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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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1answer
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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 ...
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10answers
897k views

What is the difference between discrete data and continuous data?

What is the difference between discrete data and continuous data?
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3answers
18k 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 ...
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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 ...
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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) ...
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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 ...
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4answers
51k 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 ...
20
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1answer
10k 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) ...
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2answers
380 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). ...
5
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1answer
700 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 ...
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5answers
38k 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 ...
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2answers
9k 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:...
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2answers
6k 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 ...
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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 ...
7
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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 ...
7
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1answer
474 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 ...
3
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1answer
151 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., ...
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0answers
230 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. ...
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2answers
626 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 ...
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1answer
72 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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2answers
416 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 ...
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1answer
310 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 ...
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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 ...
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3answers
9k views

Probability formula for a multivariate-bernoulli distribution

I need a formula for the probability of an event in a n-variate Bernoulli distribution $X\in\{0,1\}^n$ with given $P(X_i=1)=p_i$ probabilities for a single element and for pairs of elements $P(X_i=1 \...
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4answers
33k 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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3answers
3k views

Implementing a discrete analogue to Gaussian function [closed]

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 ...
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1answer
2k views

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 ...
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2answers
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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1answer
3k views

How best to normalize count data to compare two distributions

Say I have a vector of length 1000. At each position (1 ... 1000) there is a count. I have two vectors with different range of counts such that in vector A the maximum number of counts at a position ...
4
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1answer
1k views

Discrete Time Survival Analysis - Correct Way to Write Survival Function

I have seen several ways to write (and calculate and interpret) a survivor function in discrete time survival analysis and I wonder which is correct or if they both are, but the interpretation and/or ...
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1answer
170 views

how to analyze overdispersed binary data

In my substantive research, I often use dichotomous scoring (1 correct, 0 wrong) for my tests (tests with $15~yes/no$ items). My goal is often to compare the the proportion of correct answers to all ...
17
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1answer
3k 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 ...
6
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1answer
444 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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1answer
4k views

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 ...
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0answers
1k views

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 ...
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2answers
490 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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2answers
1k views

How to decide on the MLE when pmf is 0?

Suppose you have $\theta=\{1,2\}$ and the sample of (0,1,2) with the task of finding MLE: \begin{array} {|c|c|c|} \hline x & p(x|\theta=1) & p(x|\theta=2) \\ \hline 0 & 1/2 & 1/4 \\ \...
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1answer
809 views

Analysis of discrete (count) time-series data

I have a 2X2 factorial experiment where I am interested in seeing the effect of two different nutrient solutions (N and W) on the appearance of root tips of two different plant species (A and B). I ...
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2answers
521 views

Generate random number from a specific probability mass in R

How can I generate sample from a distribution with probability mass $P(X=x)$ in R? I know that probability mass, but it is not from a known distribution, also it is not linear, instead it has a ...
2
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1answer
302 views

Equivalent to K-S test on discrete data with uneven quantization

I have some data resulting from a simulation that consists of several groups, each containing a single real datapoint and a variable number of matched controls. I take the rank of each real value ...
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3answers
121 views

Assessing predictive validity of choice models

I am trying to assess predictive validity of a discrete choice model. When with a testing set consisting of 6 choices in each set, it has the hit ratio of 33% (i.e., 33% of the time it correctly ...
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0answers
3k views

How to model categorical (discrete-valued) time series?

Just want to make a little survey, What are, according to you, the best approach to model categorical time series? I'm building a model able to generate time series reproduicing the characteristics ...
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1answer
344 views

Exploring the relationships between discrete and categorical data

When you want to test the relationship (correlation) between two continuous variables, the main methods are easily learnt and very well documented. Scatterplots with regression lines, pearsons ...
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1answer
111 views

Combining Forecasts for Discrete Outcomes

Suppose you have $n$ forecasts for an event which can have discrete outcomes, for example $X$, $Y$ and $Z$. Let forecast $i$ give the probabilty of each event occuring as $x_i$, $y_i$ and $z_i$ ($x_i+...
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2answers
136 views

Classifying integer sequences by their first difference

I don't know exactly how to describe what I'm looking for, but I will try to make some examples. Let's take three different data series: Series A: 1,2,3,4,5,6,7,8,9,10,9,8,7,6,5,4,3,2,1 Series B: 1,2,...
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1answer
694 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 ...
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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 ...
4
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1answer
56 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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3answers
1k views

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, ...
3
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1answer
319 views

Alternative to Wilcoxon signed-rank test, for data where many pairs are equal

I have several discrete datasets with a small range (-2 to +2) which I want to test against the null hypothesis "the distribution is centred around zero". The Wilcoxon signed-rank test was suggested ...