A distribution is a mathematical description of probabilities or frequencies.

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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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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 ...
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308 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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Finding the distribution of $\bar{Y}_{1+} - \bar{Y}_{2+}$ in randomized block design

I'm trying to find the distribution of the following but I am having quite a hard time as Mathematics/Statistics has always been difficult for me. Here is the question: Consider the Randomized Block ...
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1answer
26 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 ...
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7 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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6 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 ...
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10 views

Trap 66 (post condition violated) error at WinBUGS

I want to analyze a multilevel differential model in WinBUGS. The model is as below. When I run the model I receive ...
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2answers
70 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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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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16 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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34 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 ...
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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
19 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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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 ...
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11 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 ...
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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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54 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
51 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
23 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
26 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: ...
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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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19 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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48 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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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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58 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
44 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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25 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 ...
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21 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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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
38 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 ...
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1answer
26 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 ...
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22 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
23 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 ...
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Testing GLMM residuals against specific families and link functions (R)

When running a GLMM in R with family=gaussian and link=identity, it's easy enough to test whether normality and homoscedasticity ...
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30 views

Data structure for Inverse Cumulative Distribution when columns are *NOT* separate variables

I am trying to structure data to conduct a Frequency analysis and output an Inverse Cumulative Distribution histogram for a biomechanics study. The goal is to compare 4 devices with respect to their ...
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1answer
31 views

Jensen Shannon Divergence vs Kullback-Leibler Divergence?

I know that KL Divergence is not symmetric and it cannot be strictly considered as a metric. If so, why is it used when JS Divergence satisfies the required properties for a metric? Are there ...
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1answer
22 views

Why is the posterior probability for the total number of carts being 60 about 0.006?

I’m reading Think Bayes by Downey and exploring the famous locomotive problem. After seeing cart 60 of a train zoom by, I’m trying to determine the posterior probability of there being X carts in the ...
2
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1answer
35 views

Empirical Distributions

I am working with a small data set that is clearly non-Gaussian. This data is bound within a fairly narrow range. I have been asked to estimate the quantiles of the population that this data is from. ...
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1answer
45 views

Using R to calculate qt (t-dist) using qf(f dist) help?

I am having quite some trouble using R to calculate, say, qt(0.975,6) using qf instead of qt. I know the relationship between the t-distribution and the f-distribution which I understand as follows: ...
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1answer
203 views

Why don't we use the unbiased sample variance to calculate the standard error?

The standard error is an approximation of the standard deviation of the sampling distribution of the sample means. The real standard deviation of the sampling distribution, $\sigma _{\bar x}$ is: ...
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Difference between two data distributions

I have the following problem: I have two datasets: A and B. From each of the datasets, I extracted the same features. I also know the data labels. So, I would like to perform 10-fold CV to see how a ...
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17 views

Mean in Cumulative frequencies distribution

Monthly expense Cumulative Freq. up to 50 7 up to 80 25 up to 120 49 up to 200 58 over 200 60 Calculate ...