# 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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### 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.: ...
191 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 ...
1k 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 ...
73 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?
1 vote
74 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 ...
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 ...
341 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 ...
4k 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: ...
60 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.
1 vote
196 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
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 ...
378 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 ...
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 ...