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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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Python: compare 2 discrete distributions

Lets say I have a population consisting of items A, B, and C. I dont know the distribution ...
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Correlation between discrete and binary variables

I have a binary variable representing happiness. This variable can take binary values of 0 (not happy) and 1 (happy). I have another discrete variable representing valence (representing if emotion is ...
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How to test for statistical difference for discrete data

I'm designing an experiment to evaluate reagents used to develop fingerprints. There will be a variety of objects with different surfaces, 2 different reagents, 3 different fingerprint donors (prints ...
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41 views

Discretization simulation of a Wiener Process

I got some problems with this homework which I have totally no idea, never got into this field before and I really need some help. First, we have a wiener process like Which means the probability of ...
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1answer
59 views

Checking assumptions for Mann-Kendall trend test

I have a data on counts of images submitted with requests overtime. I would like to test the null hypothesis of no trend vs alternative hypothesis that there is a downward trend. My data is a ...
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nested logit with individual level fixed effect (panel data)

As is stated in the title, I have several questions concern the combination of nested logit and panel data. 1, Can we run nested logit with the individual fixed effect? this is useful when one has ...
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Fitting a continuous normal distribution to an incomplete score distribution

Given a sample of data that contains only the score frequency distribution for scores below a certain threshold, is it possible to fit a complete normal distribution so to estimate what the will be ...
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26 views

What is the best approach to transform scale from 1 to 10 into three categories?

I want discretize my attributes according to the class quality which is the output variable. quality ranges from 1 to 10 in my ...
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1answer
60 views

Levels of measurement and discrete vs continuous random variables

In psychology studies the levels of measurement of variables that are investigated limit/influences the statistical tests that should be performed such as explained here: https://www....
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449 views

Can the discrete variable be a negative number?

I read in a book "An Introduction to Statistical Concepts [3 ed.] p.8): A numerical variable is a quantitative variable. Numerical variables can further be classified as either discrete or ...
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How to estimate the probability mass function of a discrete variable from moments

Consider a bounded, discrete random variable $X$ whose range is $(0,1,\ldots, M)$. We are given the first $k$ moments of this distribution, call them $m_1, \ldots, m_k$. We are interested in ...
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How to predict how many customers are going to purchase based on population purchase frequency?

I am trying to calculate a metric "frequency of purchase of a customer" to determine when I would expect a customer to then purchase an item next. Say, the distribution of my customer base looks like ...
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How to determine the longitudinal duration of effect of one time series on another?

I have two time series related to app usage: Notifications- a time series of notifications sent to the user from the app. User Activity- time series of the user interaction on the app. I am trying ...
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How to evaluate $\mathbb{P}(XY=a)=\mathbb{P}(X=\frac{a}{Y})$, when $X$ or $Y$ take multiple values?

Assume $X,Y$ are discrete and have a finite outcome space. How to evaluate $\mathbb{P}(XY=a)=\mathbb{P}(X=\frac{a}{Y})$, when $X$ or $Y$ take multple values? Does one write out the result for each ...
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Approximate discrete probability distribution

I have a discrete probability distribution with can take a large number of discrete values, say $x \in \{1,\ldots,N\}$. I know $p(x)$ for all these $x$. Typically, quite many of the values have a ...
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Question about continuous and categorical variables

We have 211 measurements of iron and carbon export rates across 5 sites and 2 temperatures, and each of those 5 sites has its own discrete set of physical and chemical characteristics. Would it be ...
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33 views

Using `glm()` in R for correlated count data (data provided)

I have data from one group ($n = 25$) of subjects pre- and post- tested on an $15$-item dichotomously scored test (see below). Given that the data are from the same subjects (i.e., correlated), how ...
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1answer
73 views

Outliers on discrete data

Is there any robust methodology to identify outliers in the discrete data distribution. I am specifically concerned with discrete geometrical distribution? P.S. Data transformation does not seem to ...
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1answer
22 views

Analyzing/visualizing tightly grouped discrete results

I've been having a very hard time finding a good representation (visual or analytical) for lots of data points on a very small, discrete scale. e.g. given a set of results from 1 to 5 in increments of ...
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391 views

Difference between geometric distribution and negative binomial distribution

How do I differentiate between a problem of geometric distribution and that of Negative Binomial Distribution? Both include something around first success or failure. I'm confused.
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Meaningful Sample Size

I have a set of 100 people each assigned to one of the four groups (very short, short, tall, and very tall). How many people's height do I have to measure to know the general distribution of people ...
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How to determine if a dichotomous variable is randomly distributed or is predicted by other instances

I have a product with a measurement of X features. Each feature can either be a PASS or a FAIL. Which statistical test can I use to tell if the failures are randomly distributed across all features? ...
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1answer
49 views

Multi-dimensional CDF on a discrete support

Suppose I have two discrete-support random variables, $X$ and $Y$. They have joint CDF $F(X,Y)$. If I want to find $\Pr(a \leq X \leq b , c \leq Y \leq d)$. It is obviously not: $F(b ,d)-F(a-1 ,...
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Most powerful test for deciding probability mass function

Let $X$ be an integer valued random variable supported on $\{0.1.2...,12\}$ whose pmf is either $g(x)=1/13; x=0,1,...,12$ or $ f(x)=\dfrac x {36} 1_{\{0,1,...,6\}} + (\dfrac 13 - \dfrac x{36})1_{\{7,...
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Model time series as real-valued or integer-valued?

I have a positive-valued time series of daily prices (a sample is listed below -- there are a few thousand observations) that is recorded to two decimal places. It is stationary after computing the ...
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Censored Dummy Regressor

I have a dataset that contains factors corresponding income ranges of sampled persons, like people with factor 1 earn between 10,000 to 20,000, 2 between 20,000 to 30,000 . I could just make dummies ...
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1answer
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How to calculate the covariance matrix for a categorized variable?

Let $X$ and $Y$ be jointly distributed as a multivariate normal with the following parameters: $$ \mu_{XY} = \begin{bmatrix} 0 \\ 0.2 \end{bmatrix} \qquad \Sigma_{XY} = \begin{bmatrix} 1 & 0.05 \...
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Is there a method to find optimal discrete options from continuous data?

I have human perceptual data measured in a continuous scale. I am however not sure that the underlying variable being measures is in reality continuous, in fact I believe it might be a discrete scale. ...
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1answer
44 views

Comparing two discrete independent variables

I would like to perform something like two-sample Wilcoxon tests/T-test (paired = FALSE) to compare two method's expected scores. Here is the table of counts: ...
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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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1answer
159 views

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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1answer
312 views

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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1answer
32 views

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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2answers
183 views

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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How to estimate a histogram for two correlated input parameters when the resulting histogram is known?

Let's assume there are two (slightly correlated) parameters (A and B). Both parameters are rated with discrete values (range: 1-5). The sum of the two parameter-ratings gives the cumulative-rating (A+...
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1answer
383 views

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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68 views

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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38 views

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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1answer
42 views

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 ...