A distribution is a mathematical description of probabilities or frequencies.

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What is the distribution of the random variablle [on hold]

An aircraft passenger is tested to check if he is infected by H1N1 virus.
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261 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, ...
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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 ...
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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 ...
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0answers
19 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. ...
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30 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 ...
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2answers
131 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. ...
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1answer
44 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.
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12 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 ...
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19 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 $m_w$ ...
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31 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 ...
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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 ...
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9 views

Finding a percentile of joint, correlated distributions [on hold]

To give an economics example, lets say I have a distribution of House Price Indices (HPI) and Unemployment Rates - both non-normal and correlated to each other. I want to know how to calculate the ...
6
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1answer
387 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 ...
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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
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1answer
31 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, ...
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0answers
7 views

Custom kernel in R [on hold]

There are many kernels in common use, apparently. How can I implement a custom kernel in R? For example, is there a density-like command that takes a kernel ...
4
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2answers
73 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 $Y_1=\frac{X_1}{X_2}$ ...
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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. ...
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0answers
17 views

Normal distribution probabilities [closed]

Suppose that one out of every ten plasma televisions shipped has a defective speaker. Out of a shipment of n=400 televisions, find the probability that there are: a. at most 40 with defective ...
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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?
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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
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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 ...
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1answer
21 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: ...
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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 ...
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1answer
30 views
+50

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 ...
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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 ...
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60 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 ...
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1answer
55 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
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1answer
24 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 ...
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1answer
21 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 ...
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2answers
49 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, ...
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1answer
28 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
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1answer
21 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 ...
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20 views

prior predictive distribution negative binomial in R

I have a prior distribution Gamma(1.71,1.05) from a Poisson(2.2), and I know that the prior predictive distribution will be a Negative-Binomial of Gamma parameters i.e. Neg-bin(1.71,1.05). I would ...
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1answer
50 views

Regession diagnostics

Why is it necessary to have the number of independent variables less than the number of data points in a regression setup? If suppose, it is the other way round, i.e. the number of independent ...
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0answers
10 views

Distribution of Trace of non-centered Wishart matrix

I am looking for the distribution of trace of the non-central Wishart matrix with different variations along different axes. Is there a general formula for such distribution? If not, is there a ...
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1answer
19 views

Numerical problem in own code to derive pdf of Tukey g

Given a $X\sim N(0,1)$ and $g>0$, the random variable $$Y=\frac{\exp(gx)-1}{g}$$ is said to have a Tukey $g$ distribution with parameter $g$. I wrote the following R code to get the pdf of the ...
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59 views

Maximum minus average?

I have some legacy code that is doing some stats that I can't figure out. It's taking the maximum value of a data set, and subtracting the average of the data set. I've tried looking into what this is ...
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1answer
45 views

Estimating age distribution from first names

Is it possible to estimate an age distribution of a specific population (e.g. actors, customers, etc.) from a list of their first names? Given that data of the number of individuals grouped by birth ...
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27 views

Union of independent events

Let $ A_1, A_2, A_3 $ be independent events with probabilities $ \frac 12,\frac13,\frac14,$ respectively. How to compute for $P(A_1\cup A_2 \cup A_3).$ My solution starts from using the probability ...
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When do we “bootstrap” and then use “t-dist” versus just using “t-dist”?

I'm taking a Data Analysis class on Coursera, and we are learning about bootstrapping when you have a small sample size (>30). What I don't understand, is when do you bootstrap and then use the ...
2
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22 views

Truncated Gamma distribution parameter estimation

I need to estimate the parameter of a Gamma distribution form the data, but I only have samples from 0.05 to 3 (most of the samples are concentrated here). I tried MLE but due to the truncation is ...
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34 views

Density distribution of outcomes of 2 dice rolled [duplicate]

This question is related to: http://stackoverflow.com/questions/26153925/r-studio-a-histogram-with-a-bar-for-each-frequency-value Amongst the outcomes of 2 dice rolled, the chances of 2 are equal to ...
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1answer
40 views

R - MLE of modified Champernowne density

I've come across an article (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=704903), in which author wrote about maximum likelihood estimates of parameters in the so called modified Champernowne ...
2
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1answer
27 views

How to draw these t-statistics in R

When determining the necessary sample size for a t test of a difference of mean of two populations a good rule of thumb is typically $$ n = 16 {\sigma^2 \over ...
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1answer
63 views

What probability distribution to use for a variable X for which only an estimate is known?

I demand that... X must be in the interval (0,1). The estimate given is the expectation of the unknown distribution. EDIT: Kind of heavy as an assumption, I would suspect. Would it be possible to ...
0
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1answer
28 views

GMM estimation of linear regression with intercept restriction

Say I have a time series regression as follows: $$y_t = a_i + \beta_i x_t + \varepsilon_t^i \ \ ; \ \ t = 1, 2, \cdots, T \ \ \text{for each } i$$ Now say I impose the following restriction on the ...
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38 views

Distribution for $Y = \sqrt{X_1^2 + X_2^2}$, when $X_1, X_2$ are dependent and normally distributed with different variance? [duplicate]

Is there a closed form distribution for the transformation given by $Y = \sqrt{X_1^2 + X_2^2}$, when $X_1, X_2$ are jointly normal but dependent random variables with different variance? OBS: I know, ...
2
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1answer
25 views

Sampling under assumption of log normal distributed data with sample mean and standard deviation

I have the sample mean and the sample standard deviation of income calculated from individual tax data of all citizens in country (let's call this data X). I do not have access to this tax income ...