# 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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### Dropping one of the columns when using one-hot encoding

My understanding is that in machine learning it can be a problem if your dataset has highly correlated features, as they effectively encode the same information. Recently someone pointed out that ...
10answers
919k views

### What is the difference between discrete data and continuous data?

What is the difference between discrete data and continuous data?
3answers
19k views

### Is Kolmogorov-Smirnov test valid with discrete distributions?

I'm comparing a sample and checking whether it distributes as some, discrete, distribution. However, I'm not enterily sure that Kolmogorov-Smirnov applies. Wikipedia seems to imply it does not. If it ...
1answer
3k views

### Discrete functions: Confidence interval coverage?

How to calculate discrete interval coverage? What I know how to do: If I had a continuous model, I could define a 95% confidence interval for each of my predicted values, and then see how often the ...
1answer
2k views

### Determining an optimal discretization of data from a continuous distribution

Suppose you have a data set $Y_{1}, ..., Y_{n}$ from a continuous distribution with density $p(y)$ supported on $[0,1]$ that is not known, but $n$ is pretty large so a kernel density (for example) ...
2answers
6k views

### Explanation of the different variable types in statistics?

One thing that has always tripped me up when trying to learn new methods in statistics is understanding what type of features/variables can this method be applied to. The variable types that ...
4answers
52k views

### Predicting with both continuous and categorical features

Some predictive modeling techniques are more designed for handling continuous predictors, while others are better for handling categorical or discrete variables. Of course there exist techniques to ...
1answer
11k views

### Kolmogorov-Smirnov with discrete data: What is proper use of dgof::ks.test in R?

Beginner questions: I want to test whether two discrete data sets come from the same distribution. A Kolmogorov-Smirnov test was suggested to me. Conover (Practical Nonparametric Statistics, 3d) ...
2answers
388 views

### Discrete choice model

I have a ordinal probit model. The dependent variable, say walkability, is a Likert scale variable (1,2,3). The main independent variable, say connectivity, is also a Likert scale variable (1,2,3). ...
1answer
719 views

### Dependent Bernoulli trials

The probability of a sequence of n independent Bernoulli trials can be easily expressed as $$p(x_1,...,x_n|p_1,...,p_n)=\prod_{i=1}^np_i^{x_i}(1-p_i)^{1-x_i}$$ but what if the trials are not ...
1answer
77 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 ...
5answers
39k views

### Clustering a dataset with both discrete and continuous variables

I have a dataset X which has 10 dimensions, 4 of which are discrete values. In fact, those 4 discrete variables are ordinal, i.e. a higher value implies a higher/better semantic. 2 of these discrete ...
2answers
10k views

### Optimal Binning with respect to a given response variable

I'm looking for optimal binning method (discretization) of a continuous variable with respect to a given response (target) binary variable and with maximum number of intervals as a parameter. example:...
2answers
7k views

### Problem in discrete valued time series forecasting

I have a temporally ordered discrete valued data. The only possible states for the data are: {1,2,3,4,5,6}. So the series is something like {1,2,3,5,6,4,3,5,2,......} I want to forecast the next value ...
3answers
1k views

### 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 ...
1answer
1k views

### Expected value for discrete (nominal) variable?

I'm trying to understand the concept of the expected value. Especially, what bothers me is the expected value for discrete random variables. I will try to formulate it by examples: The expected value ...
1answer
2k views

### Power-law fitting and testing

I want to test the distribution that best fit a specific metric (that I call SD) extracted from the source code of systems. I have a guess that they follow a power-law behavior. My sample: 20 systems ...
1answer
482 views

### Multinomial choice with binary observations

Is there a standard name for a multinomial choice model where the observations are in the form of binary questions such as "do you prefer A to B" and "do you prefer B to D"? This seems like a common ...
1answer
178 views

### 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., ...
0answers
250 views

### Combining Bhattacharya Distance (or A Measure of Similarity) — across Different Variables (Properties)

We have a series of observations of different properties (such as heart rate or blood sugar level and others as well) across different days from different people from different geographical regions. ...
2answers
643 views

### Cumulative Distribution Function Inequality (Discrete Distributions)

Let a discrete Random Variable $T$ have CDF $F_T(T)$. Could you please help me understand why $$P \left[ F_T (T) \leq a_1 \right] \leq a_1$$ I know that the result holds with equality for the ...
2answers
2k views

### Test identicality of discrete distributions

Is there a standard way to test whether two vectors were drawn with the same discrete distribution in R? Something like a Kolmogorov-Smirnov test, but for discrete distributions. I think two-sample ...
3answers
669 views

### Is my random variable discrete or continuous?

Suppose I have a discrete set of (finite) data (values are only positive integers) (which always remains discrete whenever the observation/survey is taken), divided into some identical categories . ...
2answers
440 views

### Gibbs sampling and mixed distribution

For a project, I need to simulate from a joint distribution with both continuous and discrete variables that are dependent. The conditional distribution of any variable given the rest is known. I ...
2answers
268 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 ...
1answer
317 views

### Using counts of a continuous random variable to establish an unknown probability density function

The precision of a given measuring device defines a window over the probability density function of whatever is being measured. For instance, if a measuring tape is precise to 0.1 inches, then the ...
2answers
15k views

### How to fit a discrete distribution to count data?

I have the following histogram of count data. And I would like to fit a discrete distribution to it. I am not sure how I should go about this. Should I first superimpose a discrete distribution, say ...
3answers
9k views

1answer
736 views

### Estimate probability mass function from observed samples?

This question is related to but is distinct from Estimation of probability mass function using finite samples. As in the related question, suppose we have a discrete random variable $X$ with known ...