1.4.1. The moment generating function is M X ( θ) = E ( e θ X). In statistics, L-moments are a sequence of statistics used to summarize the shape of a probability distribution. What's the current state of LaTeX3 (2020)? Direct integration (usually split the integral at the point $\mu$ where the sign changes. I'm quite familiar with that specific page, thanks. In probability theory and statistics, the log-Laplace distribution is the probability distribution of a random variable whose logarithm has a Laplace distribution. If I have some data that fits the laplace distribution fits well with a very high b, should I be concerned? There is a good discussion about this for the Cauchy distribution which does not have defined moments see http://en.wikipedia.org/wiki/Cauchy_distribution. For the empirical rule, I'm assuming the OP is using the shorthand for the probability of observations within $\sigma$ of the mean, $\mu$, $2\sigma$ of $\mu$ and $2\sigma$ of $\mu$ respectively. (1973). Then use conditional expectations. The Laplace have infinite tails like the Cauchy, the support is $x \in (-\infty, \infty)$. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Fixed now. Laplace Distribution. Use MathJax to format equations. What makes cross input signature aggregation complicated to implement? Note that the central moments of the Laplace are the raw moments of the corresponding exponential, and it's trivial to show that the raw $k^\text{th}$ moment of a standard exponential is $k!$. Description. I'm studying the distributional properties of a laplace distribution, and I'm trying to get some intuition beyond plotting the distribution of what it means to have an undefined moment. MathJax reference. Ergo, the manner in which you arrive at your conclusion is flawed. Now the second part of my question is trying to understand undefined moments. if you evaluate this for $\theta=0$, then you get $E(X) = \mu$ as expected. This allows you to set $\theta=0$ and use the moment generating function to produce moments. So for the Laplace we have $E(e^{\theta X}) = e^{\mu\theta}/(1-b^{2}\theta^{2})$ (from Wikipedia), $E(X) = d^{1}(M_X(\theta))/d(\theta)^{1} = (e^{\theta\mu} (\mu + b^2 \theta (2 - \theta \mu)))/(-1 + b^2 \theta^2)^2$. c) A positive value (Leptokurtic) implies heavier tails and peakier tops (e.g. Introduction. There may be generalized Laplace distributions, but this isn't it. Hi phubaba, could you please generate a short explanation of how moments relate to the MGF based on your new understanding, including how to get say the first moment of the above Laplace from that and post it as an answer? Asking for help, clarification, or responding to other answers. (You only need investigate $b=1$; the fact that $b$ is a scale parameter immediately leads to the factor of $b^k$. It may be instructive for the OP and others. The L-moments in terms of the parameters are λ_1 = ξ, λ_2 = 3α/4, τ_3 = 0, τ_4 = 17/22, τ_5 = 0, and τ_6 = 31/360. What is the benefit of having a defined moment if you have the distribution? Moments and Moment Generating Functions. I am working on the Laplace distribution for my algorithm. Thanks for contributing an answer to Cross Validated! scipy.stats.laplace¶ scipy.stats.laplace (* args, ** kwds) = [source] ¶ A Laplace continuous random variable. ... Find the distribution of Y. Moments of Laplace distribution. Active 1 year, 9 months ago. 1 Moments, Factorial Moments, and Central Moments For g(x) = x, we call EXthe mean of Xand often write X or simply if only the random variable Xis under consideration.