Questions tagged [transform]

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26 views

How to convert a normal random variable to a truncated normal distribution? [duplicate]

Is it possible to transform a normally distributed variable into one that defined by a truncated normal distribution? I am currently using a KL transform to generate Gaussian random fields. I would ...
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1answer
23 views

How can I fix the residual plot though transformation

What transformation can I use to fix this residual plot (make the red line horizontal). I tried square root, log, 1/y, and squared. None of them helped. The data is of a 2 way ANOVA: Response ...
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10 views

How to transform an interaction plot toward additivity

Draw an interaction plot that when $x^2$ transformed may help move the model towards additivity. I know that an additive model has no interaction, so the squared transformation should result in the ...
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1answer
135 views

Distribution of i.i.d. random variables $X$ and $Y$ if $XY \sim \text{Beta}(\alpha, \beta)$

This is a follow-up to the question Square root of a Beta(1,1) random variable, which received two great answers. If $XY \sim \text{Beta}(\alpha, \beta)$, and $X$ and $Y$ are two independent ...
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2answers
454 views

Square root of a Beta(1,1) random variable

If $X^2 \sim \text{Beta}(1,1)$, is there a closed form for the distribution of $X$? If yes, what does it look like? And if this is not too much to ask, is there a general way to find the distribution ...
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17 views

Can I transform percentage data using just the square root?

I have a data set with the number of larvae (out of 100) that have metamorphosed after 0,1,2, and 5 days. I want to perform a repetitive ANOVA on the results but they are not normally distributed. I'...
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1answer
99 views

Calculation of integrals transforming $N(μ,σ^2)$ to $N(0,1)$

Let's say $X\sim N(\mu,\sigma^2)$, where $\mu$ and $\sigma^2$ are known. How can we calcuate the following integrals by transforming $X$ to $Z\sim N(0,1)$? $$ \int_{c_1}^{c_2}(x-c)\frac{1}{\sigma\sqrt{...
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0answers
12 views

Confusion in the domain of transformation of random variables

I have two random variables $X$ and $Y$. Let us assume both ranges from $0<x<\infty$ and $0<y<\infty$. Let is also assume both are having exponential densities. I am making two different ...
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1answer
35 views

What distribution is this? [duplicate]

Basically, I am told that $\varepsilon$~$N(0,1)$, and $\omega$~$IG(\frac{v}{2}$,$\frac{v}{2})$ where $IG$ is the inverted gamma distribution Now, I am told that the distribution of: $\varepsilon(\frac{...
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2answers
101 views

Finding the pdf of Y from that of X, linear transformation

The question is Let $X$ be a continuous random variable with pdf $f_X(x) = 2(1 − x)$, $0 ≤ x ≤ 1$. If $Y = 2X − 1$, find the pdf of $Y$. I understand these steps$$F_Y(Y ≤ y) = P(2X-1 ≤ y) = P(X ≤ (y+...
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1answer
44 views

Z transform of $ 2^{-|n|} $

Dears, I'm trying to compute the Z-transform of $$ x(n) = 2^{-|n|} $$. My procedure is as follows: Using definition of Z transform: $$ X(z) = \sum_{n=-\infty}^{\infty}2^{-|n|} z^{-n} = \sum_{n=-\infty}...
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22 views

Transforming Logistic Regression Model

I have a Logistic Regression Model in R ...
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1answer
61 views

Copula between a distribution and its univariate transformation

I'm trying to compute the copula (or joint distribution) between x and a univariate transformation, like say sin(x). That is compute $C_{XY}$ (or $F_{XY}$) given that $x \sim U(0,1)$ and $y = sin(x)$ ...
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1answer
259 views

Inverse Gaussian chi square connection

The inverse Gaussian distribution $IG(\mu,\lambda)$ is associated with the density $$f(x;\mu,\lambda) = \sqrt{\frac{\lambda}{2\pi x^3}}\,\exp\left\{-\frac{\lambda(x-\mu)^2}{2\mu^2x}\right\}\qquad \...
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1answer
63 views

PMF of $aX_1 + bX_2$ (Bernoulli)

Let $Y_1 = aX_1 \sim \text{Bernoulli}(p)$ and $Y_2 = bX_2 \sim \text{Bernoulli}(p)$, what is the PMF of $Z = Y_1 + Y_2$ for $a > 0$, $b > 0$ and $a \neq b$? Can somebody check my result? $$p_{...
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1answer
24 views

A Normal distribution variable in the power of N

If $X$ is normal distributed random variable, what is the distribution of $|X|^n$? I am struggling to understand the distribution. Any guidance would be appreciated.
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1answer
202 views

Why can I interpret a log transformed dependent variable in terms of percent change in linear regression?

Looking at resources such as this one and this one, you see claims like "Exponentiate the coefficient, subtract one from this number, and multiply by 100. This gives the percent increase (or ...
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2answers
297 views

How do you get the double sum or integral from $E(X+Y)$ (expected value)?

I was given a proof for $E(X+Y)$ = $E(X)+E(Y)$ for cases where both variables are either discrete or continuous: Discrete: $$ \begin{align*} E(X+Y) &=\sum_{x\in\mathcal X}\sum_{y\in\mathcal Y}(x+y)...
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0answers
46 views

Laplace-Stieltjes Transforms and distribution

I was going through a paper, I came across below relation, \begin{equation} T=\begin{cases} C, & \text{with probability $P(H<C)$}\\ 0, & \text{with probability $P(H>C)$} \...
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0answers
54 views

Is the copula function invariant only under deterministic monotonic transformation?

I read about the following theorem (see Proposition 3 in the picture below) on the invariance of copula under monotonic transformation, my questions is: 1. Are the $T_i$ mentioned in the following ...
3
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1answer
165 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(...
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1answer
54 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 ...
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0answers
12 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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1answer
120 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 ...
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1answer
35 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?
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2answers
69 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 ...
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0answers
47 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 ...
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1answer
91 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 ...
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0answers
46 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,...
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1answer
131 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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1answer
314 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
1k 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
65 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
32 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
97 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
271 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
36 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
1k 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
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
139 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
91 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
182 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
26 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
977 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
655 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
1k 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
929 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
209 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
69 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
186 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, ...