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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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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Goodness-of-fit for Discrete Distributions

I've been doing some data analysis with Scipy. So far I accomplished this with continuous distributions: I can fit a probability distribution to a set of data points using a maximum likelihood fit. ...
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How to define and model consumption bundles?

Imagine an a la carte buffet with n different rooms. On entering the buffet you pick a room (let's say American, Mexican or Italian food) where you stay for the duration of your visit. Once in a room,...
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Books for mixed distributions (continuous and discrete)?

What is a good book that covers mixed distributions? Most statistics books either only briefly mention them or do not cover the topic at all. I'd like to have a comprehensive resource covering ...
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Causal inference, stratification to mitigate confounders in continuous variables?

Handling confounders in continuous variables In Statistical Rethinking, the author shows that in different situations, a confounder (fork, pipe, collider, descendent) will induce spurious correlations....
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Is there a name for the probability distribution arising from the Hockey-stick Identity?

The Hockey-stick Identity: ${n \choose k} = \sum_{r=k}^n {r-1 \choose k-1}$ This naturally gives rise to a discrete probability distribution with parameters n and k, where the probability mass ...
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Representation of Noise in Fourier transform

I perform an experiment where I sample $M(k)$ which is in theory related to $|f(x)|^2$ via $M(k)=\int e^{ikx}|f(x)|^2\,dx$. I perform the discrete FT on my data in order to obtain $|f(x)|^2$. Without ...
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Sampling discrete distributions given their entropy

Can we (uniformly) generate a discrete random variable over $n$ possible outcomes given its entropy? I am interested in non-parametric methods, that do not require the random variable to follow a ...
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How can I test whether an empirical discrete distribution is symmetric?

For example, I have a distribution with mean = 55.46; med = 54.5; mode = 45. The Shapiro-Wilk is non significant, the data are unimodal, and there is no significant skew or kurtosis. At a glance, the ...
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Estimating a probability distribution with a discrete and continuous part

This is a question more for advice and a suggested starting point than anything else (though anything else is cool as well ) The data that I have is something like this - 1,000,000 data points of ...
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Application of likelihood ratio test to test the Markov property

Do you know a reference (freely available on the web) where the likelihood ratio test is applied in order to test for the Markov property? The setting is a directly observable discrete Markov-chain ...
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How to model the distribution of a word game in order to find correlation between demographics and chosen words

I have an experiment (in the form of a word game) whereby people are asked to choose a set of words to describe associations with a topic with the aim of having another person guess the topic. I ...
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Stopping rule for chi-squared discretization algorithm

I developed an algorithm that uses the chi-squared test to perform supervised discretization of a continuous variable. I described it in the paper "ChiD-A Chi-Squared Discretization Algorithm" ...
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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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How can I fit a normal (von Mises) distribution to discrete angular data?

This bears some explaining: I have a set of data from a psychophysics experiment where participants selected a response from a discrete set of 8 possible responses. These responses were actually ...
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Dealing with Discrete numeric variables in logistic regression model

i have one relevant variable in my model like number of additional services taken by customer with visual inspection it is clear more the number of additional services customer opts in lesser the ...
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Unified Variable Classification

I am trying to go beyond Stevens' Level of Measurement Typology. Here is what I have so far: Discrete Variables Nominal (like Apple, Banana) Ordinal (like 1, 2, 3) Count (like 0, 1, 2) Incremental (...
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Discrete Choice Models

For multinomial (or mixed) logit models, when the choice set is too large, either strategic sampling or random sampling of the choice set can be used. My question is: Is that also true for panel data ...
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Conjoint analysis or discrete choice analysis ? And which software?

Suppose I would like to model the light-bulb preference of respondents. I would like to ask their preferences between existing bulbs on the market. And when you choose a bulb in a shop you usually see ...
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3-4-5 Rule How to partition the sets?

In Data Mining course, we are taking 3-4-5 Rule to segments the data uniformly. I'm trying to understand these lines below, and how they are linked to the graph below too. If an interval covers 3, 6, ...
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455 views

Detrending Discrete Data

I am trying to detrend some discrete data and I am having difficulty finding a model to describe the trend. There is a number of discrete data points and there is a linear error being introduced with ...
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Discrete time survival analysis with varying length event windows

I have data that appears very well-suited to discrete-time survival analysis, in that each subject has a consecutive sequence of observations from its entry into the system until its exit, and I'm ...
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646 views

Calculating $R^2$ when one variable can only take integer values

I am a programmer, not a statistician, so pardon my botched use of the terms. My basic problem is this: I am wanting to calculate $R^2$ between a known concentration (which can be any non-negative ...
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272 views

Quantifying differences in a discrete distribution across several populations

Suppose you have a discrete random variable, $Y$, with a large number (say, $300$) of discrete (which happen to be nominal) possible outcomes. The mass function, $p(y)=P(Y=y)$, is unknown but a sample ...
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Is it valid to model discrete numerical test scores as coming from a continuous random variable?

I'm working with a sample of test scores which range from 0 to 100. These scores are generated from a set of 100 binary responses (0 or 1), so the higher the resulting sum, the better the performance. ...
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493 views

Averaged continuous Kernel Density Estimates in lieu of a discrete Kernel Density Estimate in Monte Carlo Proceedure

I am thinking of using this code in a Monte Carlo routine to generate Kernel Density Estimates for subsequent use in a Naive Bayes Classifier (see this earlier post). The author of the code states ...
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107 views

Mixed logit with only one choice situation/observation per individual - valid to use?

I have data from an experiment where participants had to choose one of 12 alternatives. I analyzed the data with a conditional logit model. That is I used the attributes of the choices to explain ...
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2 votes
1 answer
99 views

How can I compare the predictive power or association of two variables of different nature?

I am dealing with the following problem: We have 3 variables: A continuous variable (0 to 1), that is a scoring for people. A discrete variable, offered by a partner, in the range 1..10. That is also ...
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1 answer
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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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2 votes
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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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Modelling resampling as conditioning on sum for independent discrete variables

I am trying to model a discrete data generating process where I first draw $Y = (y_1, ..., y_N), y_n \sim F(\theta_n)$ independently from some family of discrete distributions $F$ (e.g. negative ...
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636 views

What method should I use to forecast discrete data?

I have data which can take discrete values (between 0 and 5). I have 2 values per day during 2 years which contain a lot of 0 and 5. I know that my data are correlated with end of week, end of month, ...
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Variance of n discrete time series

I'm currently having problems understanding how to calculate the variance between n given time series, each containing data of exactly one day. So basically, I'm given one array containing double ...
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How to fit parameters of a stochastic model applied to agent modeling?

I have a network of agents, these are modeled roughly according to the paradigm of "Agent_Zero: Toward Neurocognitive Foundations for Generative Social Science". The main feature is that the equations ...
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2 votes
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Discrete Choice Modeling from Aggregate Data

I am working on a problem where customers make choices. A traditional setting for problem for example would be: Model the Travel by air, bus, car. Each choice is made based on several variables ...
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235 views

Numerical optimization of discrete lognormal likelihood

Problem Template I am trying to numerically optimize a log likelihood function of the form: $$\displaystyle \mathcal{L}(\vec{x}) = -n\log\left(1-\mbox{erf}\left[ A(m-1) \right] \right) + \sum_{i=1}...
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2 votes
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234 views

Entropy for a discrete multivariate variable?

Suppose I have a multivariate discrete random variable $Y=(Y_1,\dots , Y_n)$, where $Y_{i}$'s are independent and not identically distributed Binomial variables. How can one calculate the entropy of $...
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2 votes
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362 views

glm link functions for multinomial and ordered probit regression?

Here's what I understand, could someone please tell me if I'm wrong, and how? For a categorical variable $Y$, the expected value $\text{E}(Y)=\mu=\sum_{y}i\cdot\text{P}(Y=i)$. Using the descriptions ...
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2 votes
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Finding an MLE fit when a model predicts two kinds of data, each with a different distribution / data model

My problem is as follows: I am fitting some multi-parameter models which predict two different kinds of data. I can find a best (MLE) fit to the first kind of data. I'm currently expressing both the ...
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Picking tuples from a list with low discrepancy

Given a list of m items, I am looking for a way to repeatedly pick a tuple of n distinct items from this list with low discrepancy. For example, suppose I have a list of 3d points, and I want to ...
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Bias of sample correlation for discrete distributions

Is there a proof showing the bias (or lack thereof) of the sample Pearson's correlation for discrete interval variables? In particular, I am interested in how such a proof handles the expected value ...
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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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Problem on Clustering Discrete Input using GMM

I want to do clustering using Gaussian Mixture modeling (GMM) on a set of data which is a 5-dimension vector of real values $(x_1,x_2,x_3,x_4,x_5)$. However the clustering result were pretty bad, ...
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2 votes
0 answers
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How to compare a one-day count against a historic mean to identify an external change

A few months ago a client's website had some good press and their daily site visits spiked. Now, every time their traffic shows a bump, they think something external has caused it to happen. I'm ...
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2 votes
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192 views

expectation of multivariate discrete distribution

The expectation of a function $f(x)$ over a probability distribution $p(x)$ where $x=(x_1,\dots,x_n)$ and $x_i \in \left\{1,\dots,K\right\}$ requires a summation over all possible $K^n$ combinations. ...
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deterministic sampling for multivariate discrete distributions

Unscented transform can approximate expectations well via deterministic sampling. if $f(x) = N(\mu,\Sigma)$ and $x\in \mathbb{R}^d$ then $\int f(x) h(x) \approx \frac{1}{2d}\sum_{i=1}^{2d} h(x_k)$ ...
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A good alternative to data binning?

I read many times that data binning of continuous variables is a very bad idea. For instance, let's take something like heart rate and let's define the following 2 bins: (125 - 135), (136 - 145) ...
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Testing equality of two or more contingency tables

Which options are there to test, whether two contingency tables of the same variables, say $X$ and $Y$, are equal across the levels of a third discrete variable, say $Z$? I can think of a log-linear ...
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Predicting Naive Bayes model in R on a test data with a single record

I built a naivebayes model using the Housevotes84 data(discrete data) in mlbench package- model <- naiveBayes(Class~., data=HouseVotes84) I took one record ...
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2 votes
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339 views

Assumption tests in discrete-time hazard model

I am currently working with a random coefficient discrete time hazard model. The following assumptions are subject to this sort of model: linear additivity assumption proportionality assumption no ...
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