A distribution is a mathematical description of *probabilities* or *frequencies.*

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simulating distributions with non-symmetrical confidence intervals in R

I have a software package that outputs estimates that have non-symmetrical confidence intervals. I am simulating these distributions for further Monte-Carlo estimates. In the below example I am trying ...
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Combined hypergeometric distribution of exclusive sets

Given the following: a set of numbers, 1 to 20 four sets of five numbers from the set above (each number used once) a draw of five different numbers from the first set How would I determine the ...
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20 views

Calculating probability based on mixed variables

Assume there are $K$ people and iid. parameters $a_1,\ldots,a_K$ associated to them with $a_i \sim U(0,1)$. Person $i$ observes his own fixed $a_i$ with some noise: \begin{equation} X^{(1)}_i= a_i+ ...
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1answer
97 views

Why is the sampling distribution of normal distributed variable automatically also normal distributed

I am currently reading about the standard error. I know about central limit theorem, but I don't understand why, if my variable is normally distributed in the population, the sampling distribution ...
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1answer
33 views

How to convert mean and standard deviation to a single meaningful and quantifiable value?

I look at mean and standard deviation of various map like data and each give meaningful information but sometimes they provide different information. For example, let's take states in a country. One ...
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13 views

Comparing distributions of proportions

Some research shows that female politicians put forward a more diverse issue platform than male politicians--meaning they discussion greater variety of issues than men. I would like to see whether ...
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11 views

1/F distribution equality significance level

A question about equality $$F_{r_{1},r_{2},\alpha}=\frac{1}{F_{r_{2},r_{1},1-\alpha}}$$ We know if $X\sim\chi^{2}\left( r_{1}\right) ,~Y\sim\chi^{2}\left( r_{2}\right) $ and $X,~Y$ independent ...
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2answers
68 views

Identifying distribution of a variable

Consider a variable that can take both negative and positive values, and that has the following density plot: I am trying to identify the distribution of this variable. The density plot resembles ...
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2answers
28 views

Cosine similarity between a clean signal and its noisy version

Given a $D$-dimensional datum that is an iid sample from a spherical Gaussian distribution, and the noise-corrupted version of that datum generated by adding spherical Gaussian noise, is there a ...
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48 views
+150

A stochastically increasing exponential family for which $\lim_{\theta\rightarrow\inf\Theta}\mbox{P}_\theta(X\leq x)\neq 1$

Question A little something that I've been wondering about for a while: Let $P_\theta$ be a stochastically increasing (one-parameter) exponential family on the sample space $\mathcal{X}$ with ...
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17 views

Can I estimate Variance of Gamma from Negative Binomial distribution distributed data, given NB is Gamma-Poisson compound

I believe the data I have follows Negative Binomial distribution (over-dispersed Poisson). We know Negative Binomial is a Gamma-Poisson compound distribution. The variance of this Gamma distribution ...
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40 views

Any practical uses of inverse uniform distribution?

To motivate a paper in game-theory I need examples of real-life uses of the inverse uniform distribution (http://en.wikipedia.org/wiki/Inverse_distribution#Inverse_uniform_distribution). Which type of ...
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24 views

Generate data based on existing data and their distribution

Consider the following dataset: patient id, gender, age, systolic blood pressure, diastolic blood pressure 1, male, 66, 120, 80 1, male, 66, 119, 83 2, female, 45, 119, 90 3, female, 55, 120, 19 ...
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1answer
62 views

Non parametric Wilcoxon Signed Rank test

I have the following data vector(in fact its 2392 data points long): ...
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3answers
138 views

Estimating the distribution of a variable

I am trying to estimate (fit) the distribution of a variable. The first step in doing so is to draw a normal probability plot. This is what I have obtained (using R): ...
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22 views

square of normal distribution with specific variance

What is the distribution of a normally distributed random variable $X^2$ with $X\sim N(0,\sigma^2/4)$. I know $\chi^2(1)=Z^2$ is a valid argument for when squaring a standard normal distribution, but ...
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2answers
21 views

Distribution of max of samples with replacement

Suppose you have a set of numbers $\{1,2,...,m\}$ where $m \ge 5$ . Now you randomly choose five of those elements with replacement, $\text{a}_1$ ... $\text{a}_5$. What is the distribution of ...
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3answers
99 views

If $X$ is normally distributed, can $\log(X)$ also be normally distributed?

Suppose $X$ is distributed $N(\mu, \sigma^2)$ where $\mu \neq 0$. Can I use the Delta Method to say that $log(X)$ ~ $N(log(\mu), \sigma^2/\mu^2)$?
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34 views

R package fitdistrplus: function fitdist shows unusual error

I used the package R fitdistrplus in order to estimate parameters of different distribution function. In one case it shows a strange error message I can't interpret: ...
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1answer
32 views

Big O notation preserved under convex functions?

Suppose that the random variable $X_T$ is $O_p(1)$ as $T \rightarrow \infty$. Does this imply that the random variable $\max\{0,X_T \}$ is $O_p(1)$?
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10 views

R: Shapiro-Wilk test with relation of W and P-Value? [duplicate]

I'm currently learning about the Shapiro-Wilk test for normality and using R for conducting simple experiments. One thing which is confusing me is that I found some results would produce a high W ...
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14 views

Weak convergence implies uniform convergence in distribution?

Consider an empirical processes $\{v_T(\theta), T\geq 1 \}$ and assume it is weakly convergent to the stochastic process $\{ v(\theta); \theta \in \Theta\}$., i.e. $$ E^*(f(v_T(\theta)))\rightarrow ...
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1answer
31 views

Compare distributions with uneven and small sample sizes

I will be performing my analysis in R but any general mathematical-based answers will be appreciated. I realize similar questions have been asked before but I am new to statistics so please excuse my ...
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1answer
42 views

showing a random variable has an exponential distribution

Let $X_{1},..,X_{n}$ be independent, each with a exp($\lambda$) distribution. Let $Z=min(X_{1},..X_n)$. Show that $n\lambda Z$ has an exp$(1)$ distribution. I calculate that $P(Z>z)=e^{-n\lambda ...
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23 views

How to interpret log-likelihood outputs from MASS::fitdistr (R)

AIM: Fit the best distribution to columns in a dataset (30k records) so that I can to go on to produce test data that is in a similar distribution. WHAT I'VE DONE SO FAR: Using R, I have found and ...
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43 views

Poisson distribution help

In many cities, neighborhood Crime Watch groups are formed in an attempt to reduce the amount of criminal activity. Suppose one neighborhood that has experienced an average of 10 crimes per year ...
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2answers
90 views

How to use the chi-squared test to determine if data follow the Poisson distribution

The figure below (Figure 1 from p. 646 of this paper) compares observed values against expected values under the Poisson distribution. It then runs a chi-squared test to see if the observed values ...
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13 views

Wilks's lambda distribution

Please help me, I don´t have any idea how to solve this problem. If $\textbf{A} \sim W_p(\mathbf{\Sigma}, m)$ and $\textbf{B} \sim W_p(\mathbf{\Sigma}, m)$ are independent Wishart matrices, show that ...
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2answers
130 views

Choosing a discrete non-uniform distribution for generating random integers

I have a list $l$ containing integers in the range $[1,max]$ On list $l$ I do an operation $isPresent(x)$ which return true if ...
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33 views

estimating product of 2 independent variables

I have 2 independent variables with distributions: $X \sim \text{beta}(\alpha_1,\beta_1)$ and $Y \sim \text{beta}(\alpha_2,\beta_2)$ I would like to estimate $P(X * Y >= \text{val})$, and I am ...
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1answer
60 views

Using Poisson distribution to generate random integers

I'm trying to generate random integers which have Poisson distribution. The open source library GSL has one such distribution. Function: ...
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11 views

Implication of uniform stochastic boundedness?

Let $\theta \in \Theta \subseteq \mathbb{R}^d$ be a parameter vector. Let $Q: \Theta \rightarrow \mathbb{R}$ be a function mapping from the parameter space to the real numbers. Let $Z_T$ be a a ...
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7 views

Applying Beta distribution for calculation latent variables

I would like to find the probability distribution function for the below scenario,its similar to Computer Adaptive technique (IRT) I need to estimate the ability of a student from answered questions ...
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15 views

Smallest Spectral Norm / Deviation Inequality

Consider $A_{m \times n}$ be an i.i.d. random matrix with finite first to fourth moments. There is a good number of asymptotic and non-asymptotic results regarding the spectral norm of $A$, $\|A\|_2$, ...
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3answers
57 views

Given two sets, how can I say statistically if they are similar/different

This is a very open ended question. Suppose I have two sets of data samples of the same form, say [item, rating]. Rating is a value on the interval [0,100] and item is a unique identifier given to a ...
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1answer
29 views

What is the distribution of a sum of a subset of probabilities, with each probability having the same distribution?

Suppose I have k outcomes with probabilities, pi, with p1+p2+...+pk=1. Each probability has the same distribution. What would the distribution of a sum of probabilities be? For example, what would the ...
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27 views

Deconvolution of sum results in negative numbers

Given $T=G+A$ where $A$ and $G$ are independent random variables, I'd like to estimate the distribution of $G$ given empirical (measured) distributions of $T$ and $A$. Of note: all three random ...
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31 views

How to compare the price of two sets of business transactions?

A business transaction can be defined as a function of 6 independent categorical variables (representing the customer and the product). Sales representatives are allowed to charge whatever price their ...
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22 views

Analyzing the shape of distribution on a histogram [duplicate]

I have three different histograms which are generated from one sample. In each of the histograms, both variables are the same. Although binwidths for each histogram is different. By looking at each of ...
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30 views

multivariate distributions bounded on [0,1] where parameters can be solved for from known mode

I need some kind of multivariate distribution which has the following properties support is $x_1,$ $x_2$, ..., $x_K$ where all $x_i \in [0,1]$ Though not required it is true that elements of the ...
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22 views

How to assess if a ratio significantly differs from a population of ratios?

Dear statistics experts, assume I have a 100 bowls of differently colored balls. There are up to four colors: Black, White, Red, and Green. Each bowl can contain a different total number of balls, ...
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12 views

Estimating distribution function for dependent observations

Let $X_1,\dots,X_n$ be identically but not necessary independent distributed with distribution function $F$. I'd like to estimate $F$ efficiently. In case, $X_1,\dots,X_n$ are i.i.d., we can estimate ...
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2answers
111 views

How are the numbers of modes of marginal and joint distributions related?

Can a unimodal multivariate distribution have a multimodal marginal distribution? If all marginal distributions are unimodal, can the multivariate distribution be multimodal?
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1answer
20 views

Can I use an F-test to test the equality of variances if my distribution is leptokurtic?

I have the data for two leptokurtic distributions. I want to use the f-test of equality of variances but as I understand it needs to satisfy the assumption that 'the two populations are normally ...
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23 views

Can conditional distributions be considered as a parameterized family of distributions?

Given two real-valued random variables $X$ and $Y$, are the conditional distributions of $Y$ given $X$ taking different values, $ \{ p(y|x), \forall x\}$, considered as a parameterized family of ...
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11 views

Markov-Switching model of distribution

I was wondering if anyone knows of any work concerning markov-switching models and more precisely that changes the distribution of the error terms? I've found some literature for conditional mean, ...
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1answer
45 views

Does the Central Limit Theorem only work for iid random variables?

Can we say anything about the distribution of the sum of not iid random variables?
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1answer
55 views

What is quasibinomial?

I'm hoping someone can provide an intuitive overview of what quasibinomial is and what it does. I'm particularly interested in these points: How quasibinomial differs to the binomial distribution ...
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3answers
231 views

Is it better to select distributions based on theory, fit or something else?

This is bordering on a philosophical question, but I am interested in how others with more experience think about distribution selection. In some cases it seems clear that theory might work best (mice ...
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1answer
52 views

Is my understanding of this “confidence interval” solution correct?

I was faced with a problem of automatically detecting regions of continuity in a vector. I have a lot of these vectors, hundreds. One example of such vector is here. Basically looking at the vector, ...