Questions tagged [transform]

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23 views

How to present Confidence Interval for Log-Transformed Means & Mean Difference?

After trying to read on this topic, I still have some clarifications remaining. Context: Comparing between 2 arms (categorical), measuring microbiological plate-counted bacteria concentration (...
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1answer
33 views

How to reduce kurtosis of data

I'm trying to reduce the kurtosis of my dataset and make it approximately Gaussian, with a common-sense uni-modal shape. The raw data looks like this: I first tried ...
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0answers
18 views

Data transformation - pointwise or batch?

A data transformer performs a pre-preprocessing step ("transformation") before an estimator can fit or classify the data. The transformation step is a projection (any idempotent map: $T^2 = T$), ...
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0answers
59 views

What is the laplace transform of the below given PDF?

Really am interesting to know more about statistical properties of the following PDF , of the Random variable $z$: $$F(\sigma,\mu,z)= \frac{(z-\sigma )^2 \exp \left(-\frac{(z-\sigma )^2 \sqrt{\left(...
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0answers
24 views

How to transform/convert likelihoods to scores?

I have the probability of loan default for a labeled dataset where the distribution of probabilities is heavily skewed. Labels are defined as "good/0" for no default and "bad/1" for defaults. My goal ...
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1answer
30 views

Transformation of Confidence Interval = Confidence Interval of Transformation? [duplicate]

I am wondering about the following situation: I have a confidence interval estimator $\delta(x)=[lb, ub]$, which returns valid a%-confidence intervals for a value $\theta \in \mathbb{R}$ (not ...
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1answer
36 views

Modelling exchange rates: how to log transform percentage changes?

I'm trying to model an exchange rate to test for extreme values. However, I have percentage changes from day to day. Given some changes are negative, I can't take the logarithm. Any idea how I could ...
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1answer
24 views

Is SVM RBF applied to both classes?

Lets say i have following 1D data (position on x), color is target class and I need a classifier which classifies green from red: I decided to use SVM. Data is clearly not linearly separable, so i ...
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2answers
554 views

How can I obtain a Cauchy distribution from two standard normal distributions?

I am interested in Let $X\sim N(0,1), Y \sim N(0,1)$ independently. Show $\frac{X}{X+Y}$ is a Cauchy random variable. My work: $f_{X,Y}(x,y)=\frac{1}{2\pi} e^{\frac{-1}{2}(x^2+y^2)}, -\infty&...
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4answers
3k views

Why is the mean of the natural log of a uniform distribution (between 0 and 1) different from the natural log of 0.5?

For a uniformly distributed variable between 0 and 1 generated using rand(1,10000) this returns 10,000 random numbers between 0 and 1. If you take the mean, it ...
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0answers
101 views

Can ADVI (Variational Inference) Induce Weak Multi Modality in a system with Uniform Priors, if a Gaussian Variational Family is Used

Question Set Up If I have a weakly multi modal (see below in the edit) target posterior distribution which I am aiming to approximate using ADVI (Automatic Differentiation Variational Inference) with ...
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1answer
55 views

Transformation of Uniform Distribution to Real Number Line in ADVI

In the Automatic Differentiation Variational Inference (ADVI) paper, the authors claim to solve the VI problem in a transformed parameter space, which is over $\mathbb{R}$, in order to simplify the ...
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1answer
55 views

How can I generate 2 sets of variables from different distributions with a correlation between them in r? [duplicate]

I am working in R and would like to generate 40 numbers from $\mathrm{N}(0,1)$ and another 40 from $\mathrm{Uniform}(0,2)$ with a negative correlation (for example: $r = -0.45$) between them. The ...
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15 views

How to interpret hourly rate data given in one miniute intervals

I have time series data on natural gas flow, which is in units of "tonnes/hour". But the data are given in one minute intervals (each row represents a single minute of time duration). Here is a sample:...
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1answer
252 views

What does 'km' transform in cox.zph function mean?

I'm trying to understand how cox.zph function in r programming language works and I find myself not knowing what km transform ...
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0answers
273 views

Techniques to apply Discrete Wavelet Transform (DWT) to denoise and predict time series

I just started playing with wavelets and have been using this library (https://github.com/rafat/wavelib) to further my understanding and see if 'denoising' the series at all possible levels is ...
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49 views

scale with z-transform with the outliers in the data

I have 2 different columns X1, and X2. As you can see scale of X1 is larger than X2. These 2 columns represent the predicted value of performance of my two products. However the range or scale of X1 ...
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1answer
369 views

How does the inverse transform method work in discrete r.v.?

In this question How does the inverse transform method work? it's mentioned the general procedure to generate r.v. U <- runif(1e6) X <- qnorm(U) X How ...
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1answer
314 views

CDF Variable Transformation

Let $X$ be uniform on $(-1, 2)$ and let $Y = X^2$. Find the pdf of $Y$. So far I have noted that $F_X(x) = P(X \leq x) = \int_{-1}^x \frac{1}{3} dt = \frac{1}{3}(x+1)$. Then, since $Y=X^2$, $y \in [...
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1answer
107 views

Transforming non-normal to normal distribution and back-transform

I would like to transform non-normal distribution to normal distribution, and back-transform to its original state (or at least close to the original state). From this article, I've read that you can ...
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0answers
50 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 ...
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1answer
79 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, ...
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1answer
43 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 ...
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1answer
2k 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. ...
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3answers
172 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 ...
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0answers
78 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 ...
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1answer
67 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?
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1answer
122 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,\...
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1answer
6k 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 ...
2
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1answer
55 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 ...
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1answer
40 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 ...
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0answers
239 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 ...
2
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1answer
54 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
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1answer
503 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/...
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1answer
3k 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 ...
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2answers
955 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{...
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2answers
2k 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 ...
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1answer
813 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(...
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1answer
52 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 $R^{K-1}$.
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1answer
46 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 $Y$...
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0answers
92 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 ...
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0answers
83 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{\...
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0answers
31 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]...
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1answer
307 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=...
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0answers
145 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?
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2answers
6k 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, $\lambda = -0.5$ ...
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1answer
279 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 ...
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1answer
3k 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
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1answer
156 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 ...
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1answer
370 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 ...