geometric mean?

Apologies if this is confusing at all, I'm very unfamiliar with geometric means. For context, my data set is 35 month-end portfolio values. I found the month to month growth rate [Month(N)/Month(N-1)] ...
6
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1answer
43 views

“Normalising” join probability of n events, by taking n-th root

I have a group of events which I guess you could call a compound events. Each event is something like: $$A=A_1\cap A_2\cap...\cap A_{n_a}$$ I am estimating the probability of the over all event by ...
5
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3answers
135 views

combining a random variable and its inverse

I am measuring two scientific entities, X and Y using empiric measurements. Each has its own mean and sample variance based on Nx and Ny sample measurements. I know from the underlying science that X ...
5
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2answers
4k views

Arithmetic or geometric mean to calculate an annual average price index?

I have monthly indices (Consumer Price Indices for 12 months) for a set of countries. I want to calculate the annual average for each country in order to have an average Consumer Price Index for a ...
4
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1answer
776 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?
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2answers
2k views

Difference between geometric and arithmetic mean

I still have problems to exactly understand the difference between geometric and arithmetic mean. I know that e.g. for returns, the arithmetic mean can be wrong (e.g. if I start with 100 $ and if my ...
3
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1answer
2k views

Calculate the average rate of population increase per decade of a country

The population of a country increased by 20% in the first decade, 30% in the second decade and 45% in the third decade. What is the average rate of increase per decade in the population? The answer ...
3
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1answer
81 views

Transformation among power-means

It is well-known that arithmetic and geometric mean are strongly related via logarithmic transformation, i.e. if we take arithmetic mean of logarithmic-transformed values we get the same as if we take ...
3
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2answers
727 views

dealing with zeroes while using geometric mean

In case of creating an index using standardised variables(between 0 and 1), how do we deal with the zeroes(while using Geometric mean for aggregation)? it could be the case that only one indicator is ...
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0answers
63 views

Is it dangerous to take the mean of ratio measurements?

I'm going through a Computer Architecture course and in one of the lectures they mention that when measuring the difference in runtime performance between two systems, using for example multiple ...
3
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0answers
425 views

Geometric Mean Standard Error [duplicate]

I read from wikipedia that the geometric standard deviation is $$\sigma_g = \text{exp}\left( \sqrt{\frac{\sum_{i=1}^n\left(\frac{A_i}{\mu_g}\right)^2}{n}}\right)\,, $$ where $\mu_g$ is the geometric ...
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3answers
170 views

What comes after the geometric mean?

The geometric mean is a multiplicative alternative to the arithmetic mean, which we could call additive mean, thereby calling the geometric mean multiplicative mean. My question is the following: what ...
2
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1answer
451 views

Estimating with the geometric mean

I heard about an interesting technique for making ballpark guesses: If you need a variable that you have no idea about (like the average number of pianos per household), you can try to come up with ...
2
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1answer
45 views

How is that possible that simple arithmetic mean works well even for strongly skewed distribution?

I was taught, that the arithmetic mean is sensitive to outliers and skewness. This was natural to me - the observations lying far from the "central point" of the distribution "pull" the measure ...
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2answers
210 views

Arithmetic mean from geometric mean

For the data set the geometric mean is 10 then arithmetic mean will be? I tried hard to calculate the arithmetic mean from geometric mean which is given as 10 but unable to find it.
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0answers
291 views

Help with log-transformed data in meta-analysis

I am performing a meta-analysis of pharmacokinetic crossover trials with drug-metabolising enzyme activity as their endpoint(s), and as to be expected, the data are a mess and are reported in a ...
2
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0answers
413 views

Arithmetic mean of normalized scores or a direct geometric mean?

My question is about studies like the following: The 2015 SEDA Scores by Country, PDF is available here. The authors collect 43 indicators for 149 countries and compute a well-being index based on ...
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0answers
77 views

What is the geometric mean of the first hitting time distribution of Wiener process?

I'm looking for an analytic formula. Approximate formulas are welcome, in which case I give more importance to simple and nice expressions rather than to precision of the approximation. I'm looking ...
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0answers
85 views

Using geometric mean to take median of an even number of data points

When taking the median of a data set consisting of an even number of data points, generally the arithmetic mean of the two middle points is taken. Suppose a set of data points has a suspected ...
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1answer
30 views

Is expected value different in meaning from central tendency? Isn't both about “typical values”?

I was taught, that for any distribution having the 1st raw moment defined, the "expected value" is equal to it and it's also the arithmetic mean. "Expected value" sounds to me like "typical value". ...
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1answer
205 views

What is the definition of the geometric mean of a random variable?

I haven't found any definition online although searching for hours: So here is the thing: The geometric mean(GM) of an (iid) sample drawn from some random variable is given by: $$\text{GM}(X_1,...,...
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1answer
262 views

Confidence interval for geometric mean of fractions

Is there any opportunity to create such interval where a variable ($\{\ln(X_i)\}^n_{i=1}$) is the fraction of prices for two periods? $$ X_i = \frac{price.new_i}{price.old_i} $$ Please, look at my ...
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1answer
156 views

What does it mean by “approach the performance of the Bayesian gold standard”?

It is a sentence in Dropout paper(Dropout: A Simple Way to Prevent Neural Networks from Overfitting). "This can sometimes be approximated quite well for simple or small models, but we would like to ...
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1answer
582 views

Geometric vs. Arithmetic mean to determine diameter of object

I want to estimate the volume of irregular objects (coral fragments) by simplifying their structure to a cylinder and then calculate the volume of this cylinder (i.e. Ecological Volume). The length ...
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1answer
679 views

An analytical framework for considering the geometric mean

Is there an analytical method of looking at the geometric mean that will allow one to break it down to its various components? The focus of the question is more for financially related returns, but I ...
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0answers
25 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" ...
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2answers
355 views

In R, find geometric mean of monthly data converted into quarterly data

Looking to find geometric mean of monthly data that's been converted into quarterly data. I've tried several methods but only provide simple arithmetic mean as shown below. Thanks. ...
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0answers
727 views

Testing Geometric mean

we know that t-test consider the arithmetic mean only. How could I compare the geometric means of two different groups or several groups?
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144 views

Choice of mean: arithmetic, geometric, harmonic?

I've followed the discussion stream about different types of means, towards which end I'd like to pose the following query: I have two columns of biological data tht have been log-transformed (e.g. ...
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0answers
351 views

Difference of means hypothesis test with geometric mean and geometric standard deviation?

I have some distributions which are only reported by their geometric mean, geometric standard deviation, and their sample size n (all output by closed box scientific software) - is it possible to use ...
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0answers
703 views

Proxies and uses for the Geometric Mean of negative (or even complex) data

I use the geometric mean (GM) as a scale factor for data normalization. To avoid the $0$ cancellation effect with positive values, I use the simple offset GM: $$ \hat{x} = \sqrt[n]{\prod\limits_{i=1}^...
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1answer
95 views

Comparing performance of 2 comparable tests

So I have sets of data, 15 responses for test A and 15 separate responses for test B. Tests A and B have 6 perception questions and the object is to compare the performance of representing data one ...
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1answer
78 views

Robinson's Geometric Mean Test

I am reading this book: Ending Spam: Bayesian Content Filtering and the Art of Statistical Language Classification by Jonathan A. Zdziarski page 78 is about the Robinsons Geometric Mean Test. This ...
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0answers
77 views

Should I use arithmetic or geometric mean here?

So I have monthly indices (Consumer Price Indices for 12 months) for a given country. I want to calculate the annual average for each country in order to have an average Consumer Price Index for a ...
0
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1answer
102 views

Show that the Geometric Mean $g$ can be expressed as $\log g=a+\dfrac{k}{n}\sum_{i=1}^r f_i(i-1)$

In a frequency distribution the upper boundary of each class interval has a constant ratio to the lower boundary. Show that the Geometric Mean $g$ can be expressed as $$\log g=a+\dfrac{k}{n}\sum_{i=1}...
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1answer
43 views

Geometric mean intuition and interpretation

When simple mean is generally quite an intuitive term, and may be interpreted among others as average value in terms of distance, central value in terms of weight, expected value in terms of ...
0
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1answer
318 views

Geometric mean and geometric standard deviation

When summarizing normalized data (for example, percentage data), one must use the geometric mean instead of the arithmetic mean. Thus, instead of using the arithmetic standard deviation, one shall use ...
0
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1answer
225 views

How would I calculate a combination of the Binomial and Geometric Distributions?

To be specific with my problem, I'm calculating a formula for a game. There's 6 independent trials, each with an independent probability of success = 0.34. I know that from the Geometric distribution, ...
0
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1answer
111 views

Find $E(x^2)$ given $E(log(x))$

Suppose I have a blackbox generating values $x_n$. If I take mean($x_n^2$) it flies all over the place as new values are added -- a supermassive 48-digit value could suddenly ramp up a previously ...
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0answers
27 views

Why summarise right-skewed distributed (log-normal) data with geometric mean rather than its expected value?

I am very confused. The first raw moment calculated from sample, the arithmetic mean, is the BLUE estimator of its expected value. So there is no better one. At the same time, I was told that the ...
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0answers
11 views

Need advice on acceptable means to convert lower and upper confidence limits of a lognormal distributions to median and geometric standard deviation

I have offered to help convert a monte carlo simulation from guesstimate (a streamlined monte carlo simulation tool) https://www.getguesstimate.com/ to Analytica in order to perform a more in depth ...
0
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1answer
52 views

Geometric mean: Why root instead of divide? [closed]

I use the geometric mean to create standardized ranking between several disparate variables, so I can compare different variables combination: the higher the GM, the higher all the variables will be. ...
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0answers
38 views

Compare 2 sets of numbers by Ratio of Geometric means rather than Student t-test

In a medical article published today(!), ratio of geometric means and its confidence interval is used to compare 2 independent groups rather than Student t-test. My specific questions are: What ...
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0answers
184 views

Which test should I use to compare three geometric means?

I'm trying to use some test to compare three geometric means of some dataset, to see if there are significant differences. I want to compare A with B, B with C and A with C, but I'm unsure of which ...
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0answers
22 views

How can I calculate confidence for a multiplicative (growth) dataset?

I have a dataset of daily price changes, represented as decimals. Perhaps: 0.5, 1.5, 2.0. That's to say it lost 50%, then it gained 50%, then it gained 100%. I'd like to know how confident I should ...
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0answers
47 views

Combining both arithmetic and geometric mean in dataset with zeros and extreme values

I have a some datasets that I want to take an average of - a typical dataset might look something like this: 0 0 0 1 100 100 10000 30 10 10 0 0 0 0 0 Ordinarily ...