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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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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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342 views

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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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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180 views

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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49 views

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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419 views

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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108 views

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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366 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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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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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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399 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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49 views

Combining beliefs in probabilistic models

I have multiple Bayesian network models, each producing some estimate or inference about a variable $PW_2$, which is given by $P_1(W_2|W_1)$ in one model and $P_2(W_2|W3)$ in the other, but I want ...
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133 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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143 views

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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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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73 views

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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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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128 views

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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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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150 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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174 views

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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510 views

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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95 views

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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1k views

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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321 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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428 views

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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431 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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345 views

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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How to determine if a dichotomous variable is randomly distributed or is predicted by other instances

I have a product with a measurement of X features. Each feature can either be a PASS or a FAIL. Which statistical test can I use to tell if the failures are randomly distributed across all features? ...
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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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AIC and BIC and number of quantization level

I want to test how many quantization levels (discretizing levels) are the best for the given data(time series) set I have. Therefore I am applying different levels of binning (like discretisize data ...
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39 views

Experimental design for discrete choice response

I'm designing a survey where people need to choose one of three transportation alternatives. Here are the alternatives, their specific factors/attributes and the levels I intend to use for each: <...
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24 views

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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24 views

Non-target attribute is imbalanced, is it class imbalance or is there another term?

I have come across the term class imbalance in classification problems. From what I understand, it means the target variable is split into two (or more) categories where on category is significantly ...
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179 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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107 views

Extract features from discrete time series data

I am working with time series data of discrete (i.e. nominal) values instead of numeric values. In other words, my time series is a sequence of "class values" like: "A", "A", "A", "B", "B", "A", "C" ...
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342 views

Fitting higher order Markov chains in R

For $n$ individuals I observe their states at fixed times. So I have $n$ observations of a data generating Markov chain. Using the markovchain-package I then can fit a time-homogeneous Markov chain ...
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References on calculating posterior mode in multiclass discrete Ising model

I'd like to calculate the posterior mode (maximum a posteriori estimate) for $\Pr[\,X \,|\, Y\,]$ for a model where $X$ is generated by an Ising model on a two-dimensional lattice and $Y$ are noisy ...
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392 views

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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33 views

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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125 views

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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523 views

p-value distribution under null hypothesis and discrete data?

Wikipedia says that p-values are uniformly distributed over [0,1] if the null hypothesis is true and for continuous data. What is the expected p-value distribution if the test statistic is discrete? ...
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Approximating a discrete variable with a continuous distribution - when is it appropriate?

When is it appropriate/viable to model a discrete variable with a continuous distribution? For example, say you have a class of 40 students who took two maths tests of equal difficulty on the same ...
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179 views

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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114 views

Determining number of states for Discrete Hidden Markov Model used as Classifier

I want to train a discrete HMM on two different datasets containing user clickstream data, to classify new user sequences. The datasets contain 41 different observations (41 different API calls), and ...
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43 views

Constructing estimators for a distribution

I'm using the following probability mass function: $$P[X=k] = \frac{2}{\cosh(a)+\cos(a)}\cdot\frac{a^{4k}}{(4k)!}\, \text{ for } k∈N∪{0}$$ I have derived the following: Mean = $a^4/4$; variance = $...