# Questions tagged [discrete-data]

Refers to data generated from a distribution that has a countable sample space. The discrete data tag may encompass categorical data, whether nominal (e.g. the distribution of race in a sample of individuals) or ordinal (e.g. socio-economic status), or an actual discrete random variate, such as a set of event counts (e.g. the number of errors on a page of text). Discrete data need not necessarily be integer, however.

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### Need help figuring out what statistical test to use (ANOVA or MANOVA)

I am trying to figure out what statistical test I need for my eye tracking study. I have 2 dependent variables: Dependent Variable 1 is continous (gaze behaviour, which is subdivided into fixation ...
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### Discrete choice models: truncated or censored model

I am reviewing some practice. Suppose we have a random sample of households reporting their share of financial wealth invested in stocks (alpha). The minimum alpha in the sample is 0.15, and the ...
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### Two-sample Kolmogorov-Smirnov discrete distributions

Let's say that two Census takers interview a number of couples and ask for the number of children they have. I want to compare the two resulting samples to find out if they could have come from the ...
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### Regression model for integer response

Let the response be $Y_i \in \mathbb{Z}$ and the covariate $X_i \in \mathbb{R}^p$. For counting data where $Y_i$ are restricted to be nonnegative, we have Poisson regression or negative binomial ...
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### Replicating a study with a discrete dependent variable in linear mixed effects model (1-4 scores) [duplicate]

As the title says, I want to replicate a study that runs linear mixed effects models with a dependent variable that is discrete, with scores from 1 to 4. So, I have two main questions about that. 1 ) ...
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### Fitting discrete data to continuous distributions

I'm creating a simulation model, in which some stochastic factors are included. On of my stochastic factors is the amount of containers arriving daily for a specific delivery location. A plot of this ...
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### Construction of statistics of a discrete distribution

I have the following problem: we consider an i.i.d sample $\mathbf{X} = (X_1,...,X_n)$ of the discrete set $\{1,...,N\}$. An agent has to infer the probability distribution of $X_i$. I wanted to use ...
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### Two Samples Test for Discrete Variable and Different Size Groups?

Hello there and apologies for my English and lack of statistic skills! Two different groups of participants, one comprised of children and the other of adults, run once, at different times, the same ...
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### Alternative to SimPy for continuous event simulation?

The python library, SimPy, is pretty explicit that it only handles discrete event simulation. Though it is theoretically possible to do continuous simulations with SimPy, it has no features that help ...
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### Salary of a group of people is continuous or discrete

I have salary data of 3000 employees ranging from 3000 - 10000 dollars. Based on my understanding:(https://mathbitsnotebook.com/Algebra1/FunctionGraphs/FNGContinuousDiscrete.html) Continuous data is ...
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### Problem on Discrete Random Variable

Please kindly give a pointer to this question. Generating the discrete variables seems unlikely! Entrance to a country can be denied for a number of reasons. When someone arrives by air, and their ...
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### How do I quantify the homogeneity of discrete data?

I have a subset (of some bigger set, lets say of size $N$) containing $S$ different things. Now each of these $S$ things belong to a category. The total number of categories is $<=N$. What can be a ...
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### Which type of variable are week numbers?

I have a dataset where measurements on animals were done on multiple weeks of experiments. So I have measurements for week 1, week 2, etc. So I was wondering which type of variables are these? I ...
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### Can an ordered logit model be used to predict points scored by an NBA player?

I am interested in getting the probabilities of a player scoring exactly 1 point, 2 points, 3 points etc. Can an ordered logit be used for this? If not what would be the best way to get the ...
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### Bootstrapping quantiles of integers [duplicate]

Given an i.i.d. sample of 36 integers: [6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6] A bootstrap resampling procedure is performed to ...
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### Estimating a discrete distribution given expected value

I have an expected mean of a discrete variable. I would like to estimate the distribution so I can generate random samples of the value for a simulation. I have historical expected values and observed ...
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### Quantile estimation for discrete data

For quantile estimation for data coming from a discrete distribution, do you have to use one of the quantile estimators R-1, R-2, or R-3? For example, R-3 uses the nearest even order statistic after ...
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### How do you do a qq plot in R for a discrete Weibull distribution?

To do this, I think I need to calculate the inverse CDF, but I have learned here that the discrete Weibull (type I) as given by: $$F_{I}(x)=1-\exp\left[-\left(\frac{x+1}{\alpha}\right)^\beta \right]$$ ...
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### Quantiles from histogram?

Is it possible to calculate quantiles from a probability histogram P(x) rather than from the data x itself? I have an unbinned histogram for discrete random variables, and I'm wondering if I can ...
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### Sum of sample given a priori knowledge of its maximum

Given a sample of discrete random variables $X_1, X_2, \ldots, X_n \sim F$, I am looking to calculate the distribution given by the probability mass function: P\left(\sum_{i=1}^n X_i = x~\middle|~\...
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### Likelihood that observed relative frequencies match a probability distribution

For this question, please assume probability distributions are discrete. If I have $N$ data points ($x_1, x_2, ..., x_N$), and I want to know the likelihood that these samples came from a discrete ...
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### Marginalizing out discrete response variables in Stan

There's been quite a bit of discussion and confusion about how to marginalize out discrete response variables in Stan (e.g. binary or ordinal data). See, for instance: Impute binary outcome variable ...
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### Derivative of a probability

If $Y$ is a discrete random variable, and I define $F(x)=P(Y \leq x),$ where $x \in \mathbb{R},$ can I differentiate $F(x)$?
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### Formulas for Combinations of Colored Balls

Recently, I thought of the following question relating to "ordering colored balls according to some choice of constraints". Suppose there are 5 balls: Red Blue Green Yellow Orange Normally,...
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### Sum of Discrete Uniforms, but each value can be picked no more than N times?

Suppose there are i.i.d. variables $X_{1,..n}$ with discrete uniform distribution with the support $[1, n]$. What would be the distribution of such a sum if we introduce the condition that each value ...
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### How to break up the following scale into equal segments?

In Excel, there is a conditional formatting feature like this: Let's say in order to figure out what color to use for a value, I split the gradient into 14 steps, such as: Red:6Parts,Yellow:0Parts ...
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### How to model the joint distribution of continuous and discrete features (and estimate the model)?

Suppose a typical house in the market has 3 features $X_1$, $X_2$, $X_3$. $X_1$ is the square footage of the apartments interior living space, $X_2$ is the square footage of the land space and $X_3$ ...
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### Suppose $X$ follows normal and $Y$ follows Bernoulli, wrt which measure does $(X,Y)=(-0.005,1)$ have a measure zero?

Suppose $X$ follows standard normal distribution and $Y\in\{0,1\}$ follows Bernoulli(0.5),i.e., $Pr(Y=1)=0.5$. Intuitively, I know the point or event $(X,Y)=(-0.005,1)$ has a measure of zero. But I ...
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### KS-Test on Discrete Distributions on Poisson-type Process

I have two distributions of data from a Poisson-like process. The data is based on randomized searches and tallies the amount of results found in one hour. One distribution has over 300 searches, ...
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### Number of bins for discretization

How do I decide on the right number of bins to discretize my continuous data? Are there are tests/techniques to do the same? Could someone give me some idea into existing approaches?
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### Paired t-test to compare mean of responses to a questionniare. (Binomially distributed data)

I have data from of people filling in a questionnaire where they for each statement give a score on a scale from 0 to 4 where 0 corresponds to them fully disagreeing with the statement and and 4 fully ...
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### How to statistical analyze a discrete variable which is not necessary for an event to occur but which favours it?

I am trying to assess if a quantitative discrete variable has an impact in the occurrence of an event. However, I am aware that this variable is not necessary for the event to occur, because it also ...
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### Why do discretised predictors have lower statistical power than continuous predictors?

In designing an analysis, I'd like to decide between using discretised variables versus using the original, continuous variable (the reason being that in this particular case, collecting discretised ...
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### Which statistical test should be used for comparing two discrete/count data?

Supposing that in an experiment there are two groups: Group A and Group B, each consisting of 30 participants. The participants are required to play a game for ten rounds. In each round, the ...
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