Questions tagged [dispersion]

This tag is very ambiguous. Dispersion is a general term for how spread apart values are. For questions related to disease dissemination content, use the tag epidemiology. For other meanings of dispersion consider using a related tag or creating a new one.

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26 views

Significant dispersion test

I used DHARMa for my residual diagnostics. For two models, the dispersion test is significant even though the rest of the diagnostic output looks good. I am wondering if both my models are correct ...
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Which is the right measure of dispersion to be used as a proxy for risk for a fat tail distribution?

Which is the right measure of dispersion to be used as a proxy for risk for a fat tail distribution ? Standard Deviation, Mean deviation, Value at risk, what else?
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34 views

Finding the distribution of [F; X]

I need to find the distribution of \begin{bmatrix}F\\X\end{bmatrix} where = (F1, F2, X1, X2, X3)^T This is the solution to the problem: I don't really understand the part of $D([F; X])$. Why there ...
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Is it possible to perform negative binomial regression with known theta?

Is it possible to perform negative binomial regression (in python, R) where you can supply a known value of theta? Say I want to compare different negative binomial regression models, the changing ...
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17 views

Dispersion parameter of exponential family (phi) in glmer

I need to extract of a glmer adjust the dispersion parameter (phi) for Gamma and Inverse Gaussian. I know the relation phi=1/sigma^2, however, the glmer summary gives a different sigma: "sigma: ...
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Test homogeneity of multivariate dispersion with regard to the Modified Raup-Crick Metric

Please find a citation for the modified Raup-Crick Metric below Modified Raup-Crick Metric (Chase et al. 2011 As an extremely brief review, this metric generates a dissimilarity matrix containing ...
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burstiness in time data

So i have time of arrival data like this: time of arrival = [1,1.5,1.6,1.7,1.8,3,4,6, 8, 9, 10] we can see that there is a burst between 1.5s and 1.8s. i have already tried to create a plot of ...
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Measuring “regularity” of musical timing

Apologies if the term regularity is improper, I cannot find what the actual term I am looking for is. I'm looking for a method for calculating how "regular" rhythms are for musical notes. ...
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99 views

Description (dispersion) of dates

I'm working on an R package which does an automatic description of datasets (here if you ever want to check it out). For now, the default behavior of the package is ...
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1answer
27 views

Measures of spatial dispersion

I have a series of data points in R^3. I am considering different measures of the spatial dispersion of these points. I have noticed something interesting. I have considered two different measures ...
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53 views

Vector-valued estimators, intuitively why $var(\widetilde{\beta})-var(\widehat{\beta})$ being p.s.d. means $\widehat{\beta}$ more efficient?

For two scalar unbiased estimators $\widehat{\alpha}$ and $\widetilde{\alpha}$, we know that if one has smaller variance, then we say it is more efficient, which intuitively means that this estimator ...
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35 views

Why do we need F test of two variances if we have the Ansari-Bradley test?

I just read that the Ansari-Bradley test is a test of stochastic equality of two variances regardless of any distributional assumptions. If it is so flexible, why do we even need the F test? I am ...
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Check which parameter causes less dispersion in a sample set - When to use CV (Coefficient of Variation) or CD (Coefficient of Dispersion) etc

The overall goal is to extract/engineer features from approximately 100 segments (various lengths but always more than 80 data points) that are as similar as possible to each other and have a very low ...
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1answer
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Mean and variance and special distribution of events

A hospital Accident and Emergency (A&E) department receives an average of 6 ambulances an hour. It can process patients in 30 minutes, but if it receives more than five patients in 30 minutes, ...
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215 views

Concept of a z-score for a gamma distribution

This is a somewhat general question. For the normal distribution we have the handy concept of the z-score that can be used to measure distance from the mean in a standardized way. I've encountered a ...
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1answer
73 views

Negative Binomial GLM confusing effect on p value of model by changing theta

I am interested in generating a p-value for two small groups of count based data that I believe to show overdispersion. The groups are for example: ...
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24 views

Metric for dispersion that corrects for sample size

I'm looking for a metric to measure dispersion of a set of points in 2D (or higher dimension) space. This post gives some examples, such as the sample mean of all points to be the center point and ...
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1answer
256 views

GLM Tweedie dispersion parameter

I am running a tweedie regression and I need to get the dispersion parameter(phi). Here a simple R code: ...
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62 views

Is “dispersion” a parameter in Gaussian glm?

Let do a simple glm in R: > y=rnorm(100) > gnul <- glm(y ~ 1) > gnul$coefficients (Intercept) 0.1399966 However, of course, as the distribution is ...
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Looking at two PDF plots, is it possible to guess which distribution has a greater Gini coefficient?

By observing the PDF of two different distributions over the same support (as in the image), is it possible to infer which PDF describes the distribution with the greater Gini coefficient? I assume ...
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Test or measure for “stability” of dispersion in many samples

I'm looking for a way to quantify if a variable has a "stable" dispersion over many samples. More precisely, I have approximately 1000 subjects, each with 50 observations of the variable. The mean ...
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98 views

High-dimensional dispersion statistic

I'm looking for a metric of dispersion for data in a high dimensional space (say, 70 or so components). The idea is that my data has several groups that I suspect are similar within some or many of ...
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1answer
81 views

Variance (maybe?) of categorical data

I don't really know the correct terminology to ask this question well. I have categorical data with counts and I want a measure of how "diverse" or "spread out" the data is. Variance comes to mind, ...
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105 views

Definition of exponential family with dispersion parameter

I was recently reading a discussion of generalized linear models that considered the response to come from an exponential family with a dispersion parameter so $$ f(y|\theta,\phi) = \exp\left(\frac{y\...
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1answer
62 views

Is the Coefficient of Variation valid for data which does not follow a normal distribution?

I am trying to compare the dispersion of several data vectors. As an example I have that via two methods produces one vector of data that fits a normal distribution and other one that follows an ...
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1answer
284 views

The use of the quantile regression

I would like your help regarding the quantile regression. I was wondering if it makes sense to use the quantile regression when the relation of the number of data between variable x and y is 1 to 1, ...
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244 views

Transfering the approach of GLM/GLM.NB to FEGLM in R to find the best dispersion parameter

I would like to analyze my dataset with around 1 million observations and 10 thousand fixed effects with a negative binomial regression model. Due to the high number of fixed effects I cannot apply '...
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2answers
1k views

Choosing the optimal theta / dispersion parameter for negative binomial regression (glm / glm.nb) in R

I am applying a negative binomial regression to my data in R. For this, I use the package MASS and have two different ways to calculate it: ...
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1answer
412 views

Negative Binomial Regression: Offset Variable and Dispersion Parameter

My case is that previously it's assumed that the counts of events follows a negative binomial distribution, and the annualized exacerbation rate is 1 with a dispersion parameter of 1.5, and all 500 ...
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80 views

Measure of dispersion around the mode

I usually associate the standard deviation with the mean and the IQR with the median. Is there a measure of dispersion typically associated with the mode?
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54 views

Which measure dispersion would one use to evaluate ratio conservation?

I am wondering which would be the most appropriate dispersion measurement in the following situation: In my experiment I am measuring two proprieties of multiple objects (e.g. height and weight) in ...
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1answer
218 views

Pros and cons of using a median version for measuring dispersion?

If a data set is in the presence of some outliers, then the sample average could not be a "fair" measure of the centrality of that data set. Instead, the sample median could be a better choice. ...
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1answer
41 views

Uncertainty of the dispersion parameter

I am trying to retrace the steps that Gary King and colleagues suggest in their article "Making the most of statistical analyses: Improving interpretation and presentation" to calculate quantities of ...
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1answer
881 views

How to measure diversity (dispersion) of a categorical variable?

I have unemployment rates for 3 regions (North, Center, South). The unemployment rate is defined by (number of unemployed ($u$)/ active population ($pa$)). The unemployment rate by region ($r$) is $\...
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1k views

What are the differences of Standard Deviation, Variance, Co-variance, Coefficient of Variation when it comes to measures of dispersion or variation?

When we talk about measures of dispersion or variation(not sure if they are 2 different tools), then for what purpose we use what exactly? Where are we bound to use only Standard Deviation, not ...
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1answer
185 views

How to measure the spatial dipresion of multiple clustered data

Context: My data are binary maps that represent the spatial distribution of events. Whenever an event occurs at a location, the pixel representing that location is assigned with the value 1. Below are ...
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1answer
127 views

Interpreting dispersion for Inverse Gaussian GAM (log linked)

After reading Wood (2006), Zuur et al. (2009) and all questions related to GAMs here, I still haven't found the following: Should I calculate the dispersion for an ...
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168 views

Name of the test for over/under dispersion

When testing for over or underdispersion in a count variable there is a test (available for example in the glm.nb() function in the ...
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1answer
280 views

Dispersion value with glmmTMB versus mgcv::gam()

Assume we parametrize the variance in a negative binomial regression model as: variance = mu(1+mu/theta). Fitting the model with glmmTMB, I check theta from: <...
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94 views

Has the Weibull distribution got pseudovariance?

I have a scholar question about the Weibull distribution, which can be parameterised, among other options, like follow: $f(t)= \lambda \alpha t^{\alpha-1}{exp} \left \{ \lambda t^\alpha \right \}$ ...
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246 views

Bimodal distribution dispersion

what is the correct way to study the variability of a data set when all the observations are distributed like a bimodal distribution? For instance, here I identified the two modes as central index. ...
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801 views

How to measure dispersion in word frequency data?

How can I quantify the amount of dispersion in a vector of word counts? I'm looking for a statistic that will be high for document A, because it contains many different words that occur infrequently, ...
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1answer
1k views

Evaluating dispersion parameter and goodness of fit for binomial regression in r

First, I have looked at other posts but none address this specific question. I am trying to evaluate goodness of fit for a negative binomial regression, and what the dispersion parameter indicates in ...
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1answer
670 views

What is the best way of measuring the dispersion or concentration of categorical data?

Let me provide some background. I am writing a paper on the effectiveness of specialist vs. generalist software companies. I have data on the number of products of theirs that are being used across ...
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1answer
885 views

How does dispersion parameter affects results of gamma glm

I ran a log-linked gamma glm and noticed that the estimated coefficients and AIC did not change when I update the model with a dispersion parameter. However, I did noticed that the standard error of ...
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1answer
1k views

Why do we need coefficient of mean deviation?

Mean deviation can give us a sense of how much data is dispersed from one of the average measurements (mean,mode,median). Mean deviation depends on the difference between the data and the average ...
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1answer
740 views

Dispersion parameter in mass and PSCL package (zero-inflated negative binomial and negative binomial)

I have run Zero inflated negative binomial and negative binomial model with same data set in R. I get log(theta)= -2.47 for Zero inflated negative binomial and log(theta)= -5.149 for negative binomial ...
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0answers
169 views

Estimating dispersion parameters in GLMs

I've been working on implementing a glm library in python for my students to use (for various reasons, the existing implementations are not sufficient). My reference for the material is Marlene ...
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1answer
483 views

Clustering: measure of dispersion based on distances

I am having a set of strings, they have been alligned and I have a matrix of pairwise distances. Now the objects have to be clustered yet I do not know the number of clusters beforehand. I would like ...
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3answers
242 views

Which measure of dispersion is this function related to?

Consider a sample $x=\{x_1,...,x_n\}$. Define the average as $\bar x$. Consider the following formula: $$ \dfrac{\sum_{i=1}^n\left(\dfrac{x_i}{\bar x} \right)^c}{n} $$ or equivalently: $$ \dfrac{\...