A distribution is a mathematical description of probabilities or frequencies.

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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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56 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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39 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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35 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
44 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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41 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
36 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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19 views

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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1answer
15 views

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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20 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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30 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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14 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
48 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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1answer
28 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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33 views

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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27 views

“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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17 views

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
131 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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13 views

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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25 views

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
34 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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2answers
53 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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8 views

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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22 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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17 views

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 ...
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1answer
29 views

About the burr distribution 3 parameters

In my papers the probability density for a burr distribution is given as $f(x) = \dfrac{\gamma \tau \alpha^{\gamma}x^{\tau - 1} }{(\alpha + x^{\tau})^{\gamma + 1}}$ however i have encountered this ...
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2answers
43 views

Tweedie distribution GLM for manyany() in {mvabund} package

My data follow a Tweedie distribution, and I'm working with multivariate abundances. So I'm trying to use the manyany() function in the ...
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16 views

Should I still compare my distrbution to others if I've found a fit?

I'm using the ghpy package in R to model some currency data. I currently comparing fits with the lik.ratio.test with the ...
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Estimating distribution from pairwise comparisons (crowdsourced)

I would like to estimate a discrete probability distribution, for instance, occurrences of animal species in a geographical area (e.g. from all the animals 20% are bears, 10% are wolfs, 5% are ...
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asymptotic distribution of outlier detection tests

What is the asymptotic distribution of Dixon and Grubbs discordancy test statistics, if the data are from a normal distribution (such as simulated data, perhaps).
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1answer
27 views

What is the canonical link function for a Tweedie GLM?

I was just introduced to the Tweedie distribution (see this or this) but I'm having a hard time finding what the link function is for a Tweedie generalized linear model. Thoughts?
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9 views

Distribution of the ratio of dependent magnitude square of complex Gaussians

Assume that $X=X_1 + X_2 +...+X_n$, where $X_i \sim CN(0,\sigma^2)$ and independent. Here $CN$ means circular complex Gaussian. The question is, what is the distribution for $Z = ...
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1answer
88 views

Should I find this big parameter suspicious?

I have some kind of disagreement with a groupmate. We have some data, and we have to fit a loglogistic distribution. Our highest data point is less than 14,000,000. The average of our data is ...
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14 views

How does distribution of the digits of $\pi$ changes for different numeral systems?

I'm aware of most common calculations of frequency of each digit of $\pi$, but the problem is that we rely on decimal system which is natural for us, but could be not natural for the universe. How ...
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1answer
149 views

What is the limiting distribution of exponential variates modulo 1?

I have tried to find the limiting distribution of $X_n\sim\text{Exponential}(\lambda/n)$ by finding the cdf and taking the limit. I got: \begin{align*} F_{X_n}(X)) = \int_{0}^{X} \frac{\lambda}{n} ...
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1answer
35 views

Estimating the true distributions from a sample of distributions

I am having a hard time formulating the following problem. Consider a company that runs a survey across several cities in the US to estimate the percentage of right-handed people and left-handed ...
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Estimating a complete income distribution from decile values

I haven't be able to find an answer to this so any suggestions would be really useful. I've been asked to post stratify a survey and I'm currently trying to do this for gross personal income. The ...
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1answer
94 views

Distribution of “normalised” Gaussian random variables

Let $X_1, \dots, X_n$ be independent normally distributed random variables. What is the distribution of: $$ Y_i = \frac{X_i}{\mathrm{stdDev}(X_1, \dots, X_n)}, $$ where $\mathrm{stdDev}(X_1, \dots, ...
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2answers
124 views

Can I say that my samples are different just by looking at box plots without performing a test?

Is it possible to say that my samples are significantly different (or not) from each other just by looking a box plots? If yes, what do I have to look at and what is the theory behind it? I read ...
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0answers
22 views

Notation for a random vector whose length depends on another random variable?

I have the following process that I'm trying to describe with random variables. First, I have a random variable $X$ that takes on values drawn from a Poisson distribution with parameter ...
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2answers
30 views

In a statitical experiment involving independent coin tosses, what is the number of heads required to get $m$ tails?

I know that the solution is a negative binomial distribution. However, I was a looking for a proof for the same along the following lines. If the number of coin tosses is fixed to be $n$, then the ...
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3answers
210 views

Why does a Cumulative Distribution Function (CDF) uniquely define a distribution?

I have always been told a CDF is unique however a PDF/PMF is not unique, why is that ? Can you give an example where a PDF/PMF is not unique ?
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27 views

Approximation of “translated and scaled” Poisson distribution by normal distribution?

If I have a random variable $Y=a(\frac{b}{c}+\frac{X}{c})$, where $a,b,c$ are all integers and $X$ is Poisson distributed with a mean which is large enough to be approximated by the normal ...