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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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2answers
19 views

Checking of Measurement in Grouped Data

My teacher uses the formula below when looking for the median and mode of a grouped data. $$ median = L_m + c\frac{\frac{n}{2} - F_{m-1}}{f_m} \\ mode = L_m +c\frac{f_m - f_{m-1}}{2f_m-f_{m-1}-f_{m+1}...
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10 views

Define optimal Data Volume for Model Development Population?

I would like to ask and learn some approaches, analyzes about representativeness of modeling data. I want to know what is the optimal date range for model development population? I want to ask that ...
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54 views

Exploratory data analysis before pefrorming Canonical Correspondence Analysis (CCA)

I want to perform CCA, but I read that, remember that observations (for example, species abundances) have to present unimodal distributions along gradients (for example, environmental variables). ...
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17 views

Significance of modes in a distribution

I have several datasets with angular measurements, i.e. circular values from 0 to $2\pi$. These datasets tend to have peaks at 0 and/or $\pi$, and I need to tell if the peaks are detected/significant. ...
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19 views

Point estimator and confidence interval for median and mean [duplicate]

I want to find point estimator and confidence interval for both median and mode of number of samples that we've collected from a number of simulations. What I've done so far is that I found a point ...
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25 views

Finding the mode of the posterior distribution

I have the following hierachical bayesian model - $\mathbf{x}|\mathbf{c},\sigma^2 \sim \mathcal{N}(\mathbf{x}|\mathbf{c},\sigma^2)$ $\mathbf{c}|\mathbf{c}_1,\sigma^2_2 \sim \mathcal{N}(\mathbf{c}|\...
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2answers
647 views

Right-skewed distribution with mean equals to mode?

Is it possible to have a right-skewed distribution with mean equal to mode? If so, could you give me some example?
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48 views

What is the mode of the convoluted probability density function?

If I am aware of the distributions of both $V$ and $U$, is there general guiding principle in terms of the position of the mode of the distribution of $\varepsilon =V-U$. As I am not specifying the ...
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0answers
43 views

Finding mode of posterior using Newton method in R

I am attempting to approximate the posterior $\tilde{\pi_{G}}(z|\theta,Y)$ which is the Gaussian approximation to the full conditional of $z$, and in order to do this I need to find the mode $z^{*} \...
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1answer
36 views

Is there a probability distribution function (PDF) that maximizes entropy for a given mode value?

I want to have a PDF that maximizes entropy for a given mode value. I searched in Maximum entropy probability distribution but here we have maximization done over a certain moment constraint.
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1answer
53 views

Two ways of obtaining Dynamic Mode Decomposition modes - are they equivalent?

In this lecture prof. Kutz gives the Dynamic Mode Decomposition modes: $\Phi = X' V_r \Sigma_r^{-1} W $ which are the eigenvectors of the linear propagator matrix. This results from splitting the ...
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1answer
44 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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1answer
180 views

Is this distribution unimodal, even though there is no data on one side of the mode?

... or does there need to be data on the left side of the mode? The logic to "not unimodal" would be that there must be a peak to be unimodal and there's no peak if the data only decreases on one side....
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2answers
526 views

What is the mode in a multimodal data set?

Given the data set {10,10,14,14,15,15,17,17,27,27,30,30} is the mode {10,14,15,17,27,30} or is there no mode?
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1answer
60 views

binomial distribution interpretation

I am working on a binomial distribution problem, where I would like to calculate the probability of observing 48601000 successes in 69430000 trials, where the success probability is $p = 0.70$. I ...
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35 views

How to numerically find the mode of a joint probability distribution from samples? [duplicate]

I have a large number of samples (say $N$) from a multimodal joint probability distribution, for example: ...
2
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1answer
260 views

Modes of a multinomial distribution

Is the multinomial distribution an example of a multimodal distribution? I was just curious about this. I know of continuous distributions that are multimodal, but didn't know if you could talk about ...
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2answers
81 views

Why is the center of data important?

I have recently begun learning statistics along with Python with the Anaconda IDE and started a Machine Learning course by Andrew Ng. I understand the mathematics behind what I am doing as the ...
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1answer
5k views

In a given set of numbers can there be more than half above mean, median or mode?

Suppose I have a set of numbers, for example - exam scores of 20 students. Can there be more than half of students scoring above the mean ? similarly, can more than half the class score above the ...
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1answer
49 views

Modal estimator for proportion in Binomial

Given a random variable X~B(n, p) I would like to estimate p using the mode. In this particular case, I cannot use $\hat{p}=\frac{X}{n}$ as an estimator. I have found that in general, that for a ...
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1answer
789 views

Posterior mode, posterior mean and posterior variance of a posterior distribution of dirichlet form

What is the significance of finding the posterior mean, posterior mode and posterior variance in Dirichlet - multinomial conjugate pair Bayesian estimation? Are all of them equally important while ...
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2answers
457 views

Is the MAP the maximum value of the posterior or its mode?

According to the WP definition of MAP: In Bayesian statistics, a maximum a posteriori probability (MAP) estimate is an estimate of an unknown quantity, that equals the mode of the posterior ...
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2answers
1k views

How do I prove that the mode of a Gaussian distribution is given by its mean?

I'm trying to show that the mode (i.e. the maximum) of a Gaussian distribution is given by its mean. Consider that the Gaussian distribution is given by Equation 1: $$N(x|\mu, \sigma^2)=\frac{1}{(2\...
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71 views

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-...
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2answers
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 ...
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2answers
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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1answer
22 views

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 ...
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1answer
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 ...
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0answers
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 ...
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2answers
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 ...
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1answer
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 $\alpha_0 = \sum_k{\alpha_k}$. ...
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0answers
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 ...
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3answers
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 ...
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3answers
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 ...
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3answers
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 ...
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1answer
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.
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1answer
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 ...
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1answer
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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1answer
693 views

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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0answers
185 views

Bounding the distance between the mean and the mode of a unimodal distribution

It can be derived from here by the triangle inequality that for unimodal distributions, the distance between the mean and the mode satisfies the bound $$\left|\overline{X} - \text{mode}(X) \right| \...
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237 views

Detecting distribution peaks and their significance

I have (a lot of) datasets with points having 1d distributions like these: Note, that the data is periodic in nature, like time of a day, so left and right sides of the plots above correspond to the ...
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2answers
53 views

Can modes be defined without assuming the existence of density function

Surprisingly I have not found any literature. I would like to know if it is possible to define a (generalized) mode for general probability distributions, possibly defined on an infinitely dimensional ...
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1answer
69 views

Is there a term for the datum with the least (non-zero) frequency?

The mode of a (finite) data set is the value with the most number of appearances. What about the opposite of the mode? That is, the value (from among the data) with the least number of appearances? Is ...
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4answers
6k views

Does mean=mode imply a symmetric distribution?

I know this question has been asked with the case mean=median, but I did not find anything related to mean=mode. If the mode equals the mean, can I always conclude this is a symmetric distribution? ...
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2answers
670 views

Unimodality Test for Discrete Distribution

I have several collections of discrete datasets of integer values, say, from 1 to 10, inclusive. I am interested in characterizing the various distributions in these datasets, and it is important for ...
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1answer
311 views

Udacity claims that the F-distribution peaks at 1, but Wikipedia has counterexamples. Which is true?

Here's a transcript of the first minute, though you may watch the video here: The F distribution is positively skewed, meaning it peaks on the left side and is stretched off to the right side. ...
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4answers
19k views

Expected value vs. most probable value (mode)

The expected value of a distribution $f(x)$ is the mean, that is the weighted average value $$E[x]=\int_{-\infty}^{+\infty} x \, \, f(x) dx$$ The most likely value is the mode, that is the most ...
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1answer
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 ...
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2answers
214 views

Why not take the mode of a bootstrap distribution?

Say that I had a bootstrap distribution, can I return the mode as a point estimate? It's right-skewed, so the mean does not accurately summarize the distribution.
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1answer
2k views

Expected Value and Most Likely Outcome

I was watching this Khan video on Expected Value as a refresher. He mentions in passing that the expected value is the most likely outcome... Well, that's only true because he's using a binomial ...