Tagged Questions

A distribution is a mathematical description of probabilities or frequencies.

learn more… | top users | synonyms (1)

0
votes
1answer
15 views

quantile regression with e.g. gamma distribution and log link

I have a basic question about quantile regression (I'm new to it): Why doesn't it seem possible to do a quantile regression with a specified family (e.g. gamma) and link function (e.g. log), as in a ...
1
vote
1answer
41 views

More flexible bell shape than log normal distribution

I am looking for a very flexible bell shape function, with asymmetry on both sides of the bell, also with the possibility that the left arm of the bell had a milder slope while the right had a steep ...
0
votes
1answer
40 views

Randomly constructing a probability distribution for simulation

For a simulation, I want to construct the probability distribution of a random variable $X_k$ that takes only finite number of values $x_1, \cdots, x_N$. I have to assign values to each probability: ...
1
vote
0answers
19 views

Probability of seeing observation > x based on historical observations

I have a number of historical observations, let's say they represent the number of car accidents per day for a certain region. I don't know what the true distribution or probability is, but want to ...
3
votes
1answer
72 views

Sum of truncated normal with two normal distributions

Suppose I have one normal distribution $W \sim N(\mu_{w},\sigma_{w}^2)$ with a known cuttoff point (percentile) on this distribution called $c$. The first part of $W \in [-\infty,c[$ needs to be ...
3
votes
1answer
26 views

asymptotic distribution of joint random variables

I am trying to understand the asymptotic distribution of the following expression under normality $$ {\hat \sigma \hat S - \sigma S} $$ Where $\sigma$ and $S$ are the population standard deviation ...
0
votes
0answers
18 views

Distribution of average and median of a random variable [duplicate]

Suppose I have some random variable, which is defined by certain distribution (e.g. triangle or normal or some other). Suppose I do $N$ independent measurements on this random variable and then ...
7
votes
0answers
76 views

What Ratio of Independent Distributions gives a Normal Distribution?

The ratio of two independent normal distributions give a Cauchy distribution. The t-distribution is a normal distribution divided by an independent chi-squared distribution. The ratio of two ...
0
votes
1answer
28 views

How to bound a probability with Chernoff's inequality?

In my class, we were given Chernoff's inequality as $$P(X\le -t) \le e^{(-(\lambda*t - \log( E(e^{-\lambda*x}))))}$$ $$P(X\ge -t) \le e^{(-(\lambda*t - \log( E(e^{\lambda*x}))))}$$ It says that to ...
4
votes
1answer
69 views

Why is the sampling distribution of variance a chi-squared distribution?

The statement The sampling distribution of the sample variance is a chi-squared distribution with degree of freedom equals to $n-1$, where $n$ is the sample size (given that the random variable of ...
4
votes
1answer
75 views

Unintuitive interpretation of probabilities when doing logistic regression

The observations in my dataset can be split in two classes. The observations in class 1 are for sure correctly labeled. The observations that has been designated to class 2 have a huge percentage of ...
0
votes
0answers
17 views

Performing a comparison between a sample distribution and population distribution in excel or nvivo

What is a relatively easy stats test to perform in excel/nvivo that is arguably reliable and valid and a good method for comparing a sample's normal distribution with a population's normal ...
0
votes
0answers
10 views

reduce joint probability distribution of an image

I'm new in probabilistic graphical model. I'd like to know how the number of parameter needed to describe fully joint probability distribution of an image 10000by10000 that each pixel is 8byte (255). ...
0
votes
1answer
30 views

Expectations of the geometric mean of a random sample from a uniform distribution

If I have a random sample of size n from a Uniform(0,1) and I define the geometric mean as G can anyone give me insight in to how I can find the expected value of G, E[G]? Once I can get my head ...
2
votes
2answers
64 views

What characteristics should a distribution have for CLT to work?

If a "distribution" is constant, then CLT is not going to work, obviously. However, even if it is not a constant, but variance is very small, the distribution of the sums is still not normal. For ...
0
votes
0answers
13 views

P value distribution skew & hypothesis testing

On this page it says ...if HA holds, the p-values have a distribution for which values near 0 are more likely than values near 1. However the p-values may have a distribution that is not ...
1
vote
1answer
38 views

Statistical measure of international diversity

I've got a large collection of geotagged tweets, each linking to an article from a given author. For each author, I'd like to derive a number that describes how diverse is their list of tweeting ...
8
votes
2answers
227 views

What is a log-odds distribution?

I am reading a textbook on machine learning (Data Mining by Witten, et al., 2011) and came across this passage: ... Moreover, different distributions can be used. Although the normal ...
3
votes
0answers
20 views

Distribution of a binary matrix times a Bernoulli vector

Suppose we have the vector $\mathbf{Y} = (Y_{1},\ldots,Y_{n})$ where $Y_{i} \sim \textrm{Bernoulli}(p_{i})$ independently. For the applications I have in mind, $n$ will typically be several thousand, ...
-2
votes
0answers
13 views

What is the distribution of the random variablle [closed]

An aircraft passenger is tested to check if he is infected by H1N1 virus.
7
votes
4answers
491 views

How to sample when you don't know the distribution

I'm fairly new to statistics (a handful of beginner-level Uni courses) and was wondering about sampling from unknown distributions. Specifically, if you have no idea about the underlying distribution, ...
0
votes
0answers
7 views

Determine accuracy distributions from measurements

Is it possible to determine the distribution of a certain measurement accuracy if one have a serie of measurements, carried out under fluctuating conditions, and the accuracy of the measurement ...
1
vote
0answers
6 views

Quantifying Reliability of Qualitative Testing

If a visual grading system is implemented to calculate the correlation between exterior and interior conditions (i.g., good, medium, bad), and a sample is taken from a known population to test the ...
0
votes
0answers
21 views

Sum of two independent Weibull Random Variable

If $Y_0$ and $Y_1$ both have Weibull distribution i.e. $Y_0 \sim Weibull(\lambda_0,\beta_0)$ and $Y_1 \sim Weibull(\lambda_1,\beta_1)$ then what will be cumulative density function of $Y_0+Y_1$, i.e. ...
1
vote
0answers
33 views

What is relationship between Fisher Information and Variance in natural exponential Family?

I know that $Var(\hat\theta)\geq 1/I(\theta)$ where $I(\theta)$ is Fisher information. Let take an example of natural exponential family with density $f(x)=\lambda\exp(-\lambda x)$. In this case we ...
5
votes
2answers
143 views

What is the probability distribution of $1-\text{mean}(|A-B|)$ where $A$ and $B$ are independent U(0,1)?

I'm not well versed in statistics so I'm not sure if my question is worded exactly correctly but basically here's the problem I'm trying to solve: imagine you have two equal sized arrays of size n. ...
1
vote
1answer
46 views

bivariate normal density function

I know how to show the first part, but I am confused about the second part, how to express the relationship between the two? Any hint, advice or suggestion is appreciated.
1
vote
0answers
13 views

Distribution of large set of fold changes

My background in stats is limited to a few undergraduate classes. However, I have a question that intuitionally seems to have a statistical answer. Let me describe my intuition first. I do systems ...
0
votes
0answers
20 views

Hypergeometric distribution and its continuous counterpart

I'm modeling an urn without replacement. I'm drawing $m$ balls from an urn containing $p_w$ white balls and $p-p_w$ black balls and I want to know what is the probability that I draw at least $m_w$ ...
1
vote
0answers
35 views

Compare 2D maps

I have a bunch of samples to compare. Each sample is composed of 30,000 cells (dots) for which I computed 2 dimensions (30,000 x 2 matrix). Each dot represent the expression of two parameters for a ...
1
vote
0answers
20 views

Unique matching for quantiles from one half of the density to a subset of the other half?

I am interested in finding the median absolute distance to quantiles. So, for $Q_\alpha$ the $0 \le \alpha \le 1$ quantile, I would like to find $Q_\gamma^*$ such that $Q_\gamma^*$ satisfies ...
6
votes
1answer
414 views

Why should we use t errors instead of normal errors?

In this blog post by Andrew Gelman, there is the following passage: The Bayesian models of 50 years ago seem hopelessly simple (except, of course, for simple problems), and I expect the Bayesian ...
1
vote
1answer
41 views

Probability distribution of Y in regression?

I'm trying to predict the probability distribution of $Y$ given $X_0, X_1, ...$ with a nonlinear regression. The probability distribution of $Y$ is likely not normal. So far, I've set up and trained ...
0
votes
1answer
35 views

Undefined real result error at WinBUGS

I am currently working on my thesis and interested in estimating a multilevel differential item functioning model and I using at WinBUGS. Until I had done model check-up, there are no errors. However, ...
4
votes
2answers
76 views

Problem obtaining a marginal from the joint distribution

Suppose $X_1$ and $X_2$ have the joint pdf $$f_{X_1,X_2}\left(x_1,x_2 \right)=4x_1 x_2,\quad\text{for}\quad 0<x_1<1, 0<x_2<1$$ From that I found the joint pdf of $Y_1=\frac{X_1}{X_2}$ ...
0
votes
0answers
11 views

How to calculate the distribution of spend on options of a new car

I have a bit of a real world conundrum and I have reached the limited of my knowledge. The problem in question relates the distribution of the amount of money spent on options when buying a new car. ...
1
vote
0answers
35 views

z scores, highest percentile ranking, different distributions

Let a value $x$ have a z-score of (say) $+0.10$. With respect to which distribution(s) can $x$ have the highest percentile ranking: normal, positively skewed, or negatively skewed?
1
vote
0answers
21 views

Sampling from a distribution with a margin of error

A survey of a population is taken using sampling. It is determined that 70% prefer option A and 30% prefer option B with a margin of error being 5%. Normally when simulating the process with the ...
2
votes
1answer
17 views

How to choose a kernel for KDE

There are a lot of kernels available for a univariate KDE. R uses normal by default, but the efficacy discussion seems to support the use of Epanechnikov. What should influence kernel choice for ...
0
votes
1answer
25 views

Stable Distribution Log-likelihood and AIC values

I have used the stableFit function from the fBasics package to come up with parameters (alpha, beta, gamma, and delta) for a stable distribution as you can see below: ...
0
votes
0answers
10 views

Meta-analysis - generating null distributions of test statistics.

I'm having trouble obtaining p values for effect sizes from a meta-analysis because the distribution of t-statistics is not normal. The analysis involves eight studies, each containing measurements ...
0
votes
1answer
33 views

Help interpret Distribution of Wlan Signal Strength Measurements

For my project I need to evaluate large amounts of wlan signal strength measurements. Measurement is in dBm which is a logarithmic scale for milli watt (so every 3dBm the milliwatts double) where ...
1
vote
0answers
27 views

Standard Deviation and Variance

Can someone help me with this question because I'm not sure of how to do it exactly: There are two routes for a worker to get to his office. Both the routes involve hold ups due to traffic ...
0
votes
0answers
62 views

Distributions where higher variance in sample estimates leads to smaller loss when estimating mean

Let's say I have an unknown distribution a. I do not know the shape, mean or variance of this distribution but I have access to another distribution ...
1
vote
1answer
58 views

Parameters for a Levy distribution in R

Can someone help me figure out how I can get parameter estimates for a levy distribution using R? Unlike the normal distribution and Student T distribution which has functions ...
2
votes
1answer
30 views

Mean and Variance for a sum of independent weighted bernoulli random variables with different probabilities of success

Suppose $Z_i$ are independent Bernoulli random variables with differing probabilities $P_i$. Also suppose weights $W_i$ are positive and constant. Can you tell me the mean and variance for the ...
0
votes
1answer
22 views

Frequency distribution and number of samples

Suppose I have a frequency distribution of some process of f_n(x) that is based on n samples, with ...
1
vote
2answers
50 views

Ratio of CDFs $F(x)/x$ property

In my research project is useful to classify cumulative distributions functions of random variables with support in $[a,b]$ with $0\le a<b\le+\infty$ depending on whether the ratio, ...
-2
votes
1answer
29 views

How to simulate a prior for a Poisson distribution? [closed]

I would like to simulate random variates from a Poisson distribution to act as prior for a predictive model, but I fail to do it correctly. Here is my attempt: ...
2
votes
1answer
23 views

Distribution of Sample Means Compared to Population Mean

Assumptions I have a population (n=5000) and I know everything about it (all point values, mean, standard deviation, etc.) From this, I will sample 1000 items. I can calculate the mean of the sample ...