# Questions tagged [transform]

If possible, use a more specific tag, such as [data-transformation], [mgf], [wavelet], or [probability-generating-fn]

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### What is the distribution of bit counts of a binomial random variable?

Suppose I have a binomial random variable $X \sim B(n,p)$ and I apply the following bit counting operation $$Y = \operatorname{bit\_count}(X)$$ where $\operatorname{bit\_count}$ is defined in the ...
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### Do linear transforms of IID random vectors make the resulting covariances sufficient to describe statistical dependence?

This question is motivated by the fact that a linear transformation of an IID standard normal vector gives the multivariate Gaussian distribution, and that the statistical dependence of such ...
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1 vote
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### Deriving distribution under change of variables between spaces of unequal dimension

For a function of random variables $T:\mathbb{R}^n \mapsto \mathbb{R}^m$ Wikipedia outlines how to handle three cases: $m = n = 1$ $m=n > 1$ $n>1 \land m=1$ There seems to be two missing cases:...
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### Complicated Transform of a Beta Random Variable

Consider a Beta distributed random variable, $X \sim Beta(a,b)$ Then consider the transform $$Y = \sqrt{K\frac{X}{1-X}}$$ where $K > 0$ is a constant. How could you go about finding the PDF of $Y$?...
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### Distribution of the Square Root of a Beta Prime Random Variable

Given a Beta Prime distributed random variable $X \sim BP(a,b)$ with probability density $$\rho_X(x) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}\frac{x^{\alpha - 1}}{(1+x)^{a+b}}, x > 0$$ Consider ...
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### Scale of X axis in forest plot

The question is very simple. For the help file of the meta package, let's consider this forest plot: ...
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### What is the distribution of a random linear combination of gamma random variables?

Let $U\sim \mathcal U(0, 1)$ be a random variable uniformly distributed over the interval $[0, 1]$. Let $X_1, X_2\sim \Gamma(a, b)$ be two iid random variables with a Gamma distribution. Now it is ...
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### log transformation with the self-reported health score variables

With self-reported health scores (as a dependent variable) - such as CES-D for depression which typically ranges from 0 to 60, I was wondering whether log-transforming these scores would allow me to ...
54 views

### How does skewness in the independent features affect the performance of classification algorithms?

Do we need to take action when we encounter a skewed feature (not the target)? We can log transform for regression etc., but does it matter in also classification models?
1k views

### If a data set appears to be normal after some transformation is applied, is it really normal?

Suppose you have a data set that doesn't appear to be normal when its distribution is first plotted (e.g., it's qqplot is curved). If after some kind of transformation is applied (e.g., log, square ...
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1 vote
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### 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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1 vote
125 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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### 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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### 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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1 vote
52 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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### 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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### 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,...
558 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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1 vote
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### 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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### 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 ...
1 vote
71 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(...
1 vote
44 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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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 ...