A distribution is a mathematical description of *probabilities* or *frequencies.*
2
votes
1answer
22 views
Value at Dmax from Kolmogorov-Smirnov Test in R
I am comparing two distributions using the Kolmogorov-Smirnov test [ks.test()] in R and would like to know what the numerical value is where Dmax occurs. It's not in the output of ks.test() as far as ...
1
vote
1answer
44 views
How to adjust the shape of a gamma distribution
I have a dataset (vector) to which I would like to fit a gamma distribution (x), which given the shape seems reasonable. The charts below show the histograms of the two dataset: vector and x.
The ...
0
votes
2answers
33 views
Transformation of leptokurtic data
I'm working on my BSc dissertation currently. One of my variables is created using the ratio of one continuous (mostly) normally distributed variable to another.
The distribution of ratio is very ...
0
votes
0answers
26 views
Derivation of the pdf of the Beta distribution [duplicate]
$$
f(x)= \frac{x^{(\alpha−1)} * (1−x)^{(\beta−1)}}{\mathcal B(\alpha,\beta)}
$$
Questions:
How can we derive this famous pdf?
What is the intuitive meaning of the Beta distribution? (Please ...
0
votes
2answers
32 views
Finding the distribution when the observations are dependent
How do we find information about the distribution of a variable in presence of dependency among our observations? This dependency is coming from measuring the variable on the same group of subjects ...
8
votes
0answers
84 views
Product of two independent random variables
I have a sample of about 1000 values. These data are obtained from the product of two independent random variables $\xi \ast \psi $. The first random variable has a uniform distribution $\xi \sim ...
2
votes
2answers
38 views
Applying Bayes: Estimating a bimodal distribution
I'm trying to estimate a bunch of bimodal distributions, i.e. two means and two standard deviations, based on a variable number of inputs. If no input is present, a constant value should be returned. ...
1
vote
1answer
46 views
Calculating the std dev of a 30 team league with each team having a 50% chance of winning
I just want to preface this with the fact it is not a home work question. I am also not a stats person so I am not sure even how to start with calculating this, what it is called or where to look. ...
1
vote
0answers
29 views
How to decide whether the distribution is unimodal or bimodal in grain size distribution?
In the examples given at this link, I am not able to decide whether the distribution is unimodal or bimodal. I think it is in between unimodal and bimodal, but I do not know if this kind of class ...
1
vote
2answers
36 views
The difference of two discrete uniform variables taken modulo. Is still uniform?
I have a uniform distribution that generates from the $\mathbb{Z}_q$ (so I have integers from the interval [$-q/2$, $q/2$). Then I subtract one from the other and take the result modulo $q$ (so again ...
0
votes
0answers
19 views
Changing prior for a regression model
I have a regression model trained on a particular output distribution (for example N(0, 1)). I now have to do a prediction on a test set, with a caveat that I know that the distribution of the test ...
0
votes
0answers
31 views
Bias in EM estimation for a mixture of normal distributions
Are the parameter estimates for a mixture of two normal distribution using EM algorithm biased or unbiased?
More specifically, if I use the EM-algorithm to obtain ML estimates of $μ_1$, $μ_2$, ...
3
votes
0answers
38 views
Ratio of sum of Normal to sum of cubes of Normal
Please help me to find the limiting distribution (as $n \rightarrow \infty$) of the following:
$$ U_n = \frac{X_1 + X_2 + \ldots + X_n}{X_1^3 + X_2^3 + \ldots X_n^3},$$ where $X_i$ are iid $N(0,1)$.
0
votes
1answer
48 views
How to calculate the variance of the GED distribution?
The density of the GED distribution is given by
\begin{align}
GED(l;\mu,\beta,\nu)&=\frac{\nu \exp\left[-(\frac{1}{2}) \left|\frac{l-\mu}{\beta \lambda}\right|^\nu \right]} {\lambda ...
0
votes
1answer
82 views
How to handle Regression data thats not linear
I'm new to stats and am using Python 2.7 to fit a regression model (Random Forest). When I plot the percentile plot of the prices before and after a log ...
0
votes
1answer
47 views
Robust distribution fitting?
I'm trying to fit a Johnson Unbounded distribution to a set of financial data with kurtosis and skewness, and also outliers. I started using Maximum Likelihood Estimators (MLE) but one outlier has too ...
0
votes
0answers
23 views
Distribution with fifth order moment?
I understand that the fifth moment of a distribution gives finer control of the asymmetry of the tails.
Please can you give me a reference to a distribution that can handle 5 moments (such as the ...
0
votes
0answers
17 views
Distribution terminology: distribution fitted to 1) measurements vs. 2) randomly-generated values
I am fitting a distribution to two distinct types of data: 1) randomly generated values from known distributions (e.g., using rnorm(), ...
2
votes
0answers
30 views
Manipulating Binomial Distribution
Recently, I've been reading Yudi Pawitan's book, In All Likelihood.
In the book, there's a section on profile likelihood; the methods explored in this section are subsequently applied to some data on ...
4
votes
2answers
140 views
Help me understand Bayesian prior and posterior distributions
I'm taking a course on Bayesian statistics but my mind seems rather incapable of coping with it. I've got here a very specific nut I've tried to crack open all day. Gah.
In a group of students, there ...
1
vote
0answers
32 views
R Command to fit a standardized generalized hyperbolic distribution to data?
I wanted to ask, if there is a R command, which fits a standardized generalized hyperbolic distribution to my data? I know there is one, which fits a non-standardized, but I want to fit the ...
2
votes
0answers
13 views
Computing values of the Lilliefors c.d.f
How up-to-date is the assertion in this Wikipedia article that tables of the Lilliefors distribution have been computed only by Monte Carlo methods?
(It would seem preferable to use deterministic ...
1
vote
1answer
40 views
What is the distribution of the ratio of two t-distributed random variables?
x is t-distributed;
y is t-distributed.
How is x/y distributed?
Does it have a closed-form formula?
2
votes
0answers
32 views
Fitting mixture distributions and computing goodness-of-fit?
This question is a follow-up from a previous question of mine here. Thanks to @Glen_b, @gung and @rbatt for teaching me so many new things yesterday. It was mentioned in passing that mixture ...
2
votes
0answers
15 views
Selecting priors for logistic functions
I have this confusion related to how to select priors for a logistic regression
By Bayes theorem
$P(\theta|D) = \frac{P(D|\theta) * P(\theta)}{P(D)}$.
Now my likelihood $P(D|\theta)$ is given by ...
1
vote
0answers
28 views
Help modeling school consent rate changes after an intervention
I have # of students consenting to be vaccinated and # of students eligible to be vaccinated for 77 schools in three school years (2010/11, 2011/12, and 2012/13). Between 2011/12 and 2012/13 there was ...
1
vote
0answers
16 views
Characterizing uncertainty in empirical PMF of unknown discrete random distribution
Suppose a discrete random distribution $X$ which takes integer values in some small (but not binary) range, e.g. $[0, 255]$ and whose true pmf is unknown (however, the null hypothesis is that it is ...
1
vote
1answer
27 views
How to do pre-election polling with statistics? (discrete results)
In statistics, it is taught about samples that can have some range of numbers as their values. However, in election like presidential election, there are only several candidates to choose. In that ...
0
votes
1answer
54 views
What method can be used to test if three or more categorical sample data sets are from the same distribution?
I have three data sets like this:
data1: {A, A, B, C, D, ..}
data2: {A, B, B, C, E, ...}
data3: {A, C, D, D, E, ...}
How do I test if these three data sets are from the same distribution?
0
votes
0answers
23 views
Relationship between mutual information and change of variables
On pages 11-12 of this tutorial, equation 28
$$ I(y_1,...,y_n) = \sum_i H(y_i) - H(x) - \log | \det(W)|$$
draws a connection between mutual information and an invertible linear transformation for $y ...
4
votes
0answers
37 views
How do I identify the “Long Tail” portion of my distribution?
I have a number of series that would typically be described as normal skewed or Gamma distributed. For example, say I have a group of customers and have calculated their spend over a fixed length of ...
1
vote
1answer
40 views
Covariance of a set of uniformly distributed unit vectors?
I have a set of uniformly distributed unit vectors within a "cone" (essentially a subset of a uniform distribution on the unit sphere, as described here). I've found how to get the covariance matrix ...
1
vote
1answer
56 views
How to estimate true value and 95% bands when distribution is asymmetrical?
I have a set of results of independent measurements of some physical quantity. As an example I give here real expermental data on methanol refractive index at 25 degrees Celsius published in ...
5
votes
2answers
354 views
What distribution does my data follow?
Let us say that I have 1000 components and I have been collecting data on how many times these log a failure and each time they logged a failure, I am also keeping track of how long it took my team to ...
1
vote
1answer
28 views
Mean and variance of number of tries required
So the question states that I'm trying something with an 85% chance of success, if I don't succeed I try again until I do. What is the mean and variance of the number of tries necessary until I ...
0
votes
2answers
62 views
Simple homework question about normally distributed variables
The question states:
Consider a set of random variables $X_i$, where $i=1,...n$. Each $X_i$ is
normally distributed with mean $0$ and variance $1$, i.e. $X_i$ are $\mathcal N(0,1)$.
What is ...
2
votes
0answers
21 views
Compendium or catalog of compound distributions?
Does anyone know of a good compendium or catalog of compound distributions, or finite mixture representations of those distributions?
I am trying to find out to what extent the common ...
0
votes
0answers
15 views
Approximating a compound distribution with a mixture: required n?
Suppose you have two continuous distributions, g(φ; θ) and f(θ; x), where φ and θ are parameter vectors of g and f, respectively, and the values of θ generated by g are all legal values for θ in f(θ; ...
0
votes
1answer
56 views
Fitting GEV to non-stationary time series of extremes (general stationarity question?)
I'm fitting the generalized extreme value distribution (GEV) to a series of annual maxima of variable $X$. $X$ exhibits a linear trend.
When I fit the GEV to $X$, I think I have the choice to
Use ...
1
vote
1answer
45 views
Standardized generalized hyperbolic distribution
I am interested in the standardized version (mean zero, variance one) of the generalized hyperbolic and the hyperbolic distribution. I want to include this in my analysis and therefore I need the ...
0
votes
1answer
29 views
Does the GB2 distribution have a conjugate prior?
I did a bunch of searches on this but did not find anything conclusive. Does the generalized beta distribution of the second kind, also known as the generalized beta prime distribution, have a ...
0
votes
1answer
50 views
Conditional probability distribution estimation from numerical data
I am trying to come up with a conditional probability distribution $P(B|A)$, over the continuous variables which look something like this:
...
0
votes
0answers
43 views
Bayesian inference over an unknown variance
I am observing a random variable $X \in \mathbb{R}$ which can be assumed to be normally distributed with mean $\mu$ and variance $\sigma^2$. I am interested in fitting a posterior distribution over ...
0
votes
0answers
15 views
Distribution of linear model parameters when the outcome variable values are Fisher Z transformed correlation coefficients
I am trying to develop a method for comparing individual correlation coefficients from multiple participants from different groups having performed different conditions of a task.
In terms of ...
0
votes
0answers
48 views
Bounded response variable [-1;1] - Should I transform it?
I am planning to use two response variables. One is bounded between 0 and 1, and I guess I can use a binomial (or related) error structure. The second variable is bounded between -1 and 1. I am not ...
0
votes
1answer
71 views
Correct formula for standardized Student's-t distribution
I am wondering about the correct formula of the standardized Student's-t distribution. In the rugarch package on page 15 it is given as:
whereas from a book (Carol Alexander Market Risk Analysis, ...
0
votes
1answer
68 views
How to derive a confidence interval from an F distribution?
So, this is the question I'm working on:
Suppose we observe a random sample of five measurements: 10, 13, 15, 15, 17, from a normal distribution with unknown mean $µ_1$ and unknown variance $σ_1^2$. ...
1
vote
0answers
34 views
Analysis of computer software performance
I am currently collecting data from a software system that draws conclusions about the nature of certain structures in medical CT chest scans. Structures in the chest can be classified into four ...
3
votes
0answers
40 views
Likelihood analysis for exponential distribution
Assume a collection of independent exponential random variables $y_{1}, \ldots, y_{n}$ with means $\mu_{1}, \ldots, \mu_{n}$; where $\mu_{i} = \beta_{0}+\beta_{1}x_{i}$.
How can I find the profile ...
0
votes
0answers
22 views
Contours of percentiles on level plot [migrated]
How can we estimate the level contours that correspond to what percentage of points lie inside the contour?
This post describes how to add contours to a scatterplot in R:
Scatterplot with ...
