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

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Is it valid to use Hartigans' dip test to reject uni-modal null hypothesis with large N?

first time questioner, so please be gentle :) I have two distributions of data from a simulation. By eye, one looks like it might be bimodal, one not. I copy them below A: parameter value 1 : by ...
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10 views

Digging deeper into the FitDist function

I am using the script allfitdist to find which distribution best fits my data according to the tests included (BIC, AIK etc...) - these all stem from the script ...
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1answer
22 views

Beta function approximation of delta function

I have modified the original question. Does beta distribution function $$f(x,\alpha) = \frac{[x^a(1-x)^b]^\alpha}{B(a\alpha+1,b\alpha+1)}$$ where $B$ is the beta function, approach delta function ...
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22 views

Expected number of trials before k successes where multiple successes can occur at each trial

Let's say there are $N$ balls, $l$ of them have unique colours, $N-l$ of them are black. $D$ people uniformly randomly sample $n$ balls without replacement. Each person's sampling is independent of ...
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32 views

Kruskal-Wallis Test and Mann-Whitney U Test

I have a three samples of data where each has a non-normal distribution: I want to determine whether the samples differ. Therefore I apply the KW test and it gives me a significant value, i.e. the ...
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1answer
37 views

Compare two samples

similar questions have been asked but have not managed to get a conclusion from them. I am comparing two sets of samples, where ratios have been obtained for several analytes per sample. So the values ...
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3answers
97 views

Sampling data to have specific mean and standard deviation

I have a data that I want to sample such the resultant distribution of values should have specified mean and standard deviation. I can think of rejection sampling to achieve this however that seems to ...
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6 views

How to compare two implementations of web service by parameters of distributions of their response times?

We are migrating web services to new platform. Current WS will be wrapped behind new platform's layer. We would like to define criteria for response times of wrapped WS that should be met so we can ...
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1answer
97 views

Exponential Distribution PDF: Why multiply by lambda?

Hoping you can help me understand the probability density function for the exponential distribution. Given that the distribution's PDF is described as follows when x > 0: $$\lambda e^{-\lambda x}$$ ...
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6 views

How to create a simulation for revenue distribution in some industry?

I'm doing some research on some industry, and I'm trying to predict some revenue stats. I know that the industry worth $220M and there are 360 businesses. I assume that the business income ...
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1answer
21 views

Validating assumed distributions in parametric models

When using a model that assumes a specific distribution of data, I get confused about how seriously I need to check for the assumption. For example, if we use some statistical test (e.g., based on ...
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2answers
76 views

How large does the sample size need for the t distribution to be approximately normal

According to my understanding, when we have unknown population mean and variance, we have to estimate population variance through sample variance and use the t distribution to estimate the potential ...
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1answer
26 views

Simple definition of elliptical distribution

I'm looking for a simple explanation of what an elliptical distribution is and how it differs from a non-elliptical distribution. My knowledge of stats is very basic; Wikipedia was not much help on ...
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1answer
32 views

When to use CDF and PDF for Exponential Distribution

I am doing a self-study on Exponential Distribution and noted an exponential on my text giving that: CDF of Exponential Distribution $$ F(x) = 1 - e^{-λx} , $$ PDF of Exponential Distribution $$ f(x) ...
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1answer
12 views

Normalizing Data in Multiple Categories

I couldn't decide if this question belonged here or on the Math stack exchange, but I'm posting it here since it seems more directly relevant. Basically, I have a bunch of categories, labeled, say, ...
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1answer
30 views

Continuity correction error when using normal distribution to estimate Poisson distribution

Good morning Everyone, I am doing a self-study exercise which attempts to exemplify a case where the Normal Distribution is used to approximate the Poisson Distribution, since the population mean is ...
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1answer
21 views

What kind of distribution is this via t-distribution

Suppose we repeat an experiment identically and independently 100 times. Each time we construct a 99% confidence interval for $\mu$ via the t-distribution. Let X = the number of times the confidence ...
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90 views

Fitting data sample to a distribution

I'm trying to fit a data sample to a distribution. So far I have created a histogram and fitted the data with a lognormal distribution in R and made a Q-Q plot in excel (of log(benefits paid) against ...
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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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21 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
114 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
35 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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14 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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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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73 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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29 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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168 views

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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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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44 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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26 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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67 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
140 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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27 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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100 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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37 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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11 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
44 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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25 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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44 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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92 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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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
136 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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61 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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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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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 ...