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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Calculate the likelihood at the mode of a pdf conditioned on θ [closed]

Assuming that I have the PDF of a random variable X with parameter θ (i.e., f(x|θ)). How is the likelihood at the mode of this PDF computed?
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Does Geyer's mode selection heuristic perform no-worse than burn-in?

In Charles Geyer's Burn-In is Unnecessary he writes Another possible rule is to start at a point, like the mode, known to have reasonably high probability. If no such point is known, this rule is ...
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Can I bootstrap a bootstrap (in order to estimate an error on a probability)?

I have probability distribution $f$ over a set of categorical objects $x$, and I wish to estimate the probability $p$ that $x_i$ is the true mode of $f$, given my observations. I draw a random sample ...
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finding central tendency

The following table presents frequency distribution of teachers of 1 year: Rank ----------Frequency Professor ------------7 Assoc Professor ------4 Asst Professor--------3 Instructor -----------5 ...
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Modal average in JMP Summary Statistics

The JMP Summary tool allows users to select mean or median for aggregated statistics, but does not include mode in the dropdown list. Is there some logical reason for this? Is there a way to do it?
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How do you estimate the mode of a histogram with logarithmic bin width?

For the purpose of estimating the median and other quantiles, I summarize samples in a histogram whose bins grow logarithmically in width. For example, to guarantee a 1% worst case absolute relative ...
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Constant Mode Equation for a Weibull Distribution

I am trying to build a movement class for a simulated annealing algorithm for predicting an optimal spare parts policy. For better or worse I am looking to the Weibull distribution to move about the ...
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In reinforcement learning/multi-armed bandits, why do we look at expected reward and not the most likely reward? [duplicate]

This is the dilemma that I have faced in applied probability in general. Say you have the choice to put your savings of $\$10$ in a deposit account with guaranteed retun of $\$100$ or buy a lottery ...
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How do we derive the conditional mode as the solution to linear regression, for uniform cost function?

I know that if the cost functions are respectively the least squares ($L^2$) and the absolute deviation ($L^1$), the solution to linear regression is the conditional mean and the conditional median ...
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Mean, Mode, Median of a histogram?

Based on my understandings, I would say for the below histogram that the mode is zero, the mean is between 0 & 1 and the median is 1. I'm I right?
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Mode for equal consecutive frequencies

I'd like to calculate the mode for the frequency distribution table: ...
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Understanding the Importance of "Sufficiency" within Statistics

I am trying to better understand what it means to be a "sufficient statistic". "In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown ...
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Probability Distributions : "Mode" vs. "Expectation"

I have often heard the argument that in higher dimensions: the "mode" (most common value) of a probability distribution function does not correspond to the "expectation" (mean) of ...
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Suggestions for calculating peak times using entrance and exit times

I have a set of data containing the entrance and exit times/dates of visitors to a building and I need to calculate the peak time(s) of said building. With just this information is there a way to ...
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298 views

Likert data and Likert scales - ordinal or interval?

I was reading up on the use of Likert scales and how to analyse data. I found this bit of text confusing: To properly analyze Likert data, one must understand the measurement scale represented by ...
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Mean, Median, Mode of Log Normal Distribution

Let $Y$ be Log-Normal with parameters $\mu$ and $\sigma^{2}$. So $Y=e^{x}$ with $X \sim \mathcal{N}\left(\mu, \sigma^{2}\right)$. Which of the following statements is correct? (A) The median of $Y$ is ...
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Test whether two samples have different modes?

I have a dataset with timed observations of an event across the day, in two different places. I am particularly interested in whether the peak in observation is significantly different between the two ...
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Can a sample average be multimodal?

Suppose $X_1,\ldots,X_n$ are iid with a well defined expectation. Is it possible for the sample mean $(1/n)\sum_{i=1}^nX_i$ to be multimodal for all $n$? Looking at simple examples I can see that for ...
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3 votes
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Why do we add an extra decimal place when we calculate the range in statistics?

From Mario Triola's textbook: I understand that we add a decimal place when we calculate the median (it is possible to have (a+b)/2 ). I absolutely do NOT understand why we do that when we round off ...
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3 votes
1 answer
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What are the terms involving the mode's frequency?

Suppose I have a finite multiset of $n$ elements (a "population" I guess we can call it). Suppose this set has a proper mode, appearing m out of $n$ times. What term(s) do statisticians use: ...
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Finding the mode given the probability of occurence

When a teacher asks a question, a student has a probability of 0.4 of being asked. Assume the occurrence is independent. What is the mode of the number of questions raised by the teacher it takes for ...
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1 vote
1 answer
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Can we use bootstrap to estimate Mode of the population?

I have known that bootstrapping can be used to estimate the population mean, Is it valid if we estimate the population mode too? Further, can we estimate any population parameter with the help of ...
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4 votes
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Does it ever make sense to average the median, mean, and mode?

Consider four subjects (A,B,C,D) competing 12 times in a game with 5 possible scores (5,6,7,8,9): ...
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4 votes
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Find the mode of the Weibull distribution

I am using the matlab curve fitting tool. It allows to use the Weibull distribution, using this formula: $$f(x)=abx^{b-1}\exp(-ax^b). $$ Unfortunately this is not the formula that I found on Wikipedia....
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Expected value (Mean) of a joint distribution

I saw in a textbook that if we have a joint distribution $f(X,Y)$ that is a Gaussian distribution, then we have the mode equal to the mean. The mode is just the values of $X$ and $Y$ such that $f(X,Y)$...
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How do I know which way this sample is skewed?

I have a sample where n = 15 and the median = mean but the mode is less. So I know to be: Positively skewed (mode<median<mean) Negatively skewed (mean<median<mode) Symmetric (mean=median=...
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Mode in probability distribution

From what I know that mode is most frequent occurring value e.g. in [1, 4, 51, 14, 12, 14, 2] Mode is 14 because it occurs twice and most frequent. However, in ...
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Does it make sense to impose a density curve over the bar plot and analyze the mode?

Suppose that my X variable for my probability bar plot is discrete (i.e. not continuous) and ordinal. If this is the case, does it make sense to impose a density curve (apparently this is possible by ...
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Finding the mode of multiple sample modes

I'm running an experiment where I'm collecting samples of different size (numeric data only) and computing the mean, median and mode of each sample. I'm interested in finding out the mode across all ...
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GLMs with skewed distributions - why use mean and not mode?

There's something that's a bit troubling for me. The unit deviance in GLM is defined as $2[t(y,y) - t(y,\mu)]$, when $t(y,\mu) = y\theta(\mu) - b(\theta(\mu))$ (theta being the natural parameter). For ...
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1 vote
1 answer
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Finding the most representative row in a dataset

Our goal is to model the hourly electric usage of a building given only building characteristics. We are running hourly energy models on hundreds of thousands of virtual buildings. We then take a real ...
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Computing Mode of Prior

How do you compute the mode of a prior with beta distribution $(\alpha, \beta)$?
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Is the mode considered a resistant statistic?

Is the mode considered a resistant statistic? By the definition of resistant given in our text (i.e., not changed much by outliers), I would think the answer would be "yes." On the other hand, the ...
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2 votes
2 answers
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Standard deviation around mean rather than mode or median?

Why is standard deviation calculated from arithmetic mean and not from other measures of central tendency? I do get that standard deviation is to calculate dispersion, but why not use mode or median ...
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8 votes
2 answers
469 views

Is the mode of a Poisson Binomial distribution next to the mean?

A Poisson-Binomial variable $X\sim PB(p_1, \dots, p_n)$ is the sum of $n$ independent, not necessarily identically distributed, Bernoulli variables $X_1, \dots, X_n$: $$ X=\sum_{i=1}^n X_i, $$ with $...
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Median or mode for measurements with erroneous outliers

Background: I am working with real measurements that likely contain two sources of error, (1) measurements that were performed incorrectly, and (2) natural variability of the measured quantity and ...
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Conditional log-concavity and unimodality

Let $X$ and $Y$ be two random variables (or vectors) with continuous and "smooth enough" joint distribution. Assume that the two conditional distributions $X|Y=y$ and $Y|X=x$ are log-concave for all $...
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What is a term to describe data where the mode represents a large proportion of all observations?

Below are some histograms of continuous variables, where 20-50% of all observations fall on the mode. Are there any terms to describe data that exhibit this unusual concentration of observations on ...
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Best measure of central of tendency

I just started learning stats a few weeks ago well my question is that as we know that the mean, median, and mode is the central tendency of the data and its suggested that we shouldn't go with only ...
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if the mode of a normal distribution is 0, then what's the value of the mean

so if the PDF attains its maximum at 0 it means that $f'(0) = 0$: $$f'(x) = -\frac{x}{\sigma^2 \sqrt{\pi}}\exp({-\frac{(x - \mu)^2}{2\sigma^2}}) $$ $$f'(0) = 0 \iff 0 =0$$ yep, no valuable ...
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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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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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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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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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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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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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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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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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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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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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