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Questions tagged [mode]

The mode is the most frequently occurring value in the data and can be used as a measure of central tendency for categorical data.

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central tendency as minimized variance

I'm reading John Kruschke's Doing Bayesian Data Analysis: A Tutorial with R and BUGS, in which it says that we define the central tendency of a distribution as the value $M$ that minimizes the long-...
1k views

R How to find the secondary peak of a distribution

For example, if I generate density with R code D = c(rnorm(100,1,1), rnorm(100,5,1)) Then the following density will follow: We can find the primary peak ...
1k views

Why would the median be used to summarize ordinal data instead of the mode?

I am working with ordinal data (produced from Likert-types scales). I am of the understanding that results should be presented as a mode, which makes sense to me. However, when working in SPSS and ...
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Would there exist a symmetry around the mode in a truncated uni-modal distribution (which is differentiable)?

If we truncated around the mode of an asymmetric (continuous and differentiable) unimodal distribution, would there be a symmetry around the truncation point? For example if X is generated from an ...
90 views

Probability square of a normal is in a range; mode of gamma

If $X \sim N(1,4)$ find $\mathbb{P}(1<X^2<9)$ If $x=2$ is the unique mode of the $X \sim \Gamma(2,\beta)$ distribution, find the parameter $\beta$. Well I tried transformation to solve ...
131 views

What does a ratio of PDFs mean?

In searching for an answer I came across this about the pdf/cdf ratio but I would like to know if there is any meaning, name or supporting theory relating to the ratio of two pdf values, the numerator ...
420 views

Reliability of Mode from an MCMC sample

In his book Doing Bayesian Data Analysis, John Kruschke states that in using JAGS from R ...the estimate of the mode from an MCMC sample can be rather unstable because the estimate is based on a ...
312 views

Why is the mode of the Dirichlet not the same as the modes of its marginals?

The mode of a Dirichlet distribution with parameters $\alpha_1, \alpha_2, \ldots \alpha_N$, $\alpha_i > 1$ is: $$x_i = \frac{\alpha_i - 1}{\alpha_0 - N}$$. Where $\alpha_0 = \sum_k{\alpha_k}$. ...
106 views

Valid / invalid moments in Generalized Method of Moments (GMM)

I'm preparing to conduct an estimation procedure using GMM (Generalized Method of Moments), and I'm in the process of selecting my moments. This got me thinking, can I use non-statistical moments as ...
122 views

How to represent periodic paired data?

I'm working on paired data, of which absolute values plotted over time, show periodicity with varying peak heights as shown in the following graph: The data represent the absolute distance between ...
1k views

Counterexamples where Median is outside [Mode-Mean]

This article is above my league but it talks about a topic which I am interested in, the relationship between mean, mode and median. It says : It is widely believed that the median of a unimodal ...
3k views

Median > Mode > Mean > Range

My question is: Is there a set of data which allow the median to be larger than the mode, the mode to be larger than the mean and the mean to be larger than the range? If so, is there a pattern, or a ...
1k views

Mean, Median, Mode:When to use what? [duplicate]

Is there any rule which tells when to use a particular measure of central tendency.
122 views

How to implement a classifier without features in R?

How can I build a trivial classifier in R that checks the number of each possible output value, doesn't use features and assigns the most frequent value to the test data? Each test data instance is ...
307 views

Can variation ratio ever be 0?

I think that it can't since whenever we have data then we have mode and since we have mode it's frequency is at least 1. Therefore, variation ratio can't ever be 0. What do you think?
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Calculating confidence intervals for mode?

I am looking for references about calculating confidence intervals for mode (in general). Bootstrap may seem to be natural first choice, but as discussed by Romano (1988), standard bootstrap fails for ...
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521 views

How to compare multimodal distributions?

I am logging the number of visitors per hour on two websites. The resulting data are something like 57 visits between 0:00 and 1:00, 32 visits beween 1:00 and 2:00, etc. The distributions are ...