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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31 views

POISSON regression with offset variable

Our problem is to determine if there is a relationship between the return on equity of firms (ROE) and the presence (number of indicators used) (Y) of a specific type of indicator showing up in the ...
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56 views

R-How to generate random sample of a discrete random variables? [migrated]

In R, I want to generate a random sample of a discrete random variable: $X$, where: $P(X=a)=P(X=-a)=1/2$. I have been searching for a function online but there seems no direct function doing this.
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1answer
15 views

How to test if a value is over-represented in one sample vs another

I have two multinomial data samples that both have N discrete categories. I know that a Kolmogorov-Smirnov test will let me know if the distributions of the two ...
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0answers
18 views

Metric optimization on discrete learning sample

There are a set of ("artifical") not Minkovski (triangle inequality is not guaranteed) metrics defined on set of objects. There are one etalon ("natural") metric, which estimation is known only for ...
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2answers
132 views

How to decide on the MLE when pmf is 0?

Suppose you have $\theta=\{1,2\}$ and the sample of (0,1,2) with the task of finding MLE: \begin{array} {|c|c|c|} \hline x & p(x|\theta=1) & p(x|\theta=2) \\ \hline 0 & 1/2 & 1/4 \\ ...
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23 views

Test for one category

I am doing a research in linguistics and I am not to sure what test to choose in the following problem. There is a group of 26 students. They are asked a question and two possible variants are ...
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1answer
41 views

What methods exist for finding optimal splits to discretize continuous data with respect to a target variable

I'm doing some research into methods for discretizing a continuous variable coupled with a binary target variable to find the optimal split points to maxamise a measure of impurity (gini/entropy). ...
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2answers
74 views

Accurately generating variates from discrete power law distribution

What are the best methods to accurately generate random integers distributed according to a power law? The probability of getting $k$ ($k=1,2,\ldots$) should be equal to $p_k = k^{-\gamma} / ...
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1answer
39 views

3-4-5 Rule How to partition the sets?

In Data Mining course, we are taking 3-4-5 Rule to segments the data uniformly. I'm trying to understand these lines below, and how they are linked to the graph below too. If an interval covers ...
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0answers
68 views

Fitting normalized data to discrete distribution

I have a graph which represents a P(x) vs. x data where x can have 10 possible discrete outcomes. Data looks as follows: {{200, 0.0058668}, {306, 0.0503333}, {411, 0.163055}, {520, 0.203411}, {624, ...
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1answer
74 views

One-way ANOVA appropriate?

I am assessing the performance of a hospital ward over 6 years. There have been two sets of changes to the ward over this time: after year 2 and after year 4. I have collected data in 4 sample ...
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1answer
52 views

Statistical test for testing equal proportions

I have a questionnaire item (N=6572) for which: 5064 (77.1%) subjects responded to the question, and 1508 (22.9%) subjects did not respond to the question. What statistical test should i use to ...
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1answer
66 views

Change detection for beginners

I've seen Change detection algorithm - likelihood ratio but I am afraid my question is more basic. I have a sequence $(x_j)_{j=1..N}$ of random observations. I know, these observations are not all ...
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1answer
38 views

Calculating discrete hazard rates problem

I am working on an assignment for a Stochastic Modeling class and am stuck on the following question: Let $X$ have probability mass function $p_j = P \lbrace X = j \rbrace $ for $j \geq 1$. Let ...
4
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1answer
70 views

Sufficiency of order statistics

I am told the following proof is incorrect, but I cannot understand why. Consider $X_{(1)}, \ldots, X_{(n)}$ are the order statistics of a random sample of size $n$. I want to show that the order ...
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1answer
34 views

sum of discrete random variables - am I thinking right?

I have thirty discrete random variables for a risk management application. Each of the random variables may have a value $0$ (with probability $p_1$) or $X_i>0$ (with probability $p_2$). All thirty ...
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22 views

Exponentially weighted average of data stream variance

For modeling a sequence of data, I once heard the technical term of "exponentially weighted average of the data stream variance". It is defined recursively as I am not clear why does this recursive ...
2
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2answers
42 views

Rule of thumb when drawing N samples from a discrete distribution with N possible values with replacement

I'm looking for an explanation and possibly the name of a rule of thumb: When drawing N samples with replacement from a discrete uniform distribution of N values, it is very likely that: 1/3 of the ...
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2answers
46 views

Limiting pmf as $n \to \infty$

Consider the simple pmf: $$p_n (x)=\begin{cases} 1\quad x=2+1/n \\ 0\quad \text{elsewhere} \end{cases}$$ Then my book states that $\lim_{n\to \infty} p_n (x)=0$ for all values of $x$. Is that really ...
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1answer
59 views

Probability of observing the same value for 10th percentile in two different samples

Edited: I have a categorical variable comprising of values from 1 to 7 with these probability: ...
2
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1answer
136 views

What are the dangers of using a (log)normal distribution for a discrete response?

I have seen in the engineering field some papers (one example) using normal or lognormal distributions to model discrete outcomes. Typically, the explanatory variable is binned (into equal intervals) ...
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0answers
44 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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126 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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85 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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29 views

binarization of variable - experimental threshold choice. Is it good approach?

I have some ratings averages values from 1 to 5(users were rating on 1,2,3,4,5 scale). I would like to split them into two classes: credible, ...
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1answer
119 views

Normalize vector-based integer data

I'll preface my question by saying I have a very limited knowledge of statistics, and while I've put some thought into this problem, I'm a bit stuck! Onwards... I have a collection of fixed-size ...
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29 views

Determining which pair of empirical distributions is the most similar

I'm looking at three discrete (seven-option) survey questions that were asked on two different surveys (100 < N < 150 for each question). I've paired up the six answer distributions so that each ...
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2answers
125 views

Cumulative Distribution Function Inequality (Discrete Distributions)

Let a discrete Random Variable $T$ have CDF $F_T(T)$. Could you please help me understand why $$ P \left[ F_T (T) \leq a_1 \right] \leq a_1 $$ I know that the result holds with equality for the ...
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0answers
76 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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0answers
26 views

Modeling Sequential Discrete Choices

In my experiment, I have a finite set of discrete choices (or alternatives) $S$ in which I ask each participant to select a non-empty subset $s \subseteq S$ and rank the elements in $s$ in their ...
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1answer
147 views

How to discretise continuous attributes while implementing the ID3 algorithm?

I am trying to implement the ID3 algorithm on a data set. However, all attributes are continuous and can have values between 1-10. I found that we have to specify the bin intervals for discretization ...
3
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1answer
80 views

Alternative to Wilcoxon signed-rank test, for data where many pairs are equal

I have several discrete datasets with a small range (-2 to +2) which I want to test against the null hypothesis "the distribution is centred around zero". The Wilcoxon signed-rank test was suggested ...
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1answer
117 views

Hamiltonian Monte Carlo and discrete parameter spaces

I've just started building models in stan; to build familiarity with the tool, I'm working through some of the exercises in Bayesian Data Analysis (2nd ed.). The Waterbuck exercise supposes that the ...
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1answer
74 views

What is the difference between “multinomial” and “polytomous”?

I would like to know the difference a multinomial model and a polytomous model. Both a multinomial model, for example multinomial logit / probit model, and a polytomous model are used for estimation ...
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2answers
135 views

EM algorithm to estimate discrete Markov chain transition probabilities

I'm surveying algorithms to estimate the transition probabilities of a discrete Markov chain and I found that EM approach could used. However I am not able to find any simple description on how to ...
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83 views

Generalized Moran's I test for multinomial (polychotomous) logit / probit model

Generalized Moran's I test is suggested by Kelejian and Prucha (2001). But, as far as I know, there is no empirical work using the test for multinomial discrete choice model. I am looking for a ...
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0answers
44 views

Test for unobserved heterogeneity in proportional hazard model in R

I have modeled a discrete-time proportional hazard model in R. Now I would like to test the assumption of no unobserved heterogeneity. Does anyone know a test for unobserved heterogeneity? Does ...
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0answers
51 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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1answer
233 views

Fitting discrete points on a normal distribution

I have an ordinal ranking of 16 objects. I know that the value of the first object is 0, the second value is 2, and the last object is 14. I'd like to map each of the intermediate objects to an ...
4
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2answers
703 views

How to fit a discrete distribution to count data?

I have the following histogram of count data. And I would like to fit a discrete distribution to it. I am not sure how I should go about this. Should I first superimpose a discrete distribution, say ...
3
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2answers
159 views

What is the literal interpretation for having a very low power (~30%)?

I am going to be conducting an experiment where I have two discrete samples. I have a limited number of samples, and when I calculate the Power of the test, (given a set number of samples, and ...
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2answers
82 views

Ranking different variables by standardization

I have seven numeric variables and 12 cases. All of them are measures for how well 5 different casinos are performing. The higher the variable, the better the performance. Four of the variables are: ...
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0answers
27 views

Best approach to correlate discrete and continuous variables using machine-learning technique [duplicate]

I am using a scale which consists of discrete values: 0 (normal), 1 (mild), 2 (moderate), 3 (severe) and these values are for 4 components. I have measured 200 patients on this scale. Each patient ...
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68 views

Which model should I use to fit my data?

Here is a problem I'm struggling with for some days now on ! Here is the kind of data I have ...
4
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2answers
262 views

Alternative to Kolmogorov-Smirnov test when parameters are estimated from the data

I need to compare whether two distributions are similar when the values are scaled by the mean of each of the distribution. One limitation of ks-test as per ...
0
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1answer
101 views

Multiple regression of nonparametric variable over different types of variable

I have a non normally distributed variable X (also its residuals are non-normally distributed). I have also two predictor variables, one categorical (two categories) and one discrete. Which regression ...
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2answers
165 views

A simple distribution problem

Suppose that $x \sim U(0, 255)$ and and $y \sim U(0, 255)$, and that $x$ and $y$ are independent. What is the distribution of $x - y$? If I were to draw 1,000 samples from this distribution, how ...
2
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1answer
47 views

How to model a five point rating item predicted by multiple variables some of which are factors?

I have carried a questionnaire, which has a variety of questions in which the responses are given in a rating form (e.g. 1-5, from bad to good). I now would like to test whether the response to ...
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53 views

Comparing different step functions

I measured the appearance of certain events over time in different conditions and I would like to know whether there is a difference between the happening of these events. I thought of plotting the ...
3
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1answer
251 views

Complete sufficient statistic

I've recently started studying statistical inference. I've been working through various problems and this one has me completely stumped. Let $X_1,\dots,X_n$ be a random sample from a discrete ...