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

What is the difference between discrete data and continuous data?
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 ...
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 ...
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 ...
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) ...
965 views

### Does this discrete distribution have a name?

Does this discrete distribution have a name? For $i \in 1...N$ $f(i) = \frac{1}{N} \sum_{j = i}^N \frac{1}{j}$ I came across this distribution from the following: I have a list of $N$ items ranked ...
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 ...
4k views

### Basic questions about discrete time survival analysis

I am attempting to carry out a discrete time survival analysis using a logistic regression model, and I'm not sure I completely understand the process. I would greatly appreciate assistance with a ...
8k views

### 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 ...
6k views

### Anomaly Detection with Dummy Features (and other Discrete/Categorical Features)

tl;dr What is the recommended way to deal with discrete data when performing anomaly detection? What is the recommended way to deal with ...
9k views

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### Complete sufficient statistic

I've recently started studying statistical inference. I've been working through various problems and this one has me completely stumped. Let $X_1,\dots,X_n$ be a random sample from a discrete ...
436 views

### Conservativeness of tests based on a discrete random variables

For discrete test statistics, the distribution of the corresponding $p$-value is discrete and stochastically larger than the uniform distribution. Hence the corresponding hypothesis test based on the ...
7k views

### How to test group differences on a five point variable?

I have a series of observations that fall into bins (or "scores"); that is, the data can be 0, 1, 2, 3 or 4. There are two groups of such data, control and treated. I know the number of individuals ...
486 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 ...
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 ...
559 views

### 5 defectives rule of thumb

I have taught six sigma black belt classes using consultant sourced training materials which included the rule of thumb that when estimating the rate of occurrence of discrete events, like the ...
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### What is the best way to discretize a 1D continuous random variable?

Say I have a 1-dimensional continuous random variable $X$, with PDF $f(X)$, CDF $F(X)$ and inverse CDF $F^{-1}$. What is the best way to discretize $X$? To keep things clear, let $Y$ denote the ...
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### Classification with ordered classes?

Say I want to train a classifier that assigns an image of a person as young, middle-aged, or old. A simple way would be to treat the classes as independent categories and train a classifier. But ...
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 ...
35k views

### What are the variance and standard deviation for a standard six-sided die?

I'm having trouble imagining what variance and deviation mean with a series of die rolls. That is, a fair die will fall with a flat distribution on all its values 1-6. Does the concept of variance ...
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### Discrete analog of CDF: “cumulative mass function”?

We call the integral of a probability density function (PDF) a cumulative distribution function (CDF). But what's the cumulative sum of a probability mass function (PMF) called? I've never heard the ...
459 views

### Continuous probability distribution over integers?

I have a random variable which can have any value from the set of natural numbers. For example, the probability of the random variable having a low value is higher than the probability of the random ...
1k views

### Notation for possible values of a random variable

Let $X$ be a discrete random variable that can take the values $1, 2, \textrm{and}\ 3$. What is the conventional way to write this mathematically? Is it just $X\in\{1,2,3\}$ or should I somehow write ...
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### How to be sure about the distribution of a discrete and limited stochastic variable?

I've got a stochastic variable $X$ which takes the values in $\{0,1,2\}$ with some unknown probabilities. I want to know the distribution, and can sample $X$ as many times as I want to. How many times ...
720 views

### All-Purpose Sample Entropy

When given samples of a discrete random variable, the entropy of the distribution may be estimated by $- \sum \hat{P_i} \log{\hat{P_i}}$, where $\hat{P_i}$ is the sample estimate of the frequency of ...
447 views

### What are Effective Regression Techniques for Linguistic Analysis of Linked Data?

Cross-post from MathOverflow where it was suggested that I might get better results here. I am in the early stages of a problem that involves parsing a large number ($\approx 5 \times 10^9$) of ...
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### Given a bounded number of die rolls following unif{1,6}, produce unif{1,7}

This is a twist on the traditional problem of transforming between uniform discrete distributions of different sizes. For this example, we can roll the die twice and get one of 36 possibilities. The ...
496 views

### Question about Dynkin Lehmann Scheffe Theorem

I'm self-studying for an examination, and I would like to understand how to use the Dynkin Lehmann Scheffe theorem for an applied question. I am using Bickel and Doksum's "Mathematical Statistics" (...
354 views

### Likelihood test for dividing a distribution into two separate distributions

I've been google-ing around but couldn't find an answer to my question. Any help would be appreciated. The simplest example of my problem is: Imagine I have an bag of marbles of many different colors....
397 views

### How to average quantized and truncated data?

So I have data that has been quantized by an analogue to digital converter. (continuous data has been turned into discrete data and the values range from 0 to the saturation value , which is 127 in ...
480 views

### Appropriate tests on discrete and paired data

I am going back and forth on which tests to do. I have two paired variables, that are both positive integers (0,1,2,3...etc). $n = 559$. The variables represent the error resulting from two different ...
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### What PDF should be fit to a rank histogram? [closed]

A Rank Histogram (or Talagrand Diagram) is a neat way of measuring whether your numerical model is giving appropriate variance. It's used for weather and climate forcasting, where you only have one ...
Given a Gaussian function of the form $$g(x) = ae^{-(x-b)^2/(2c^2)}$$ I am interested in a discrete analogue to this, which deals with the case where $x$ is discrete. As I understand there are two ...