Questions tagged [transform]

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3
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1answer
74 views

Change of variables in pdf

I have the joint pdf$$f(x_1,x_2)=x_1e^{-x_1(1+x_2)}I_{(0,\infty)}(x_1)I_{(0,\infty)}(x_2)$$and have to derive the joint pdf of $$Y_1=e^{-X_1}\qquad\text{ and }\quad Y_2=e^{-X_1X_2}$$ I set $x_1=-\ln(...
5
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0answers
63 views

Calculating the distribution function of function of Multivariate Normal

Let say I have a random variable which is as follows: $ Z = \min\left[X_1,0 \right] + \min\left[X_2,0 \right] + \min\left[X_3,0 \right] $ and $ \{ X_1, X_2, X_3\} $ jointly follows a tri-variate ...
1
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1answer
46 views

How can I shift the average probability keeping constraint (0.0:1.0)?

I have a large datasets of values that range from 0 to n. I am interpreting the values as probabilities for a later pseudo-random selection process. To make the values serve as probabilities, I ...
0
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0answers
4 views

Knowledge Distillation - Comparing different methods

I recently got into this field and I am a little confused. For example, in this paper by Hinton and this paper, how exactly are we supposed to interpret the results? I mean sure, this kind of training ...
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0answers
9 views

How to interpret a specific data transformation?

I came across this specific data transformation in the context of a physics application, which by itself is rather complex and hence out of the scope of this question. However since this ...
2
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1answer
33 views

How do you work with a function of a uniform distribution? [closed]

I am struggling with parts b and c. How do you solve them? Could you please give the solution?
0
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2answers
37 views

how do you transform/standardise a function to always give values between y1 and y2?

Having lost some of my math skills, I am having problems with something that I think should be fairly easy but is eluding me: I have a plateau shaped function that I would like to standardise such ...
1
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0answers
42 views

Can I use Linear Regression or do I need Nonlinear Regression

I am trying to fit these two equations to data in R via regression. First Equation: $$y(x) = a + \frac{b}{c + x^m}.$$ This equation is constant plus reciprocal function, resulting in a hyperbolic ...
0
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1answer
35 views

Normalize target value for linear regression

I'm building a regression model to predict sensor value over time. Bellow is a figure of my sensors data over time: Based on this video about transforming nonlinear data with a log function, What ...
0
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0answers
18 views

Squeeze a time series to fit in a range while maintaining shape

I have the following time series with intermediate highs and lows marked by the vertical lines: I want to transform/squeeze the series so that the resulting series would fit in a range, let's say [0,...
4
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1answer
61 views

What is the general second-order Taylor approximation to $\mathbb{V}(f(X))$?

If $X \sim \text{N}(0, \sigma^2)$ it is well-known that we have the second-order Taylor approximation: $$\mathbb{V}[f(X)] \approx f'(\mu)^2 \cdot \sigma^2 + \frac{f''(\mu)^2}{2} \cdot \sigma^4.$$ ...
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0answers
23 views

Probability of a random variable being positive

Suppose $x \sim p(x); x \in R $ is a random variable. Here I do not assume any family distribution of $x$ like x is Gaussian or exponential distribution. I would like to find a clear form of a ...
1
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1answer
31 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 (...
0
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1answer
191 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
20 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
62 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
27 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 ...
2
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1answer
53 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 ...
3
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1answer
66 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 ...
1
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1answer
31 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 ...
8
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2answers
609 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&...
20
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4answers
4k 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
112 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 ...
0
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1answer
63 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 ...
2
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1answer
71 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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0answers
16 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
465 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 ...
2
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0answers
382 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 ...
4
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1answer
561 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 ...
1
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1answer
414 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 [...
0
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1answer
134 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 ...
2
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0answers
53 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 ...
2
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1answer
106 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
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1answer
48 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 ...
2
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1answer
3k 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. ...
5
votes
3answers
178 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
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0answers
87 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
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1answer
72 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
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1answer
134 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,\...
2
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1answer
7k 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
57 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
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1answer
44 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
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0answers
290 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
58 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
538 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
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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 ...
4
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2answers
1k 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
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3answers
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 ...
2
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1answer
894 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
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1answer
56 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 $R^{K-1}$.