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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How to Choose Poisson Time Interval

A Poisson process is one where mean = var = λ. How do you decide what time interval fulfills these criteria when fitting the Poisson distribution to a process? Can all processes be modeled as Poisson ...
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Example of “alternating” mass function for discrete distribution

My question is related to this question on Math.SE where it was shown that there exist discrete distributions with probability mass functions that "oscillate" in a non-monotonic way over an ...
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What is the effect of number of points on calculation of mutual information between two variables?

I was trying to calculate mutual information between two variables as follows: mutual_info_score(x,y) This essentially creates a 2d histogram and evaluates the ...
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68 views

Hypothesis test for discrete random vector with few samples

Consider a random vector $X \in \mathbb{R}^{d}$ with support $\text{supp}(X) = \{1,2,3,4\}^d$, and let $P_X$ denote its known probability mass function. Note that $\lvert \text{supp}(X) \rvert = 4^d$. ...
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Can we compare the difference of two specific proportion in 3x3 contingency table?

I have a 3x3 contingency table and would like to compare the the specific proportion's relationship. For example,, can we test if the proportion of people give response 1 in age group 1 is higher than ...
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Does it make sense to impose a density curve over the bar plot and analyze the mode?

Suppose that my X variable for my probability bar plot is discrete (i.e. not continuous) and ordinal. If this is the case, does it make sense to impose a density curve (apparently this is possible by ...
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1answer
22 views

Discrete data: Graphs and skewness

I am studying an introductory course in statistic " Essentials of Statistics". The author mentioned that Histograms are used to represent the frequency distribution of a contiuous data. Then ...
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1answer
14 views

Showing that a discrete random variable has the same moments as a Normal Distribution

Suppose I define $X$ to be normally distributed with $\mu = 0, \sigma^2 = 1$, so that $X$ has the pdf $f_{X}(x) = \frac{1}{\sqrt{2 \pi}} e^{-x^2 / 2}, \quad -\infty < x <\infty.$ Let discrete ...
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Can we normalize both continuous and discrete numerical values

I have a sensor dataset with 16 features as numerical values (12 are continuous and 4 are discrete). I am using LSTM model to fit the data and do some classification. As both continuous and discrete ...
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20 views

Brier score: $L_1$ instead of $L_2$ [duplicate]

Assume that we have some count data $x_{1}, \dots, x_{n}$, which take values $\{1, \dots, m\}$ and we have some estimator of the probability mass function, $\hat{\mathbf{p}} = (\hat{p}_{1}, \dots, \...
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does it make sense to draw a histogram for categorical variables?

Does it make sense to draw a histogram where its x-variable is categorical? I know that normally categorical variables are represented with bar charts, but I am just wondering if in practice it is ...
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Deriving comparable probabilites from continuous and discrete data

I'm creating an elections index that's adjusted by how close the results are expected to be for a number of upcoming races in the US. My simulated results include discrete values like seat counts for ...
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How to measure whether a discrete distribution is uniform or not?

Say I have two vectors [1,2,1,2,2] and [1,2,1,1,1]. The number at each dimension is the frequency of one element. How do I measure whether these two vectors are close to the uniform distribution? I ...
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Does a random variable's distribution also carry over to its histogram-estimated probabilities?

If I have a finite sample of a continuous random variable $x$ as a vector containing $N$ observations, then I bucket those observations based on their frequency of appearance into equally-sized bins ...
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Can we apply the Nadaraya–Watson kernel regression estimator when $X$ is discrete?

Suppose $Y_i=g(X_i)+e_i$ with $E(e_i|X_i)=0$, $g(\cdot)$ being an unknown function and $X_i\in S=\{1,2,3,4\}$ with equal probability of taking each value. We want to estimate $g(x)$ using data $\{Y_i,...
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67 views

intuition behind Brier score

Assume that we have some count data $x_{1}, \dots, x_{n}$, which take values $\{1, \dots, m\}$ and we have some estimator of the probability mass function, $\hat{\mathbf{p}} = (\hat{p}_{1}, \dots, \...
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1answer
65 views

Is this an Appropriate Application of a Permutation Test?

Suppose I have count data between three groups, each with a different number of observations: $n_1 = 11, n_2 = 6$ and $n_3 = 5$. My data is listed below: \begin{array} {|r|r|}\hline group 1 & ...
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23 views

Relation between Information and the number of elements in a discretization of a continuous variable

Imagine that we have a random continuous variable X with an uniform probability between 0 and 1. (It might be a user's rating for example). We are not given the exact value but Y, the range where the ...
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1answer
36 views

Is a bounded real-number random variable discrete or continuous?

A discrete random variable is countable (such as integers and natural numbers), whereas a continuous r.v. is not countable (like the real numbers $\mathbb{R}$). If I have a dataset whose observations ...
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19 views

Regression - Transform discrete variables to continuous for prediction purposes

I searched and couldn't really find an answer to this question. I have my response variable which is a discrete ordered variable (bond ratings), and continuous explanatory variables. I would like to ...
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1answer
10 views

Store binnin models in R after fitting a dataset

I'm looking for algorithms to create bins of variables in order to reduce the noise. I have found several libraries for that, one if the chi2 library: https://www.rdocumentation.org/packages/...
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31 views

Discrete choice model with different choice set for each sample

Data I have observational data of $N$ rows (samples). In row $n$ individual $k_n \in \{1, \ldots, K\}$ from a population of $K \ll N$ individuals chooses one option $y^{k_n}_n$ from $J_n$ options, ...
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Error on the mean for discrete histogram

Suppose I have a discrete histogram, in this case the number of votes for each rating (1-5 stars) for a product. I can calculate the sample mean easily enough, and get an average score for this ...
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Predicting discrete repeated measures using a discrete independent variable in SPSS?

I have a discrete repeated measure (# of headaches in the past month) measured at time points 1 and 2, and a discrete independent variable measured at T1 (a score of 0, 0.5, 1, 1.5, 2, 2.5, or 3). ...
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44 views

Simulating from regression model with categorical variable with 4 categories?

Suppose that I want to simulate from a regression model, either linear regression or some other type of general linear model. Let $x$ be a categorical variable with 4 categories. I am interested in ...
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Confirm that an eventual over-representation in a sample is statistical significant

I need opinions on this one, so any thought you can contribute will be highly appreciated. My population is an entire set of customers, my sample is all the customers to whom something specific, which ...
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1answer
39 views

What is the difference between discrete and continuous data?

I have two datasets: one consists of expected values and the second includes observed values. I want to test the difference between these two datasets. This is dataset A ...
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1answer
36 views

How to plot the relationship of two Likert scale variables?

I have two variables which are measured on a Likert scale. I ran the Spearman correlation test to test the relationship between them and they have a negative correlation coefficient (-0.729 with a p-...
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37 views

For a simple linear regression, do we have requirements for using continuous/discrete variables on dependent and independent variables?

I am fairly new to statistics and would love to make my basics clear. I am confused about what data type should a simple/multiple regression model has? Can you please answer my question with an ...
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37 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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1answer
24 views

Comparing two discrete paired datasets

The problem: I am studying the estimated number of cases of malaria in regions of the world and found that both the WHO and IHME have their own estimates. I want to find if the difference between the ...
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1answer
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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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70 views

How to calculate the cumulative probability for discrete random variable

I am trying to calculate the cumulative probability for this given question: Q: A tree farming company is testing how many items customers purchase during their visits. Based on many results, the ...
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1answer
35 views

How to test that a subset of data is distributed no differently than original (discrete, not normal)

In the research I am doing we have initially had ~600 samples which had a certain distribution (not normal, although close). The characteristic of these samples that I am interested in is discrete (...
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1answer
32 views

Find a single-sampling plan for which $p_1=0.02$, $\alpha=0.01$,$p_2=0.06$ and $\beta=0.10$

I am not sure where to start. My previous lecture gave very limited information on what to do here, so my current toolbox only consists of these formulas: $$1-\alpha=\sum_{d=0}^{c} {n \choose d}p_1^d(...
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132 views

The Mean of a Discrete Random Variable

I understand how one gets the mean of a random discrete random variable, but not necessarily how the process makes logical sense. For instance, how does the multiplication of x by P(X = x) give the ...
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1answer
34 views

Can continuous series be converted to discrete series

Is there any method to change the given continuous series to discrete series.There is a problem I have tried every method possible but I could not solve.The problem is in the image please check out ...
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12 views

Calculate joint probability of two discrete events based on probability distribution of the discrete events

I run an experiment with $n$ participants and I am interested about the probability that a participant would be better in a real-effort task than another participant. For simplicity, assume that ...
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1answer
75 views

Quantifying the similarity or overlap between two discrete probability histograms

I am trying to learn if there's a way to quantify how close two discrete histograms that represent probability distributions (normalized) are. To give an example, I generate two lists of integers in ...
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How to model a spatially correlated multi-variate random field of discrete variables?

Please consider you have 100 spatially distribute locations (points) that are separated 1km with each other in 2D space. Also we have three building type A, B, C that can be located in each spatial ...
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How to use discrete choice models on market share for products?

I have a dataset on market share of products by time-period. Total observations is 26622. Total unique time period is 41. Unique products are around 638. There are time column, product column, price ...
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1answer
39 views

Can I get the probability of a value being 0.5 larger or smaller?

So I have some clothing data, with some body measurements and the sizing. The sizing is a discrete variable ranging from 7 to 14 with steps of 0.5. I know that a specific consumer with specific ...
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Help Correlating Particle Count (Dirtiness) to Chip Pass/Fail

I have two datasets that I’d like to correlate in a way that is helpful and predictive. In our process, we a have a single work piece that should be perfectly clean that will eventually become many ...
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56 views

Can we fit discrete data to a continuous distribution?

why some studies fit the discrete data to a continuous distribution? For example, the rainfall data used in the study are discrete but Gamma and GEV distributions are used to fit the data (https://...
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289 views

Rainfall duration is continuous or discrete?

Let's say I have 38 years of hourly rainfall data. The volume is hourly recorded like this ...
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How to Input to Neural Network Based on Discretely Observed Processes

I'm attempting to estimate the posterior mean for a set of parameters governing a Markov process, using a neural network to minimize squared error (and uninformative priors, along the lines of http://...
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How to approximate expectation and variance of an integral from a discrete Time series financial dataset?

I have discrete time series financial data, with time($u$), price($S$) and someVariable($q$) which looks something like this. ...
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1answer
42 views

Changing only one point of a discrete distribution to maximize variance augmentation

X has a discrete distribution with support $x1, x2, ...$ in $ {]}0,1{[}$. You have the right to change only one of the $xi$ to lead to the highest increase in variance (or, at least, a systematic ...
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2answers
102 views

discrete random effect in mixed linear model?

I need to know how I can define a mixed linear model with a discrete random effect ? I really googled trough the whole internet and can‘t find any solutions. In the general formulation its necessary ...
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72 views

How to calculate the standard error of a proportion estimate under misclassification?

Let's take a sample of size n from an infinite population. The population comes in three kinds ('red', 'black' and 'blue') and we want to know the proportions of each kind. For 'red' we would have $p =...

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