# Tagged Questions

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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### Error introduced by rounding values from a continuous distribution

I am implementing a sampling routine to sample from a discrete normal distribution. I use a standard technique for sampling from continuous normal distribution and then round my values. If I am ...
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### Given no knowledge of var, include both continuous and dummy

Imagine we have a variable with 5-7 unique values in a machine learning setting. One could argue that given no knowledge, we might convert it into 5 dummy variables, or one might consider it ...
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### Statistics test for paired data with discrete outcomes

I have pre-post data for several variables and I'm looking to analyze them. The responses to the questions are 0,1,2,3,4 with 4 being best and 0 being worst. For each variable could I simply find the ...
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### Efficient computation of the distribution of a weighted sum of finite discrete random variables

I have $N$ discrete random variables $X_i$, with distributions $p_i(X_i)$. $X_i$ can take integer values in a finite range $[a_i,b_i]$, where $a_i,b_i$ are integers. The distribution $p_i(X_i)$ is ...
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Let $f_{c}:Z_2^n \rightarrow \{-1,1\}$ be the character defined as $f_c(x) = (-1)^{<x,c>}$, where $c,x \in Z_2^n$. It is easy to see that since $f_{c_1}\cdot\ldots\cdot f_{c_k} = f_{c_1 \oplus ... 1answer 30 views ### Test for significance with multivariate, highly-skewed, discrete data The data The dataset comprises 10 variables: waiting times (rounded to minutes) for questions to be answered on Stack Overflow by programming language. Each is discrete, none is normally distributed ... 1answer 75 views ### Plotting PMFs and PDFs This is probably a silly question, but I was reading Computational Statistics with Python and there are a few plots describing prior, likelihood and posterior distribution in the context of ... 1answer 12 views ### How to combine a continuous effect into a function that is for discrete outcome I have a function like this: log (P(1)/P(0))= a+ sum(h(x))+ g(x), where a is the intercept, h(x) is a binary outcome: 1, or 0. g(x) is a continuous variable that contribute to the log of a ... 1answer 270 views ### Continuous probability distribution over integers? I have a random variable which can have any value from the set of natural numbers. For example, the probability of the random variable having a low value is higher than the probability of the random ... 1answer 32 views ### Transformation of variables in Poisson distribution If$X$is a random variable which follows$\text{Poisson}(u)$distribution then what is the variance of$X^2$? 0answers 10 views ### Two-dimensional discrete aleatory variable prediction I hope someone can help me a bit facing this problem. I have many item samples from a database (let's say 1000 for example) with two attributes: a price from a range of possible prices (0 to 8000€ for ... 2answers 50 views ### Notation for possible values of a random variable Let$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 ... 1answer 43 views ### Is a random variable taking every rational number or a range of rational numbers discrete or continuous? My guess would be discrete because such a variable would only take a countable set of values and "continuous" seems to imply the continuum of the real numbers. 0answers 86 views ### How do you derive AIC and BIC for discrete-valued observables? Let's say I have an experiment which yields discrete results between 1 and$N$. I am modelling the results using a number of statistical models and want to use Akaike (corrected) or Bayesian ... 0answers 13 views ### Interpreting elasticity of dummy variable This is a follow-up of my previous question. I post it as a new one since it has a different focus and may be interesting for other folks. I've read that elasticities of dummy variables are not ... 1answer 39 views ### Question about discrete, numerical data True or false: In a survey of your neighbors (asking for family size, the kind of pets they have, the grade of the youngest child in the family, the family's annual income in dollars, what the dad ... 0answers 22 views ### 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, ... 1answer 28 views ### When would one pre-specify thresholds in SEM/CFA for limited dependent variables? I'm working on a structural equation model with limited dependent (discrete) variables using lavaan (0.5-17) in R (3.1.2). I have found that if I define the thresholds for the categorical variables, ... 0answers 7 views ### How can I make a correlation in SPSS about variable 1: discrete data (amount of people), and variable 2: nominal data (white, black, hispanic)? [duplicate] I have 3 variables: var1: sex; var2: amount of people; var3: race (white, black, latino, etc). My population data is already coded. How can I establish a correlation between sex and race; or amount ... 0answers 12 views ### Spearman correlation for discrete tied data in relation to continuous variable? I want to correlate tied discrete data- reward reimbursement having only 4 reward values with continuous variable- RT performance. Can I use the Spearman rank correlation or Kendall´s tau? Thanks. 1answer 34 views ### Estimate range of values of continuous variable corresponding to every level of discrete variable This might seem a silly question, but I have Googled in vain for hours to find an answer, so here goes: I have two variables measuring the same physical parameter. Let's call these variables A and B. ... 0answers 43 views ### Regression Discontinuity on Stata with a discrete assignment variable and excluded data at the cutoff I am looking at a treatment effect of an intervention on a cutoff of age, where age data is only available discrete as year of birth. Due to this, people who turned the cutoff age during the study ... 0answers 13 views ### Distribution of Augmented Random Variable Consider the case where$\mathbf{X} = (X_1,...,X_m)$has discrete-valued elements and distribution function$F(x) = C(F_1(x_1), ..., F_m(x_m))$. Let$F_j(x^{-}_j)$be the left handed limit of$F_j$... 4answers 349 views ### Does an urn's probability distribution change as you draw from it without replacement on average? Suppose I have an urn containing N different colours of balls and each different colour can appear a different number of times (if there are 10 red balls there need not also be 10 blue balls). If we ... 2answers 56 views ### Translating and scaling a uniform discrete distribution? Is it possible to map a uniform, discrete distribution over two integers$A$,$B$(lower and upper bounds respectively) onto$[A^*, B^*]$while keeping the distribution discrete uniform? We may assume ... 0answers 29 views ### Multivariate discretization method / library for huge data Does anyone know any multivariate discretization method that can be used for large amounts of data. A library / Python library would be awesome but algorithms would also do. Also I'm not sure if ... 0answers 15 views ### Goodness of fit test for binned multi-sample data Let's say I have two samples and 5 bins. In each bin, I have a (positive) value and a measurement error on that value for each of the two samples. The value and corresponding measurement error ... 0answers 16 views ### Comparing Peptide Amino Acid Composition: 2 Independent groups, Non-normal data, discrete data I have two large groups of peptides, "positive" group (n = 368) and "negative" group (n = 880). The average length of the peptides (in each group) is about 20 amino acids. What I am trying to do is ... 0answers 13 views ### Question on Texture similarity measures I was wondering whether there is a similarity measure between a discrete image or texture image and a continuous image? I have two images one is discrete (it can be a texture also) and the other is ... 0answers 95 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) ... 1answer 129 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 ... 2answers 66 views ### Conditions to be a Joint Discrete Distribution Function I am reading a paper on modeling the dependencies in discrete distribution functions, and am having a hard time understanding the following. Let us define: $$r \leq min(p,q)$$ $$B(u,v) = ... 1answer 169 views ### How to normalize mixed continuous/discrete features for DNN? I have had some success training my deep neural network (with ReLU hidden units) by first normalizing the features of my data set to zero-mean-unit-variance. Each sample of my data set has 600+ ... 0answers 6 views ### generating discrete distribution comparison score I have constructed a distribution of some data that I am analyzing, so it is discrete, and I would like to be able to compare it to other distributions in order to generate a score or rank so that I ... 0answers 22 views ### Set probability of Discrete Random variable I want to simulate outcomes of 3 discrete events. For example lets say I have a spinner and there are 3 outcomes. The outcomes of the spinner are 3 numbers: 1, 2 and 3. The probability of getting ... 2answers 142 views ### Model for comparison of two subsets of the same data I am looking to perform an analysis on a subset of the data and compare it to a larger subset. My data is primarily categorical and the dependent variable is binary. I want to compare y^*= \beta ... 0answers 15 views ### Analysis of weighted discrete distance data I would appreciate some assistance with the following simplified version of my experiment: Imagine a row of boxes, e.g. each box is 0.5 by 0.5 m, lined up in a column of 20 boxes. At the short end of ... 1answer 39 views ### Sample discrete multivariate normal What is an efficient way of sampling from a discrete multivariate normal distribution with pdf$$ p(z) = \frac{1}{Z} e ^ {-\frac{1}{2}(z-\mu)^\top\Sigma^{-1}(z-\mu)} $$such that z \in ... 0answers 45 views ### Dvoretzky–Kiefer–Wolfowitz inequality hold for discrete distributions? I am wondering whether Dvoretzky–Kiefer–Wolfowitz inequality holds for discrete distributions? Any comments or references would be greatly appreciated. 2answers 775 views ### Does this discrete distribution have a name? Does this discrete distribution have a name? For i \in 1...N f(i) = \frac{1}{N} \sum_{j = i}^N \frac{1}{j} I came across this distribution from the following: I have a list of N items ranked ... 0answers 34 views ### How to Compute the Integral of the Auto-correlation Function for a Discrete Time Series Using the covariance$$ c(u) = \frac{1}{N}\sum^{N-u}_{t=1}(x_t - \bar{x})(x_{t+u}-\bar{x}), $$I've computed the auto-correlation function$$ r(u) = \frac{c(u)}{c(0)},$$where$x$is a time ... 0answers 145 views ### How to fit discrete data that have mode 0 to a log-normal distribution? I am trying to figure out how to fit a log-normal distribution to discrete data that have mode 0, in particular, without first removing the zeros. For example, paper citation data are said to be ... 1answer 60 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 ... 1answer 54 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 ... 1answer 749 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. ... 0answers 26 views ### Rejecting subjects based on retest analysis Are there objective criteria for rejecting subjects based on a test-retest analysis? Perceptual data on a discrete scale [1,...,9] for a number of users over groups of audio excerpts was collected. ... 1answer 575 views ### How to to find and evaluate optimal discretization for continuous variable with$\chi^2\$ criterion?

I have a data set with continuous variable and a binary target variable (0 and 1). I need to discretize the continuous variables (for logistic regression) with respect to the target variable and ...
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### Is there ever any reason to discretise continuous ground truth if doing classification?

Is there a case where discretising continuous response improves classification performance? For example: A response variable is in the range 0 to 99. There are 10 classes defined by the following ...