A distribution is a mathematical description of probabilities or frequencies.

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What is the appropriate link fucntion in GEE for longitudinal data where distribution changes in time?

I'm modeling treatment outcome data in a GEE with Group, Time, and their interaction. At baseline everyone is highly symptomatic, thus the distribution is negatively skewed. At follow up most people ...
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22 views

How to compare s shaped curves?

I have two variables A and B that can take positive values, they are two different counters of "votes" for a group of about 400 individuals. My hypothesis is that these two kind of votes are related ...
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13 views

Determining sample size n for a plant experiment

I am testing plant health by looking at height, stem width, color, and content (antioxidants and the like). However, I was unsure how to determine a sample size for each measurement, in order to have ...
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1answer
10 views

Determine if there is a difference between two large vectors of different sizes of non-normal quantiative data in R

I have two vectors that are of unequal sizes. They contain quantitative data that does not form a normal distribution. I would like to see whether or not they are statistically different. Is there a ...
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10 views

Product of 3 multivariate normal distribution functions [duplicate]

Is there a relatively simple formula for computing the product of 3 multivariate normal distribution density functions? Where each pdf is defined by: $$ \phi(\mathbf{x}|\mathbf{\mu},\mathbf{\Sigma}) ...
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24 views

R: How to define a distribution using CDF [on hold]

I want to use "ks.test()" to compare my data to a specific distribution defined by CDF, which to my understanding is possible. But, being new to R, I am having trouble trying to find the way to define ...
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1answer
10 views

Accounting for an unexpected predictor in post-hoc Kruskal-Wallis tests

Assume a set of ten simulated frequency distributions that are contingent on an independent variable that reflects two treatment groups: Nine of the distributions represent treatment group 1 (in blue ...
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1answer
173 views

Some basic questions related to the moments of a probability distribution

The available text books in most cases avoid greater details regarding some of the topics related to the moments of a probability distribution and I feel some of those topics are not really clear to ...
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35 views

How to find representative distribution among distributions

I have an agent-based economic model that is simulated with many initial conditions over a fixed period of time. I am interested in looking at a specific variable(s) (say firm size) and I get a ...
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28 views

CDF of the function of a random variable

I haven't been able to find useful information on this. I was just wondering what would be the distribution of a function of a random variable. For example, what would be the distribution of the ...
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1answer
13 views

sample from a mixture

Suppose I have two types of students, male or female. Suppose a test score of a male student follows a distribution $F_m$ and suppose a test score of a female students follows a distribution $F_f$. ...
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How do I interpret which model is the best fit for my distribution (AIC)?

I'm new here so looking for some guidance; How do I interpret the following variables to understanding which model is considered the best fit to my distribution. ...
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28 views

Binomial distribution [on hold]

folks! The problems is Suppose you can make free throws at a 70% rate. Let X be the number of free throws you make in 20 tries. Model this with a binomial distribution: 1)?= E[X] 2)?=Var[X] ...
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106 views

Tricky Poisson distribution question

Am new to probability and have been struggling to solve the following question. Assume $X_1, \ldots,X_4$ are IID with $X_i ∼ \text{Po}(λ)$. Let $Y = \frac{1}{4} (X_1 + \ldots + X_4)$. Find ...
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26 views

Representing a multivariate normal with a scaled variance

I would like to model an observation to have a multivariate normal distribution but am having some trouble figuring out the linear algebra. So, let us start with a distribution that I know how to ...
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16 views

Specifying distribution in generalized estimating equation GEE

GEE allows you to identify the distribution of the outcome variable and appropriate link function. How do you make this selection in a longitudinal model where the distribution changes in time. An ...
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1answer
83 views

Does this look like a Cauchy distribution?

This is my data there is more actually... but I just want to know if this looks like a Cauchy distribution, such as these: I'm asking about just that bump... here is the whole distribution , ...
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1answer
29 views

Choosing a line/plane to separate two classes of binned data

In high energy physics I know it is common task to find the best separation point between two classes of data, usually signal and noise. This separation point is usually determined by first binning ...
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2answers
68 views

Can I use likelihood-ratio test to compare two samples drawn from power-law distributions?

I have to compare two large samples ($N = 10^{6}$) of discrete data drawn from power-law distributions to assess whether they are significantly different. I can't do that by means of a two-sample ...
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3answers
55 views

Detecting if samples belong to a given distribution

I am a networking person and I am trying to use statistical methods for a problem I am facing, so I would appreciate any help or pointers. I have users that access the medium, but in case 2 or more ...
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1answer
44 views

Standard Deviation of small population (less than 30)

Do we calculate the Standard Deviation of a population the same no matter how small (say less than 30) population size gets? Does distribution type play any roles in this? Thank you in advance
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1answer
40 views

Bootstrap and MonteCarlo Method

I am trying to make sense of the bootstrap method. I am studying on Rice, "mathematical statistics and data analysis" Here it is its explanation of the bootstrap method: Imagine for the moment ...
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14 views

Estimate the conditional distribution of an latent variable?

What techniques might best illuminate the underlying conditional distribution of a latent variable and what information or assumptions would improve that illumination? For example, if we have data ...
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1answer
45 views

Distributions with Median=Mode=Average?

Is there any important distribution with Median=Mode=Mean, apart from the Gaussian and Student's distribution?
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62 views

One sample test of uniformity in R

I have a dataset of two columns: one with IDs and one with a column of single digits (0-9) (see below). I would like a statistical significance test for whether the data is uniform. Ideally, I would ...
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1answer
37 views

Computing the conditional distribution for the mean of a Gaussian

I have the following distributional assumptions on some on my RV and model parameters: $$ y_i \sim N(\beta x_i, w_i^{-1}\Sigma_y) $$ There is a normal prior on the parameters $\beta$ as well: $$ ...
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24 views

Poisson for percentage data if values are low?

I have percentage data for diet per area (example here.....) I have no data on the individuals contributing to this diet, only for the population as a whole for each area. I want to assess ...
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conditional distribution question

I have a joint distribution which factorizes as follows: $$ P(y, w, \beta) = P(y|\beta, w) P(w) P(\beta) $$ Now, I want to write the conditional distribution for $P(w|y, \beta)$, so this should be ...
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Adjusting Monte Carlo estimates to generate correct even moments - improving on antitthetic draws

If I want to generate a matrix 10,000 (row) samples of 3 uniform (uncorrelated) variables it is trivial to use antithetic draws to ensure the odd moments such as the mean equal their "true" value. ...
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21 views

which method should i use for determining sample size?

what is the difference between the sample size determination method of using the critical values of the normal distribution with that of using the t-distribution? as an example if replication level ...
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35 views

Uncorrelating correlated $\chi^2$ distribution

This question is related to my previous question in here So I was trying to simulate correlated $\chi^2(1)$ random variables given the desired co-variance matrix. However, it seems like the only ...
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15 views

How to model shoe price distribution?

How would you model prices for shoes? Prices on shoes differentiate on color, size and on the retailer that sells them. I'm trying to come up with a distribution that I can sample. The average of ...
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21 views

Help with t-distribution

I've been trying to show that integral of $\mathbb{R}$ of the pdf of the t-distribution is indeed equal to 1 and have been having trouble. The pdf of the t-distribution, given in my book (Statistical ...
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1answer
49 views

How do I generate two correlated Poisson random variables?

How would I simulate observations from a bivariate Poisson distribution such that they have a nonzero covariance? The hint I was given is that I need to use the fact that the sum of two Poisson random ...
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31 views

Difference between restricted and unrestricted parameter space in MLE

I searched on the internet but I could not find any clues about my question. Can anyone just simply tell what is the difference between restricted and unrestricted parameter space in MLE? I have used ...
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Strictly positive response in regression: what should my “default” model be?

For unbounded continuous responses, Gaussian errors are the analyst's default model for many reasons, one of them being that their ML estimate coincides with the OLS estimate that has many desirable ...
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“negligible” random variables

I would like to ask if the concept of 'negligible' random variables exist. For example, if $X$ and $Y$ are random variables, not necessarily independent, then the sum $X+Y$ is, for all intents and ...
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1answer
46 views

When to use empirical cdf?

I saw in some papers that people sometimes use empirical cdf or complementary cdf to quantify the distribution of data. What is the advantage of using them and what interesting can they tell about ...
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1answer
83 views

Finding probability distribution that describes data

I have tried to fit several distributions to my continuous data (Pareto, Log-normal, Exponential, Gamma). The distribution of data is given below. I used Kolmogorov-Smirnov test to compare my data ...
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When to use CRPS (Continuous Rank Probability Score)? What are the alternatives? What are the advantages and disadvantages?

Please correct me if I'm wrong, crps is new for me. I want to understand it better. We have to minimize crps, which is based on the cumulative distribution function of the data. While the information ...
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3answers
137 views

How to test if my distribution is multimodal?

When I plot a histogram of my data, it has two peaks: Does that mean a potential multi-modal distribution? I ran the dip.test in R (...
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Fitting multiple power laws, Zipf's law in the real-world

As a preface, the following questions are related: How to calculate Zipf's law coefficient from a set of top frequencies? How to estimate parameters for Zipf truncated distribution from a data ...
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Weibull distriution. Problem with paramets and qqPlot

I have 10 years worth of mean wind speed meteorological data (timely 10-minutes data). I want to compare the observed wind speed data against a Weibull distribution on a graph of the probability ...
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1answer
35 views

Simple question about finding conditional expectation

Let $X,Y \sim U[0,1]$ ($X,Y$ are independent), we want to find $E[X|X>Y].$ I tried a few approaches to the above problem, but am not confident in my answer. One approach is as follows. Note that ...
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58 views

Box-and-Whisker Plot for Multimodal Distribution

Can I use box-and-whisker plots also for multimodal distribution or only for unimodal distribution?
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26 views

Reducing the amount of data by extracting a representative sample of my population

I have 6 B&W images representing different wavelengths (i.e. Landsat bands) of the Alta Valtellina (Italy). I extracted from the images only the areas of bare soil. Now, I want to perform a PCA on ...
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How can we compare two probabilistic models(markov networks) such that its prediction(confidence) depends on amount of training data?

I have a task of comparing two CRF models where each node and edge probability is associated with reliability depending on amount of data it is trained .How can I have a confidence metric for ...
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23 views

estimate conditional distribution from data

I have a dataset defined by 2 variables ...
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1answer
33 views

Normal distribution area vs. exponential distribution area

Why is the area to the left of the mean different in normal distributions comparatively to exponential distributions? I understand that in normal distributions area is allocated symmetrically on ...
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Calculating the highest of overlapping sets

My data set looks like the following: I have information about a large number of devices. For each device, I also have the data consumed by an application per day. Note however, all the devices ...