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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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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12 views

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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34 views

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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Multinomial logistic regression with unobserved classes?

Suppose that there are 10 treatments, each of them applied to groups of $n_i=10$ patients (i.e. 100 patients in total). Three types of outcomes are measured on each group, defining categories $C_1, ...
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Modeling Multiple Discrete Choices for Categorical Outcome

I have a dataset of individuals making choices and the outcome is the assignment various objects to categories. However multiple categories may be discretely chosen by each individual for each object, ...
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What type of variable is file size?

Variables can be discrete or continuous. Discrete variables are variables obtained by counting. Continuous variables are generated by measuring something. My variable is "file size" and I ...
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Determining Stastically significant difference in sizes of descrete groups

I have data from a experiement involving DNA, where a "random" string of DNA is created. This would look like [ [A,C,T,G],[A,C,T,G],[A,C,T,G]] where the string is any of the combinations of ...
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percentage features VS discrete attribute?

I have a dilemma about some of the features in a dataset. The dataset contains some discrete features. I can represent these features as integers or I can divide them by the total sum and multiply by ...
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Discrete and Continuous variables. What is the definition?

The definition of a continuous variable in our class seems to be, well, not a definition, as there are exceptions not included in its definition. I am a 4th year math student and find it appalling ...
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36 views

How to fit data to a discrete linear model?

Say I have a list of real values such as the following: ...
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Is it better to predict one continuous target or split it to set of N discrete bins in DNN training?

I am going to train a DNN to predict a continuous target $Y$ that can reach values $<0,60>$. In a research I have read, such interval was split into a set of $N$ discrete values $Y_1,...Y_N$. I ...
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23 views

Alternatives to point biserial correlation discrete variable with more than 2 levels

I am trying to estimate the covariance between two variables, one is continuous and the other is discrete. The discrete variable has 3 levels (Red, Blue, Green). I know point biserial correlation will ...
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28 views

Estimate argmax of function that is measured at discrete points

I have gathered simulation data of a function $f(x)$, where $x$ is a continuous variable. I measure $f$ at discrete points $x_k$. Since the underlying process is stochastic, I performed Monte Carlo ...
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Simpler ways to solve this conditional probability question?

Here's a restatement of a programming problem I found on the Peking Online Judge website. Your friend paints each side of each of 4 dice red or blue, independently, with equal probability. They roll ...
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Expressing discrete random variable in terms of another discrete random variable?

I have a Binomially distributed discrete random variable $X$, so that $X{\sim}(n,0.09896)$, where $n$ can be any positive integer. $X$ represents, say, the number of people who arrive at a restaurant ...
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1answer
118 views

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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Is it possible to do the kind of discrete distribution transform / mapping?

I am not very good at math-speak and I hope my explanation is clear below. I will provide an example & hopefully I am not missing something obvious in thinking about this problem. Question: ...
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Mle on discrete distribution in table

Consider the probability distribution p(x; $\theta $ ), x=2, 3, 4, 5 and $\theta $ = 1/4, 1/2, 3/4. A sample of size 1 is drawn from the population and it is found to be 3. Obtain the maximum ...
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Discrete variables as part of the inputs to a Neural Network

I think it's best to formulate the question as an example. Let's say I want to predict the room temperature using a simple LSTM(+dense layers etc; doesn't matter what the architecture is) model. For ...
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How to estimate discrete probability distribution from a dataset of pairwise frequencies?

My problem is best explained with an example.. Suppose every day I count the cars driving down my street, but because I'm a slow counter, I only count two different types of cars per day. On the first ...
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Clustering items taking values from a discrete set

The problem setup is as follows: There a $N$ items which have to be clustered into $K$ clusters. Each Items has a certain number of dependencies, where each item takes dependencies from a discrete set ...
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2answers
64 views

Approximating non-integer median for CDF of discrete variable

In my googling, it seems the proper way to find the median of a cdf of a discrete variable is to stick to the discrete values provided, even if you overshoot and end up with an x where P(X <= x) &...
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22 views

Cochran's Q but for more than two outcomes

Formal problem I have a random variable $X$ that takes (unordered) discrete values $i\in [0, 2]\subset\mathbb N$ (there is no order here, I just don't know how to write it neater) that is measured $t \...
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How to Adjust the scale of discrete variables

Many prediction methods such as Ridge and LASSO require that the scale of features (regressors) is standardized. However, in practice, a lot of features are ordered discrete or dummy variable. In this ...
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1answer
43 views

how can i use a frequency chart and a density curve to check for normal distribution in my data

I've seen in many analysis reports that to test for normality in a discrete variable, as well as in a continuous variable, people use a frequency chart and a density plot to visually check for ...
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In a power-law distribution, does the maximum value of a measure increase with the number of measured items?

This question is motivated by the following claim in this article: There is increasing evidence that many object-oriented software size metrics are characterized by scale-free, power-law ...
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29 views

Which statistical test is appropriate?

I have a dataset of two groups, group A and group B, from the same species but different subspecies, each group consisting of 500 members. I've done a study wherein I added members of group A to ...
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1answer
94 views

Optimal setup with Categorical/Discrete data using Neural Network

I need to implement a neural network whose dataset and response are composed of only 0,1, -1 values. For those with experience, which setup would you recommend (activation function, loss, neurons, etc)...
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39 views

does mlogit and mnlogit in R require choices to be chosen at least once?

I am fitting a logit model with many choices (17665) and individuals (767). Its a recreation demand model where people are choosing to go to coastline segments with attributes and travel costs to get ...
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15 views

Is it allowable to use an open interval in a discretized factor?

I have a factor for firm size which is technically a categorical variable. The response values are: 1-49 50-199 200-499 500-9,999 10,000+ I am constructing a histogram of the response distribution. ...
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154 views

Open AI Gym for TSP problem?

In a previous question I asked about use of Open AI Gym as a vehicle for modeling business problems as MDPs. A comment suggested that I start a new question with more refined scope. In general, I'm ...
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Probability of n people having at least k successes

I have a set of numbers that corresponds to the number of objects per person, $X = (1, 1, 2, 5, 10, 1, ...)$ The data's discrete, where it's highly inflated by 1 (no zeros) and you have a very long ...
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20 views

How to use Somer's Dxy and/or Spearman's p as scoring rule for interval/ordinal predictions

I am in a situation similar to this thread. I am using a Poisson distribution to calculate the probability of different ice hockey goal amounts and am using scoring rules to test their accuracy. The ...
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77 views

Discrete value - Normal distribution [duplicate]

I have a data with discrete values and need to find if it is normally distributed. I plotted the graph and it looks normal and then I performed shapiro wilk test where the result were W = 0.78773, p-...
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1answer
86 views

About computation of Brier score

Assume that we have some count data $x_{1}, \dots, x_{n}$, generated by probability mass function $\textbf{p} = \{p_{1}, \dots, p_{s} \}$. Let $\hat{\theta}$ be some estimator of $\textbf{p}$. In ...
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134 views

What statistical tests allow for a comparison of the "roughness" of discrete functions?

I have a data set of the revenues of 10 different large companies from the years 2000 through 2019. Here they are all plotted in one graph. The y-axis has a unit of billions of Euros:                  ...
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43 views

Quasi-random sequence with discrete variables with differing number of levels

My question is probably worded incorrectly but here it is: I have (say) 3 discrete random variables: x1: has 15 levels (uniform pdf for simplicity) x2: has 3 levels (uniforms) x3: has 4 levels (...
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2answers
622 views

Expected value and standard deviation of $X^2$ in terms of moments of $X$

If $X$ is a discrete random variable with expected value $\mu$ and standard deviation $\sigma$, and $Y = X^2$, how can we describe the expected value and standard deviation of $Y$? Would expected ...
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3answers
153 views

What is the equivalent of linear Gaussian noise but for discrete data

A common framework in stats and ML is that our data is noisy observation of an underlying true value, e.g. $$ \begin{aligned} \mathbf{x} &= \mathbf{z} + \boldsymbol{\varepsilon}, \\ \boldsymbol{\...
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Count data with largely varying sample sizes. Can I get anything from the data?

I only have categorical data, between two groups, with more than three categories per data set. Here are some actual examples of the data: Comparing (https://www.strawpoll.me/4380945/r) to (https://...
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2answers
149 views

Generating random data from a discrete multimodal distribution

I have a $n \times n$ distribution grid that represents the likelihood of finding a person within an area (see below). From this I would like to be able to create $x$ samples that fit this ...
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82 views

How to Choose Poisson Time Interval

A Poisson process is one where mean = var = λ. How do you decide what time interval fulfills these criteria when fitting the Poisson distribution to a process? Can all processes be modeled as Poisson ...

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