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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22 views

Can you create continuous data from discrete data?

I am trying to understand the difference between discrete data and continuous data in a real world application. My example is this: Once a day I do pushups until my body is tired. I am counting how ...
3 votes
1 answer
334 views

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 ...
3 votes
1 answer
58 views

Poisson distribution with a constant term

I have a set of data constituted by two columns: $Y$ with non-negative discrete values, depending on a time $t$. I make the hypothesis that $Y$ is a Poisson distribution, with: $$\operatorname {E} (Y\...
1 vote
0 answers
24 views

Normalize discrete data on a scale from 0 to 10

I know this subject must have been treated already but I can't figure out how to deal with my problem on an example different from my situation : I measured pain on different location with a Likert ...
0 votes
0 answers
13 views

How to estimate the conditional density p(y|x) from the mixed data if y and x contain both continuous and discrete variables?

There may not be a a conditional density with respect to k-dimensional Lebesgue measure. But I assume that there is a conditional density with respect to a restriction of Lebesgue measure to the ...
1 vote
1 answer
28 views

How to estimate the conditional probability p(y|x) if y and x are both continuous but y is discrete given x?

For example, $P(Y=f_1(x)|X=x)=g_1(x)$, $P(Y=f_2(x)|X=x)=1-g_1(x)$. (The functions f1,f2 are unknown and need to be learned.) How can I estimate such a conditional probability? I guess that kernel ...
0 votes
0 answers
14 views

How can I code, process, and quantify the features of a hierarchical network in a scheme that admits siblingship but also auntship links?

I am new to network analysis and I am currently facing a challenge with coding, processing, and quantifying networks in a hierarchical scheme. In this scheme, nodes pertain to differing hierarchical ...
3 votes
1 answer
527 views

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 ...
6 votes
2 answers
238 views

Paired, discrete hypothesis testing

I am facing the following situation. I asked my class of 19 students to rate their interest about a certain topic on a 1-5 (discrete) scale. I then spent some time teaching them about this topic for a ...
4 votes
1 answer
27 views

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....
7 votes
5 answers
105k views

What are the variance and standard deviation for the bin counts for n rolls on 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 in 6 bins (1, 2, 3, 4, 5, 6) ...
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Need help figuring out what statistical test to use (ANOVA or MANOVA)

I am trying to figure out what statistical test I need for my eye tracking study. I have 2 dependent variables: Dependent Variable 1 is continous (gaze behaviour, which is subdivided into fixation ...
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Discrete choice models: truncated or censored model

I am reviewing some practice. Suppose we have a random sample of households reporting their share of financial wealth invested in stocks (alpha). The minimum alpha in the sample is 0.15, and the ...
2 votes
3 answers
71 views

Two-sample Kolmogorov-Smirnov discrete distributions

Let's say that two Census takers interview a number of couples and ask for the number of children they have. I want to compare the two resulting samples to find out if they could have come from the ...
3 votes
3 answers
344 views

Discrete data: Graphs and skewness

I am studying an introductory course in statistics, Essentials of Statistics. The author mentioned that histograms are used to represent the frequency distribution of a continuous data. Then directly, ...
8 votes
2 answers
383 views

Regression model for integer response

Let the response be $Y_i \in \mathbb{Z}$ and the covariate $X_i \in \mathbb{R}^p$. For counting data where $Y_i$ are restricted to be nonnegative, we have Poisson regression or negative binomial ...
8 votes
2 answers
371 views

Sum of sample given a priori knowledge of its maximum

Given a sample of discrete random variables $X_1, X_2, \ldots, X_n \sim F$, I am looking to calculate the distribution given by the probability mass function: $$P\left(\sum_{i=1}^n X_i = x~\middle|~\...
0 votes
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Replicating a study with a discrete dependent variable in linear mixed effects model (1-4 scores) [duplicate]

As the title says, I want to replicate a study that runs linear mixed effects models with a dependent variable that is discrete, with scores from 1 to 4. So, I have two main questions about that. 1 ) ...
1 vote
1 answer
47 views

Fitting discrete data to continuous distributions

I'm creating a simulation model, in which some stochastic factors are included. On of my stochastic factors is the amount of containers arriving daily for a specific delivery location. A plot of this ...
2 votes
1 answer
123 views

Salary of a group of people is continuous or discrete

I have salary data of 3000 employees ranging from 3000 - 10000 dollars. Based on my understanding:(https://mathbitsnotebook.com/Algebra1/FunctionGraphs/FNGContinuousDiscrete.html) Continuous data is ...
0 votes
2 answers
354 views

How do I make discrete predictions for discrete data that appears to have a normal distribution?

I have discrete data that comes from the distribution of a discrete random variable Y. The data appears to follow the normal distribution (ie if I make a kde plot it looks like a normal distribution). ...
7 votes
1 answer
2k 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 ...
5 votes
2 answers
369 views

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 ...
0 votes
1 answer
284 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 ...
1 vote
1 answer
38 views

Construction of statistics of a discrete distribution

I have the following problem: we consider an i.i.d sample $\mathbf{X} = (X_1,...,X_n)$ of the discrete set $\{1,...,N\}$. An agent has to infer the probability distribution of $X_i$. I wanted to use ...
0 votes
1 answer
240 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 (...
2 votes
1 answer
333 views

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 ...
1 vote
1 answer
40 views

Two Samples Test for Discrete Variable and Different Size Groups?

Hello there and apologies for my English and lack of statistic skills! Two different groups of participants, one comprised of children and the other of adults, run once, at different times, the same ...
1 vote
1 answer
202 views

Combine Multiple Discrete Probability Density Functions

I'm a bit stuck trying to figure out the combined probability from several discrete PDF's. Lets say I have a bunch of different classes (Truck, Sports Car, Station Wagon, etc) and a bunch of ...
1 vote
1 answer
777 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 ...
9 votes
1 answer
222 views

Marginalizing out discrete response variables in Stan

There's been quite a bit of discussion and confusion about how to marginalize out discrete response variables in Stan (e.g. binary or ordinal data). See, for instance: Impute binary outcome variable ...
0 votes
0 answers
112 views

Alternative to SimPy for continuous event simulation?

The python library, SimPy, is pretty explicit that it only handles discrete event simulation. Though it is theoretically possible to do continuous simulations with SimPy, it has no features that help ...
1 vote
1 answer
587 views

Can we compare the difference of two specific proportions in a 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 who give response A in age group 1 is higher ...
1 vote
0 answers
56 views

Problem on Discrete Random Variable

Please kindly give a pointer to this question. Generating the discrete variables seems unlikely! Entrance to a country can be denied for a number of reasons. When someone arrives by air, and their ...
1 vote
0 answers
23 views

To compute $P(min\left \{ X_{1}, X_{2}\right \} \ge 5)$ for two iid discrete distributed random variables

Let $X_{1}$ and $X_{2}$ be two independent and identically distributed random variables with the probability mass function as : $f(x) = \begin{cases} \left ( \frac{1}{2} \right )^x & \text{ if } x=...
0 votes
0 answers
17 views

How to model discrete bivariate probability distributions with a 'triangular' support?

I'm really at a loss as to what this is called, so please tell me if this is a duplicate and I'll be happy for the question to be deleted if that is the case (though I likely will still have follow-...
0 votes
1 answer
67 views

How to obtain the density of a sum of independent discrete random variables?

Let's $X_1, X_2, ..., X_n$, $n=1,2,...$ are independent discrete random variables. It is necessary to find the distribution law of the their sum: $p(k) =P(X_1 + X_2 + ... + X_n = k), k=0, 1, 2, ... $ ...
1 vote
0 answers
20 views

MLE estimates of regime shifted discrete process

I have a discrete process as defined, $y_t$ = $a_1$$x_t$ + $b_1$ + $\mathcal{N}(0,\alpha)$ when $t <= \theta$ and $y_t$ = $a_2$$x_t$ + $b_2$ + $\mathcal{N}(0,\alpha)$ when $t > \theta$ for $t=0,...
0 votes
1 answer
34 views

How do I quantify the homogeneity of discrete data?

I have a subset (of some bigger set, lets say of size $N$) containing $S$ different things. Now each of these $S$ things belong to a category. The total number of categories is $<=N$. What can be a ...
0 votes
0 answers
22 views

Which type of variable are week numbers?

I have a dataset where measurements on animals were done on multiple weeks of experiments. So I have measurements for week 1, week 2, etc. So I was wondering which type of variables are these? I ...
0 votes
1 answer
47 views

Can an ordered logit model be used to predict points scored by an NBA player?

I am interested in getting the probabilities of a player scoring exactly 1 point, 2 points, 3 points etc. Can an ordered logit be used for this? If not what would be the best way to get the ...
0 votes
0 answers
21 views

Bootstrapping quantiles of integers [duplicate]

Given an i.i.d. sample of 36 integers: [6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6] A bootstrap resampling procedure is performed to ...
0 votes
0 answers
30 views

Estimating a discrete distribution given expected value

I have an expected mean of a discrete variable. I would like to estimate the distribution so I can generate random samples of the value for a simulation. I have historical expected values and observed ...
0 votes
0 answers
54 views

Quantile estimation for discrete data

For quantile estimation for data coming from a discrete distribution, do you have to use one of the quantile estimators R-1, R-2, or R-3? For example, R-3 uses the nearest even order statistic after ...
0 votes
0 answers
74 views

How do you do a qq plot in R for a discrete Weibull distribution?

To do this, I think I need to calculate the inverse CDF, but I have learned here that the discrete Weibull (type I) as given by: $$F_{I}(x)=1-\exp\left[-\left(\frac{x+1}{\alpha}\right)^\beta \right]$$ ...
0 votes
1 answer
272 views

Quantiles from histogram?

Is it possible to calculate quantiles from a probability histogram P(x) rather than from the data x itself? I have an unbinned histogram for discrete random variables, and I'm wondering if I can ...
7 votes
2 answers
7k 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 ...
0 votes
1 answer
165 views

Generate viable sampling distributions of discrete data in R

I'm trying to simulate 2 X 2 data that would yield a relatively strong negative correlation. I'm using the R library GenOrd and ...
0 votes
1 answer
36 views

Likelihood that observed relative frequencies match a probability distribution

For this question, please assume probability distributions are discrete. If I have $N$ data points ($x_1, x_2, ..., x_N$), and I want to know the likelihood that these samples came from a discrete ...
19 votes
4 answers
16k 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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