A distribution is a mathematical description of probabilities or frequencies.

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Is this the sufficient condition for not having infinitely small modes in a distribution?

I was reading the paper Optimal Throughput and Delay in Delay-tolerant Networks with Ballistic Mobility (http://dl.acm.org/citation.cfm?id=2500432), and found the following proposition (page 305): ...
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To sketch a “typical” plot of a specific time series model

Let X have a distribution with mean $\mu$ and variance $\sigma^2$, and let $Y_t = X$ for all t. Sketch a “typical” time plot of $Y_t$. My thoughts: This process $Y_t$ is stationary with mean $\mu$, ...
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What are marginals?

Marginals are mentioned a lot in copula literature, what does the term really mean? For example what is the intuitive meaning behind a statement like "This function describes the dependence ...
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what is the relation between significance level and forecasting values

From the past data we estimated the future values in R with default level of significance but my doubt is if we increase or decrease the significance value then how much change will be there in ...
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23 views

How to derive the conjugate prior of an exponential family distribution

I am trying to derive the conjugate prior of the univariate Gaussian distribution over both the mean and the precision. I know that the prior I'm looking for is the normal-gamma distribution, but the ...
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1answer
71 views

Three players with their own coin flip untill they have heads. The first one with heads wins

I have been stuck with this question for some time and I'm not sure if I'm doing it correctly. There are three players who each have their own coin—each coin having a different probability for it to ...
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1k views

Quarter is to quartile as half is to…?

Is there one word to describe the sections of data on either side of the median? I'd guess "half", but it seems like there ought be something better...
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Distribution of the exponential of a mixture?

Suppose that $X$ is distributed as a finite mixture of normals $$\sum_{j=1}^k w_j \phi(x;\mu_j,\sigma_j^2).$$ Is $\exp(X)$ distributed as a finite mixture of log-normal distributions?
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Should the fumble rate of NFL teams be a normal distribution?

There's a lot of garbage statistics going around the internet regarding the Patriots, but I was just curious what the well-versed in statistics have to say about this. The main question is - in what ...
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1answer
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Developing a heuristic for maximizing the “covering” of a distribution

Context There's a board-game called Settlers of Catan in which players compete to be the first to gain 10 victory points by trading various resources in exchange for pieces (or cards) worth victory ...
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44 views

confidence intervall for the product of random variables

Suppose $X_i\sim N(\mu,\sigma^2)$ and $W_i\sim \text{Uniform}(0,d)$ are independent random variables for $1 \le i \le p$ and $p$ is large. Given $0\lt\alpha\lt 1$ and a number $c \gt 0$, I need to ...
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Latency distribution analysis

I'm trying to analyze latency distribution in the system. Latencies collected in the following way: maximal observed latency per minute is measured then, if this latency is largest latency seen this ...
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product of independent random variables [duplicate]

This may be bit a little similar to the problem I asked yesterday, but I don't understand why I can't find my mistake. I am not familiar with the indicator function notation. Let $X$ be ...
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1answer
34 views

What is the distribution family where one side is with light tail but the other side with heavy tail?

For example the distribution of weights of human. There are not many adults under 40 kg, but a lot more people heavier than 100 kg, although the average of an adult's weight is, let's say, 70 kg. ...
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222 views

pdf of a product of two independent Uniform random variables

Let $X$ ~ $U(0,2)$ and $Y$ ~ $U(-10,10)$ be two independent random variables with the given distributions. What is the distribution of $V=XY$? I have tried convolution, knowing that $$h(v) = ...
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21 views

What is first order asymptotic distribution?

I am stuck with this term in a research paper(Hansen, 1999). Its written (p 351) "Hansen (1996) shows that a bootstrap procedure attains the first-order asymptotic distribution, so p-values ...
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24 views

Probability distrubution of 3 products

A lightbulb factory produces bulbs in 3 qualities. 50% of production is Low quality, 30% average quality, 20% good quality. A randomly selected lot of 4 bulbs gets tested. Low quality lights have a ...
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30 views

Find distribution of Bus arrival time

I am currently working on a problem in my research which can be modeled into the following question: Let's say I have a rich dataset with values for the variable $A$ which is equal to ...
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5answers
341 views

Intuitive explanation of convergence in distribution and convergence in probability

I am quite unsure of the intuitive difference between a random variable converging in probability versus a random variable converging in distribution. I've read numerous definitions and mathematical ...
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36 views

Clarify terminology regarding truncated and censored distributions [duplicate]

I'm looking for clarification on the definition of truncated distributions and on terminology for censored distributions and truncated distributions. I recently had a [dialog on SO][1] regarding [a ...
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1answer
21 views

Developing probability distributions

An event occurs, and after this event has occurred there is a set of conclusions which can be drawn. All of these conclusions have results which are distinct. I am trying to keep this as general as ...
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16 views

Learning a spatial function

I have some observations of a variable y, that varies spatially. For each observation, I also have a lat, long tuple. I have some 50 or so observations. Besides conducting some exploratory analysis ...
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2answers
143 views

Why is the p-value distribution not uniform?

While learning on the q-value http://www.totallab.com/products/samespots/support/faq/pq-values.aspx I saw that, under the null-hypothesis, the distribution of the p-value is expected to be uniform. ...
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How to prove brand preference?

Real Case: We have survey data on which of 6 brands is preferred by customers in each of 4 different product usage situations. Our customer segment is well defined and we think we have a ...
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15 views

Comparing 5 pt Likert scale answers from two different groups (not the same size) [duplicate]

I have ~150 responses to a number of 5pt Likert scale questions along with lots of demographic data about my respondents. I'm now trying to divide my respondents into groups based on their demographic ...
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31 views

How to estimate mean and standard deviation of a normal distribution from noisy data?

I have $n$ observations, $x_i$ following a normal distribution. I would like to estimate $\mu$ and $\sigma$ from my samples. Normally I would simply estimate $\mu=(\sum x_i)/n$ and $\sigma^2=\sum ...
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rate of convergence of sample mean

Law of large number ensures the convergence of sample mean to population mean. But it does not tell about the rate of convergence. Now CLT tells about the rate of convergence. Then what is the ...
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Defining the probability distribution of a Random vector given the probability over a “sub-vector”

Suppose I want the probability distribution over a random vector $X={X_1 ,X_2 ... X_n }$. What I already have with me is the distribution over a subvector $X_i , X_{i+1}...X_m$, $m<n$ which I ...
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1answer
18 views

Using stat methods on summary statistics

Is it ok to use statistical methods on summary statistics, as they're random variables? I ran into an interesting problem while working with a client, but will try to keep it very general as the ...
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1answer
12 views

Frailty Models: Gamma distributed frailty and Inverse Gaussian distributed frailty

In modelling of frailty using assumptions distributions of frailty are Gamma distributed frailty and Inverse Gaussian distributed frailty. Frailty is unobservable risk factor of mortality. How to ...
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1answer
32 views

How to calculate probability that another player has a card

In a poker game, how would we calculate the probability that another player has at least one certain card? Lets say that there are five other player, there are four cards in middle of the table, and ...
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28 views

How is the probability of Weibull Distribution exceed $1$ for some value? [duplicate]

Here is R code which show that probability of Weibull distribution is $1.7$ for some value $t$. But as far i know probability lies between $0$ and $1$. How is it possible ? R code: ...
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1answer
28 views

marginal conditional distribution from MCMC output [duplicate]

I have a MCMC sampler that targets $$\mathbb{P}(U_1,U_2,...U_n \mid G(U) \leq 0)$$ where $U=(U_1,U_2,...U_n)^T$. I realize now I am more interested in estimating the conditional density $$p_k = p(u_k ...
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35 views

Variation on the urn problem and frequency distribution

I have $6$ machines each producing different coloured balls. The balls are mixed together in a large vessel. Groups of $6$ balls are extracted at random for packing. Each pack will therefore have a ...
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1answer
35 views

KL divergence between a gamma distribution and a lognormal distribution?

Is there a closed-form formula for the KL divergence $D_{KL}(X,Y)$ where $X \sim \mathrm{Gamma}(k,\theta)$ and $Y \sim \mathrm{LogNormal}(\mu,\sigma^2)$ ? Many thanks.
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1answer
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how is the 2/3 rule effected by a skewed distribution with a zero point? [closed]

If my SD makes one standard deviation below zero and negative, where the data does not go, then does the 2/3 rule stand with 68% between zero and 1 SD and is the missing negative data -1 SD and - 2 SD ...
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35 views

comparing probability histogram

I have two probability histogram samples. I know there are methods(i.e KS test etc) out there to compare histograms but I am trying to compare through simple sum of absolute difference between these ...
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2answers
70 views

how can I test if a sample was created from a specific Discrete Distribution

How can I test if a sample was created from a specific discrete distribution. For example, if I have the following distribution 1- 0.2 2- 0.5 3- 0.3 and I ...
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Proof that the probability of one RV being larger than $n-1$ others is $\frac{1}{n}$

This is a follow-on from my previous question about samples from a distribution. Suppose $X_1 \ldots X_{n-1}, X_n$ are random variables all following some fixed distribution $D$. How do I prove that ...
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1answer
47 views

How to find the distribution of a function of multiple, not necessarily independent, random variables?

If $Y$ is a random variable defined as $Y=g(X_1,X_2)$, where $X_1$ and $X_2$ are two different random variables whose distributions are known (say with pdf's $f_{X_1}$ and $f_{X_2}$), how do we find ...
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52 views

When is calculating probability based on a poisson distribution preferred over a binomial distribution?

I'm trying to understand why a poisson distribution may be preferred over a binomial one when modeling binary cases. Is there a case where you can't use a binomial distribution to solve a problem ...
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To BIN or not to BIN a continuous data to get a Fragment Size Distribution ?

I have a data set in excel of almost 6000 entries (quantitative and continuous => P(X=x)=0, I mean the possible values for my continuous random variable X are uncountably many). Each point will ...
2
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1answer
46 views

Get probability distribution function from density function

For a given density function, how does one find its distribution function? For example, I have a density function: $f(x)= \begin{cases} t ^2 / 9 & \text{if } t \in (0,3)\\ 0 ...
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2answers
42 views

Data Sampling while preserving the underlying distribution

I have a large 10-15 dimensional data set with close to 10 million points. I want to test some algorithms over a chunk of this data. But I don't want the character of this data to be lost by selecting ...
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what is the name of distribution similar to von mises distribution

I am wondering whether the following PDF is a named distribution. Over the interval $0< \theta < \pi$, the PDF of the distribution is written as $$ P(\theta) = \frac{2^{-n/2} k^{n/2} e^{k \cos ...
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1answer
21 views

Interpretation of cartesian product of the support of marginal distribution

Suppose we have a multivariate data set, $s = (s_1, s_2, ... s_p)$ and each $s_i$ is distributed with a distribution that has finite support (we'll call each $s_i$ a "source"). Let us denote the ...
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1answer
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Finding a distribution for data in $\mathbb{N}_0$

Suppose, we have a set of 10,000 individuals. Each individual falls into exactly one of 200 categories. [Edit: The categories are phenotypes (different potential outcomes) of the one property that is ...
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1answer
28 views

Question about posterior mean calibration

I'm reading the article "Prior distributions for variance parameters in hierarchical models" by Andrew Gelman(link). This is an extract that I don't understand very well: Posterior inferences can ...
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40 views

Generating a skewed distribution given the median and left and right “$1\sigma$” limits [duplicate]

Edit: I found a solution to the problem, which is at the bottom of the post. I'm going to leave the post as it is in case someone else encounters a similar problem! I was banging my head to a ...
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Doubt about conditional conjugate priors

I've just read the definition of conditional conjugate prior in this discussion but I have still some doubts. According to the definition given, it seems that the prior distribution of $\theta$, ...