Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [transform]

Very ambiguos, please try to use a more specific tag, such as [data-transformation], [mgf], [wavelet] or [probability-generating-fn]

2
votes
0answers
12 views

VaR/inverse cdf of transformation of normal variables

I have the following exercise to solve as good preparation for an exam: NOTE: $VaR_p(X)$ = Value at risk = $F^{-1}_X(p)$ Consider the bivariate normal random vector $(X_1, X_2)$. The marginals are ...
0
votes
0answers
7 views

A question about logarithmic and wave kernel [closed]

In most sources that I came across, I saw the dot product calculated by kernels of type listed in a topic of this question. Unfortunately, I wasn't able to find informations regarding coordinates of ...
0
votes
0answers
25 views

multiple regression transformations

I am creating a multiple regression model that tries to predict future volatility using volume and observed previous volatility. When I do the models individually, the best adjusted R^2 come from: lm(...
2
votes
1answer
41 views

In OLS, while using log-log and linear-log transforamtions, is valid to transform some regressors only?

In OLS I was wondering if it is valid to log-transform some regressors only. Specifically, continuous regressors, because it is advised not to transform binary or categorical variables. For instance, ...
1
vote
1answer
24 views

How to scale between a equal distribution and an empirical distribution

I am not that good at expressing things mathematically, so I'll start with the practical problem right away: I have a set of four objects: O1, O2, O3, O4. Now I want to assign a variable that scales ...
1
vote
1answer
149 views

Interpreting adjusted R-squared of a log transformed regression model

I am running a linear regression model where the dependent variable (Y) is log-transformed. I am struggling on how to interpret the adjusted R-squared of this log-transformed model that is meaningful. ...
0
votes
0answers
15 views

Finding the transformation to independent r.v's

Let $X_{ijk} = A_i + B_j + C_{ij} + D_{ijk}$ with $A,B,C,D$ each independent normal r.v's I'm trying to find a transformation to $Z_i$, $i \geq 2$, such that $Z_i$ are independent $0$-mean random ...
0
votes
0answers
11 views

Transform names (nominal) into numeric to find correlation

I have a list of names (abviously nominal) with which I want to examine if a correlation between those names and a kind of ranking (numeric, intervall 0-100) is existing. Can those independent and ...
5
votes
3answers
142 views

General approaches and techniques for developing good explanatory models for nonlinear data

Various recent efforts of mine on modelling some data through logistic regression have been... not successful. While there is still more data to look at, I've been wanting to explore nonlinear ...
1
vote
0answers
33 views

A transformation from uniform random variable to Gaussian mixture

I am attempting to describe a prior_transform for a multivariate Gaussian mixture in order to estimate the evidence integral of that prior convolved with another likelihood distribution. This is ...
0
votes
1answer
45 views

Likelihood of the product of a normal cdf and pdf

Suppose you had a random sample of r.vs X_i , i= 1....n . What is the likelihood of 2 * pdf(x) * cdf(x) , with pdf and cdf of the standard normal distribution?
3
votes
1answer
75 views

Variance after resampling uniformly from a sample from a normal population

I have recently been looking into the Bootstrap, and I was wondering, if I were to have a sample $X=\{x_1,x_2,\dots,x_N\}$ that has $N$ samples, all i.i.d coming from a normal distribution, $N(\mu,\...
1
vote
1answer
2k views

Difference between a exponential model and power model

There was given some data, in which I have carry out a linearizing procedure, using either a power model or a exponential model. From my understanding, power models and exponential models are ...
1
vote
1answer
34 views

Estimates of some function of a parameter (MCMC)

Let's say I have some MCMC framework whereby I am estimating two parameters $$(\log\alpha,\log\beta)$$ The reason for the $\log$ functions is so that the implementation of the joint prior ...
1
vote
1answer
36 views

PDF of a transformed variable; what if $g(x)$ is not increasing but $g^{-1}(x)$ is?

I am reading this tutorial http://math.arizona.edu/~jwatkins/f-transform.pdf which explains transformations of random variables. It says that the PDF of a transformed random variable $Y = g(X)$ can ...
1
vote
0answers
116 views

How to add and multiply distributions?

I saw in a statistics book a problem. Let $X$ be a distribution that gets $1$ for probability $0.4$ and $2$ for probability $0.6$. Compute the mean and variances of $Y=3X-2$ and $Y=3X^2-2$. I found ...
3
votes
1answer
48 views

Transforming a uniform PDF to a Gaussian PDF

I have a Uniform PDF from [-50, 50], I would like to transform it to a Gaussian. The methods that I read up about doing this(like Box Mueller) assume that the uniform distribution is between [0,1). Is ...
2
votes
1answer
269 views

Bivariate transformation using cdf method

Given $f_{X,Y}(x,y) = 1, 0 < x < 1, 0 < y < 1$ and $Z = XY$ I wanted to try to get the cdf using the cdf method of transformation. I did $$F_z(Z) = P(Z \leq z) = P(XY \leq z) = P(Y \leq z/...
1
vote
1answer
2k views

Transforming positively skewed data with positive and negative values

My data (see image below) is positively skewed and contains both positive and negative values. I'd like to transform it to achieve normality so I can apply a repeated measures ANOVA, but can't find a ...
3
votes
2answers
558 views

mean and variance of norm of normal random variables

If $x$ and $y$ are independent and normally distributed:$$x\sim N(\mu_x,\sigma_x)$$ $$y\sim N(\mu_y,\sigma_y)$$ and $r$ is a random variable with the following relationship to $x$ and $y$ $$r = \sqrt{...
1
vote
2answers
911 views

Cross-validation transformer fit to test set?

When applying transformers in a cross-validation routine, it is often advised to fit the transformer to the data in your train set, and transform both the train and test set using the obtained ...
1
vote
1answer
480 views

How to use the data that you get from a Discrete Wavelet Transform pwyt?

Im using the pywt (PyWavelets) python library to remove the Gaussian Noise from a timeseries dataset. b is a python list of timeseries values like this, [33.33, 34.23, 35.65...] (cA, cD) = pywt.dwt(...
0
votes
1answer
38 views

How to use a one-to-one mapping to transform the support of K-dimensional Dirichlet distribution to K-1 dimensional Euclidean space? [duplicate]

Let random K-dimensional variable $\mathbf{v} \sim \mathbf{Dir}(\mathbf{\alpha})$. I want to find a one-to-one mapping $f(\cdot)$ such that $f(\mathbf{v})$ is a random variable on whole $R^{K-1}$.
2
votes
1answer
41 views

Is there a measure of spread/scale which has this property after the distribution is transformed?

Suppose we have a continuous random variable $X$ and a transform $f(x)$ which is strictly increasing. Let $Y=f(X)$ be the variable after transforming. If $m_x$ and $m_y$ are the medians of $X$ and $Y$...
1
vote
0answers
75 views

Is it possible to conduct a logistic regression with a metric dependent variable?

I have a dependent variable that is a percentage. I initially wanted to do a linear regression, but then realized that the outcome is not bounded between 0 and 1. My teacher suggested to transform my ...
0
votes
0answers
61 views

How to Reshape Linear Regression Model using Correlation Coefficient instead of slope?

I try to reproduce Results from Harding and Pagan (2004), p.12, where they try to estimate the correlation coefficient $\rho_{S} = cor(S_{y,i},S_{x,i})$ using regression on $$ \frac{S_{y,t}}{\hat{\...
2
votes
0answers
25 views

Logit Transform: multidimensional generalization to add noise to simplex?

How to generalize the logit transform to more than one dimensions? That is, how to add noise to an arbitrary element of an $n$-dimensional probability simplex. (1) In one dimension, we have $L:[0,1]...
0
votes
1answer
202 views

Empirical Covariance for Set of Particles and Weights

In the context of particle filtering. We assume a standard state space model where k is time and i is the particle index.Note: $w_k^i$ are normalised weights. Assume I have a set $\{x_k^i, w_k^i\}_{i=...
1
vote
0answers
118 views

Distribution of transformed lognormal random variable

I was wondering: if $X \sim N(0,1)$ then $P=\exp(x)$ is lognormally distributed. However, what is the distribution of $P=c\exp(x)-d$ Will it still be lognormally distributed?
0
votes
2answers
3k views

interpretation of boxcox with lambda equal 0

I am working on this non linear data set, and running my Box-Cox I find that the best value to use is $\lambda = 0$. If I understand correctly, $\lambda =2$ implies $Y^2$. Similarly, $\lambda = -0.5$ ...
3
votes
1answer
166 views

Maximum likelihood estimate of square root of mean of geometric population

We have $n$ independently geometrically distributed values: $X_{1}, X_{2}, ... $ IID ~ Geom(p) We also assume that $n$ data values $x_{1}, x_{2},...$ are available. Now I would like to find the MLE ...
2
votes
1answer
2k views

Pdf of $y = - \log(X)$ when $X$ is beta distributed The expected value of $Y$

I want find the PDF of $Y = - \log(X)$ and $X$ has a beta distribution. I found the below formula as the answer but i think there should be (1-ey)b-1 part should added to this. Is that correct ? I ...
2
votes
1answer
131 views

IS $\int_{-\infty}^\infty e^{-\beta\cdot g(x)}g(x)^{\alpha-1}\text{d}x={\Gamma(\alpha)\over \beta^\alpha}\ \ ?$ [closed]

Is the following statement true: Let $g(x)$ be some non negative continuous function of $x$.We know that$$\int_{0}^\infty e^{-\beta x}x^{\alpha-1}dx={\Gamma(\alpha)\over \beta^\alpha}$$ Does ...
1
vote
1answer
196 views

Mean and Variance of a function of a multivariate normal

I have a multivariate normally-distributed random variable: $X \sim \mathcal{N}(\mu, \Sigma)$ And another RV which is a deterministic elementwise function of this variable (producing another random ...
0
votes
1answer
72 views

characteristic function of a linear function of a random variable

What are the broad steps required to solve a question like this? Let $Y=aX+b$, where $X\sim\text{Exp}(\lambda)\,,\:\lambda>0$ and find the characteristic function of $Y$.
1
vote
0answers
46 views

How to convert a graph into a table [duplicate]

I have seen lots of examples of how to create a table in R from a data.frame, but my question is how can I create a table from a ...
0
votes
1answer
18 views

Sum of N four-component mixture variates

I asked a similar question with two-component mixture variates, and I was wondering how it extends to a four-component mixture variate. In other words, I have a list of random variables, $X_1$, $X_2$, ...
2
votes
1answer
55 views

Sum of N two-component mixture variates

I have a list of random variables, $X_1$, $X_2$, ..., $X_N$, associated with binary random variables $A_i$ such that $P(A_i) = \pi$ is known. I also know that, for all $i$ $$X_i|A_i\sim f(x)\\ X_i|\...
2
votes
2answers
482 views

Difference between scale-space transform and wavelet transform

What is actual difference between scale-space and wavelet transform? It seems that wavelets require an orthonormal basis of kernels, whereas scale-space does not. Is it the only difference? Can scale-...
1
vote
1answer
342 views

Bayes Rule Uniform Distribution

For Bayes rule, if my likelihood, and prior distribution are both uniform, is my posterior distribution also guaranteed to be uniform? In addition to this, if I apply some transformation to a ...
4
votes
2answers
114 views

Find power transform to normalize vector to unity

What is the best way to determine an exponent $\lambda$ of a vector of probabilies $x$ so that the sum of the power-transformed vector equals one? $\sum\limits_{i=1}^{|x|} x_i^\lambda = 1$ $x$ is a ...
1
vote
0answers
350 views

Out of ideas: transformation of continuous variables to obtain normality of residuals seemingly impossible

I've been browsing stackexchange for days to come up with decent solutions, but to no avail so far. Some threads seem to apply and offer solutions (e.g. How to transform negative data to be ...
1
vote
0answers
32 views

Discrete wavelet transform to detect saturation point of start and end

can someone help me to detect the saturation point using wavelet transform which contain 2 waveform signal. I don't know the correct step to detect the saturation point of distorted waveform and I ...
1
vote
1answer
4k views

Understanding output of powerTransform

In the car package, we have the function powerTransform which transforms variables in a regression equation to make the ...
2
votes
1answer
2k views

Normalize non-normal distribution?

I have a query regarding a comment I found, which will surely shed some light. In this article: http://www.analyticsvidhya.com/blog/2015/09/naive-bayes-explained/ I found: If continuous features ...
0
votes
2answers
91 views

How to transform standard deviations from standard deviations

so I am doing a meta-analysis & have access to height and weight data (with SDs) and am trying to transform this into BMI. This is rather straight forward for the means, but I am not sure how to ...
3
votes
1answer
2k views

How to down-weight older data in time series regression

In a regression fit of vectors varying with time $t$ $\qquad y \sim [x_t\ x_{t-1}\ x_{t-2}\ ...] \cdot [c_t\ c_{t-1}\ c_{t-2} \ ...] $ , how can one down-weight the older $x_t$ to model "older is less ...