# Questions tagged [discrete-data]

Refers to data generated from a distribution that has a countable sample space. Discrete data may be nominal (e.g. the distribution of race in a sample of individuals) or ordinal (e.g. the number of errors on a page of text).

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### Is there a distribution such that a sum of its samples creates the uniform distribution? [duplicate]

Say I sample $N$ numbers from a mystery discrete distribution and add them all together. My goal is for the sum of these random variables to be uniformly distributed from $[a,b]$ and thus the ...
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### Prove bi-directional relationship between convergence in distribution and convergence of probability mass functions

Let $X$ be a random variable that is positive and integer-valued. Let $X_1, X_2, ...$ also be random variables that are positive and integer-valued. Prove that $X_n$ converges in distribution to $X$ ...
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### Is there an analytical way of determining the probability for a specific outcome given a joint p.m.f.?

I'm looking for a way to determine the probability for a specific outcome based on (what I think should probably be) a joint probability mass function. I'll try to put into words my specific case: I ...
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### Joint mass function of two perfectly correlated categorical variables

Is it possible to derive the joint probability mass function of two discrete random variables (categorical in my specific case) IF we know that they are perfectly correlated? Let's assume for ...
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### How to test significance for discrete scale survey results [duplicate]

I have the results of a device evaluation study with 16 subjects. Each subject has completed two surveys with the same questions but concerning different devices. The questions have been answered on a ...
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### Can a continuous cause have a discrete effect?

Say we have a continuous temperature as an input and a few climate categories as an output. For example, if the temperature is between 22.93 and ...
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### Compare two discrete distributions using Chi-Sq

(I am not quite sure whether the following post is better suited for CrossValidated or for StackOverflow because I have both a theoretical question about the use of the Chi-Squared test and a more ...
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### Basic understanding: Confidence interval for discrete variable

Let's say I play a game with where the outcome can be any even number from 10 to 30, with unknown probabilities. After playing this game, I have the following results: $\bar X=20, s=3$ (with $n=1000$)...
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### Conditional probability and independence

Suppose A and Y are discrete dichotomous variables $(A=0,1; Y=0,1)$ If $Pr[Y=1|A=1] = Pr[Y=1|A=0]$, why can we conclude that $$Pr[Y=1|A=1] = Pr[Y=1|A=0] = Pr[Y = 1],$$ without knowing beforehand ...
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### Maximum likelihood estimator based on 1 datum for non-canonical discrete distribution

One observation is taken from a discrete distribution with a parameter $\theta$. There are 3 possible values of $\theta$: 1, 2, and 3. The PMF is given below. What is the MLE of $\theta$? I ...
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### Fit data based on generating function

Suppose I have iid data generated from a discrete random variable $X_i \sim D(\lambda)$, and I would like to infer the parameter $\lambda$. Unfortunately, I do not know the likelihood function for $D$,...
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### Is there a common underdispersed discrete distribution with unbounded support for general mean and variance?

I have a mean $\mu$ and a variance $\sigma^2$ with underdispersion, i.e., $\sigma^2<\mu$. Is there a standard discrete distribution with these moments and unbounded-on-the-right support, i.e., ...
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### AIC and BIC and number of quantization level

I want to test how many quantization levels (discretizing levels) are the best for the given data(time series) set I have. Therefore I am applying different levels of binning (like discretisize data ...
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### How to determine if my data is discrete or continuous in java? [duplicate]

Could you mind to teach me how can I test whether the given data is discrete or continuous in java? For example, given array (98.6, 99.2, 103.1) and my statistic service should determine the data ...
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### ELI5: What is a Discrete Distribution with finite support?

A list of discrete event distributions are labeled as either with or without finite support. https://en.wikipedia.org/wiki/List_of_probability_distributions#Discrete_distributions What does it mean ...
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### Difference between continuous and non-continuous data . [duplicate]

In a dataset "survey", pulse and age are given as non-continuous data. how come these age and pulse can be non-continuous? this is the reference link https://explorable.com/discrete-variables
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### Different Types of Data

According to my Elementary statistics for Business and Economics text book revised Edition 2012 . Under a section concerning the Different types of Data . This text book says that under Quantitative ...
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### Experimental design for discrete choice response

I'm designing a survey where people need to choose one of three transportation alternatives. Here are the alternatives, their specific factors/attributes and the levels I intend to use for each: <...
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### How to sample a from p-variate discrete distribution when p is high

Suppose I have a $p$-dimensional random vector $X$, with probability mass function $f(x) = P(X = x)$, $x \in \mathbb \{0,1\}^p$. Each of the $p$ variables is binary. If I want to sample from the ...
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### Modelling resampling as conditioning on sum for independent discrete variables

I am trying to model a discrete data generating process where I first draw $Y = (y_1, ..., y_N), y_n \sim F(\theta_n)$ independently from some family of discrete distributions $F$ (e.g. negative ...
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### Discrete mathematics - combinations etc

So I got this question and we were under the topic of combinations in school. I tried it but first of all here is the question. A box contains sweets of 6 different flavours. There are AT LEAST 2 ...
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### How to deal with semi-discrete regressors?

I've aggregated a dataset based on some research I've done regarding Battery Electric Vehicles. Three of my regressors however are throwing me off: Available BEV models in the market, Estimated ...
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### Why can't we interpret likelihood as probability? [duplicate]

Something similar is asked here What is the difference between "likelihood" and "probability"? My question is (despite all verbal explanation why it is not to be interpreted as ...
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### Properties of a discrete random variable

My stats course just taught me that a discrete random variable has a finite number of options ... I hadn't realized that. I would have thought, like a set of integers, it could be infinite. Googling ...
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### Comparing distribution A to B and C

I have three discrete probability distributions, A, B and C. They are all measuring P(X) under different circumstances. I suspect that A is more similar to B than it is to C. I know that I can compare ...
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### Standard Deviation of Discrete Random Variables in Excel?

I am looking for the Standard Deviation of the Discrete Random variable. I understand how to calculate it by hand but when I use the excel STDDEV function, I am getting a different answer. Is there a ...
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### Non-target attribute is imbalanced, is it class imbalance or is there another term?

I have come across the term class imbalance in classification problems. From what I understand, it means the target variable is split into two (or more) categories where on category is significantly ...
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### What method should I use to forecast discrete data?

I have data which can take discrete values (between 0 and 5). I have 2 values per day during 2 years which contain a lot of 0 and 5. I know that my data are correlated with end of week, end of month, ...
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### Extract features from discrete time series data

I am working with time series data of discrete (i.e. nominal) values instead of numeric values. In other words, my time series is a sequence of "class values" like: "A", "A", "A", "B", "B", "A", "C" ...
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### Fitting higher order Markov chains in R

For $n$ individuals I observe their states at fixed times. So I have $n$ observations of a data generating Markov chain. Using the markovchain-package I then can fit a time-homogeneous Markov chain ...
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### Forecast (impute) missing discrete values in multiple time series

I'm looking to forecast (impute) missing discrete values in multiple time series in order to reach a target volume in a consolidated time serie. The context: I have salesmen that are selling ...
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### Finding the discrete distribution

I want to find the discrete distribution of X, where expected value of x, E(X)=3 and the Variance of X is 15. X=1,2,3,4,5,and 6. What is the easiest way to find the distribution of X. I really ...
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### References on calculating posterior mode in multiclass discrete Ising model

I'd like to calculate the posterior mode (maximum a posteriori estimate) for $\Pr[\,X \,|\, Y\,]$ for a model where $X$ is generated by an Ising model on a two-dimensional lattice and $Y$ are noisy ...
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### Generate viable sampling distributions of discrete data in R

I'm trying to simulate 2 X 2 data that would yield a relatively strong negative correlation. I'm using the R library GenOrd and ...
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### Analysing discrete data from a factorial experimental design

The dependent variable in my data can take on the values 0-7 and is, therefore, a discrete variable. I have data from a number of experiments with one, two, and three-way factorial designs. The ...
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### Testing a nominal variable against a non-continuous variable

I have a nominal IV (Group 1, 2, 3) and all of the participants (n=70) performed a 7 question quiz. I want to test the Group number against the number of correct answers (i.e. 8 possible values). The ...
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### about discrete and continuous variables relationships exploration

I have a dataset with a dependent variable that is discrete. It can take only six values. The input variables are all continuous. I am using R to do data exploration. I am using boxplot(discrete vs ...
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### Discrete vs. Continuous variables

This might seem silly but I am unable to find a clear answer: I need to define whether two variables are either discrete or continuous: "total work" and "sleep". The description of these variables are ...
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### Statistical test for sampling discrete objects from urn

I have data that looks like this: ...
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### Learning a distribution when observing a OR between several classes

I have a discrete categorical variable $X$ with values in $\{1,2,....m\}$, $m$ being rather small (say 10, 100...). I want to estimate the distribution of $X$: the histogram. If my dataset was made ...
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### How to treat discrete variables while modelling in regression

I have a small dataset Friends,Gender,Social 280,female,"13" 250,female,"12" 320,female,"15" 190,female,"14" 320,female,"11" 340,female,"15" 180,male,"10" 220,male,"8" 300,male,"11" 240,male,"9" 270,...
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### discrete = countable and continuous = uncountable?

I want to understand what a discrete random variable and a continuous one are. Let $X: \Omega \rightarrow \mathbb{R}$ be a random variable (a function). If $\text{Image} (X)$ is a countable set, ...
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### MCMC: How to choose an efficient proposal distribution with continuous and discrete variables

I am using MCMC with the Metropolos-Hasting algorithm to generate solutions of a non linear regression problem. Likelihood My likelihood is a gaussian distribution centered in 0 of the residuals ...
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### Half-normal, discrete data - What statistical test should I use?

I have difficulties identifying the correct statistical test for the following. My data show a half-normal distribution, so the histogram would look something like this: ...
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### Estimating the probability to have already been seen

Considering a discrete variable $X$ with unknown distribution and having values in an unknown finite set, and a sample of $n$ independent observations of $X$, I want to estimate the probability that a ...
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### How can I fit a normal (von Mises) distribution to discrete angular data?

This bears some explaining: I have a set of data from a psychophysics experiment where participants selected a response from a discrete set of 8 possible responses. These responses were actually ...
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### Testing out a regression coefficient through t-test?

I'm working on a dataset that refers to the Stroop Effect. The data can be found here. I would like to test the hypothesis that the beta coefficient (that is the slope) for the ...