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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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 ...
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7 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 ...
2
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0answers
47 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) ...
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1answer
40 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 ...
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2answers
62 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) = ...
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37 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+ ...
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0answers
5 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 ...
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0answers
19 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 ...
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2answers
102 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 ...
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0answers
10 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 ...
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1answer
23 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 ...
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0answers
38 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.
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738 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 ...
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0answers
16 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 ...
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0answers
62 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 ...
2
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1answer
43 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 ...
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1answer
30 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 ...
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1answer
109 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. ...
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0answers
23 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. ...
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1answer
108 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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1answer
20 views

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 ...
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1answer
77 views

Do probabilities need to sum to 1 in a choice model? [closed]

We're create a discrete choice model, in which there are more than two alternative choices. There are some options for this, such as the multinomial logit and the conditional logit.. We started with ...
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1answer
41 views

ANCOVA or not? Non continuous covariate

I have done an experiment with an independent and dependent variable. I repeated the experiment 5 times. Obviously all the repeats will be different from one another, some of them significantly so. ...
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2answers
69 views

Discrete choice model

I have a ordinal probit model. The dependent variable, say walkability, is a Likert scale variable (1,2,3). The main independent variable, say connectivity, is also a Likert scale variable (1,2,3). ...
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19 views

How do I handle continuous variables that depends on a another discrete variable?

I am trying to create a classification model with independent variables IV1, IV2 and IV3 and dependent variable DV (DV ~ IV1 + IV2 + IV3). Now the problem that I am facing is that IV2 exists only ...
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13 views

Estimating the number of units bought at a certain price in a stock

I need a way to know the value of my stock. Let $(x_1, \dots, x_n)$ be the quantity of the products $1$ to $n$ I have in stock, such that, for example, if I have $8$ units of the product $2$, $x_2 = ...
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17 views

Check two samples came from the same discrete distribution

Let's say I have two samples $X_1, X_2, |X_1| = n_1, |X_2| = n_2$. Each entity in a sample is a value of categorical variable that comes from a discrete distribution. For example, $x_1$ takes one of ...
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1answer
58 views

Finding quality of fit for two discrete variables with low statistics

I have data from an experiment which I am trying to explain using a model. I do not have an analytic formula for the prediction of the model but instead I got its prediction through a simulation. The ...
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0answers
26 views

converting discrete values to buckets to perform predictions

I have a set of continuous discrete values, which I would like to convert to a classification task. Say, my scores in an exam are anything between 0-100. I want to convert my scores in the next exam ...
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0answers
16 views

Fisher Information from Discretized Likelihood

I suppose this may sound like a general question, so sorry if it actually is. How can I calculate the Fisher information for a log-likelihood which I have calculated for a discretized set of points. ...
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1answer
109 views

Machine learning method to determine continuous values from discrete and continuous parameters

I watched online courses about multivariable linear regression which addresses the problem of determining values from numeric inputs. Like, predict prices for houses based on age, size, number of ...
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21 views

Implementing evolutionary algorithms

We're trying to to minimize the following functions using Multi Objective Evolutionary Algorithms : $\mathrm{minimize}~\lambda_q(1-a)E(N)E(X)+\lambda_xE(N)E(\max(X/a-R,0))$ ...
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2answers
54 views

Estimation of probability mass function using finite samples [closed]

Suppose $X_1, X_2, \dots, X_N$ are $N$ random samples of a discrete probability distribution such that $X_i \in \{1, 2, \dots, K\}$. The probability distribution $p$ used for sampling is ...
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2answers
103 views

How to properly state the average of a discrete number in a report?

I'm wording a report on the averages of a discrete variable, and am trying to get the most appropriate sounding wording. Consider the able below: ...
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1answer
38 views

Word-frequency and statistics

I am new to statistics and am wondering how I can apply it in linguistics. There is a conjunction in a corpus that 902 times (.91) conjoins sub-clausal units, and 91 (.09) times clausal units. How ...
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0answers
18 views

Multivariate discrete distribution

Let $\mathbf{x}=(x_{1}, \dots, x_{m})$ be a vector of discrete variable; $x_{j} \in \mathbb{Z}^+$. Which distribution can I use over $\mathbf{x}$ that allows to have dependence between each couple ...
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1answer
43 views

compare magnitude of association between pairs of discrete variables?

say I have discrete(nominal) variables Y, X1 and X2. X1 and X2 have different number of levels. I want to assess whether Y is associated more with X1 or X2. I understand that I could use chi-square ...
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161 views

How to understand from paper how to derive the CRLB for Gaussian case AR model

An univariate autoregressive process AR(p) process is expressed as $$y(n) = \sum_{j=1}^p a_jy(n-j) + u(n) $$ is excited by Gaussian sequence, $u$. Is there a resource / reference for a lucid ...
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2answers
77 views

Mean Preserving PDF Spreading

I have a histogram representing the PDF of an unknown discrete RV. The histogram is asymmetrical. To be clear, all I have is the histogram. Is there a known way to increase/decrease the variance of ...
3
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2answers
92 views

how can I test if a sample was created from a specific Discrete Distribution

How can I test if a sample was created from a specific discrete distribution. For example, if I have the following distribution 1- 0.2 2- 0.5 3- 0.3 and I ...
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0answers
28 views

Test if 2 samples are taken from the same population (multi-dimensional data) - worked example

I'm looking to learn (not just apply) how to test is two samples are drawn from a single population. The data I'm likely to apply this to is multi-dimensional so that's my target. Can anyone give me a ...
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0answers
27 views

hypothesis test for discrete disributions

I am interested in the number of instances of feature $F$ among the members of two populations, $A_1$ and $A_2$. e.g. $F$ is a some special genetic element that may occur several times within a ...
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0answers
8 views

What is the discrete equivalent to the 4-plot?

Quoting NIST, when analyzing a continuous variable, one needs to validate four assumptions that typically underlie all measurement processes; namely, that the data at hand "behave like": random ...
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1answer
338 views

Why is this random variable both continuous and discrete?

The waiting time, $W$, of a traveler queuing at a taxi rank is distributed according to the cumulative distribution function, $G(w)$, defined by: $$G(w) = \begin{cases} 0 & \text{ for } ...
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1answer
52 views

Question about the the median and the mode in skewed distributions

In intro statistics textbooks, the mode is typically described as least susceptible to skewness, followed by the median, which is in turn followed by the mean. The difference between the median and ...
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50 views

Finding n and c in single sampling plan

I am learning a quality control course and in Single sampling scheme for attribute type inspection I don't understand the method used for calculating the values of $n$ and $c$. The method is as ...
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1answer
46 views

Chi-squared two sample test for unbinned discrete data

I am wandering through the net but I cannot get a precise description of how to solve this simple task. Two sets of datas ...
2
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1answer
75 views

Number of different combinations in a sample

I hail from Mathematica SE. A friend of mine asked me a statistics question (I'm an economist and am assumed to know such things) which kind of stumped me, since I usually deal with non-discrete ...
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19 views

Monitoring high quality near zero defect processes

What are the latest techniques for monitoring discreet defects in high quality processes with defective rates in the parts per million range?
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37 views

Discrete Choice Models

for mulitnomial (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 would be: Is that also true in ...