# Questions tagged [l-moments]

A kind of moments based on linear functions of order statistics. Their interpretation is similar to usual moments, but they can often be more stably estimated.

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### "Median" version of L-moments

The L-moments are useful as robust summary statistics for various probability distributions, similar to the moments but only requiring the mean of the distribution to exist. Each L-moment is a linear ...
26 views

### Monte Carlo simulation or Bootstrap for determining sample L-moments estimates

I'm trying to estimate the sample L-moments of stations from the Annual Maximum Series of precipitation. The book by Hosking (1986a, 1990) recommend using Monte Carlo simulation in generating ...
1 vote
243 views

### Statistics of Extremes: Fitting the GEV distribution with MLE vs L-moments

I created a synthetic series that is supposed to simulate a series of peak discharges in blocks of years in arid catchments. The magnitudes were simulated via the Lnorm dist.: ...
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149 views

### Discrete, finite L-moment problem

Suppose that we have a real-valued discrete random variable, whose probability distribution has finite support on some set $S$ of real numbers. Then if $N = |S|$, we know that we can construct the ...
854 views

### Constructing an L-moment ratio diagram

How can I find the L-skewness and L-kurtosis values for different distributions? For example, I'd like to be able to plot the curves or points for the Generalized Extreme Value, Gamma, Generalized ...
• 21
69 views

### What is the typical and example use of an "L-moment" as contrasted to a conventional moment?

I have seen moments a few times, but I am unfamiliar with "L-moments". What are they used for? What do they do that other things, like classical moments, cannot do as well?
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1 vote
72 views

### L-moments derivation

The formula for obtaining the $\lambda_i$ linear moment is: $$\lambda_i=i^{-1} \sum_{j=0}^{i-1}\binom{i-1}{j}E(X_{i-j:i})$$ where $X_{a:b}$ denotes the $a^{th}$ order statistic of the $b$ sized ...
• 259
2k views

### Should we teach kurtosis in an applied statistics course? If so, how?

Central tendency, spread and skewness can all be defined relatively well, at least on an intuitive basis; the standard mathematical measures of these things also correspond relatively well to our ...
263 views

### L-Kurtosis calculation

I am doing statistical analysis on some signal data and after some reading was thinking that L-kurtosis would be a good numerical value to use in differentiating delta trains and sine waves with ...
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3k views

### Issues with fitting distribution to heavy-tailed data

I am currently trying to fit distributions to some heavy tailed data-set (see the data set below) and have a hard time producing good results: ...
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58 views

### What is the statistical efficiency of L-moments? [closed]

In particular I am interested in the scale estimator. Hopefully it is much better than that of IQR.
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1 vote
192 views

### Estimate the parameters of beta exponential distribution via L-Moments

Estimate 3 parameters of beta exponential distribution in the case of censored type 1 samples via L-moments
44 views

### How to improve location and scatter estimation conditioning on higher order statistics?

Using sample moments, how can the mean and variance estimators be improved if e.g. skewness and kurtosis are known exactly? And what about using estimates for these instead, which should imho be of no ...
• 928
1k views

### Calculating L moments of a standard normal

As part of my research, I am having trouble calculating the 2nd L moment $\lambda_2$ and the third and fourth moment ratios $\tau_3$ and $\tau_4$ of the standard normal distribution, where L moments ...
• 99
375 views

### Adding gamma and 3-parameter log normal distributions to L-moments ratio diagram lmrd()

How to adapt this piece of code but for: - gamma distribution - 3 parameter log normal More specifically, where can I find the specification of the parameter (lmom) for pelgam() and pelln3()? Lmom ...
• 21
3k views

### Alternatives to using Coefficient of Variation to summarize a set of parameter distributions?

Background I have a model with 17 parameters, and I currently use the coefficient of variation ($\text{CV}=\sigma/\mu$) to summarize the prior and posterior distributions of each parameter. All of ...
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