1
vote
1answer
11 views

Will statistical analysis of transformed data hold for the original one?

I have a data with distribution like chisq-squared one. But ANOVA and t-test need the data to be normal distributed. So I want to do the Box-cox transformation to the data, but my concern is will the ...
0
votes
0answers
36 views

One double integral elated problem

The bit I am stuck is the limits in the double integral. I tried X from 0 to uy and Y from 0 to infinity, this is obviously incorrect. I just want to know the complete double integral in the order ...
0
votes
0answers
18 views

PCA - How to calculate the scores

I'm currently learning Principle component analysis and I have, so far calculated the Eigen values and vectors. Assume that I have the following: $$ E = \begin{pmatrix} 1 & 2\\ 3& 4 ...
2
votes
1answer
32 views

Variance stabilization for Poisson data

Intro Let $Z > 0$ be a random variable with the mean and variance defined as $\mathbb{E}\{ Z \}$ and $\operatorname{Var}\{ Z \}$, respectively. The variance stabilization transform (VST) $f(z)$ ...
1
vote
1answer
112 views

Joint density of two functions of random variable

This is online homework, and I'm not always clear on which chapter questions are from, so I might be completely off base. I have two random variables, $X_1$~UNI(5,10) and $X_2$~UNI(4,10), and then ...
0
votes
1answer
47 views

Take -log of a Beta distributed R.V.

X1.....Xn~Beta(a,1) Y = -log(X) Use the transformation formula to calculate the pdf of Y. What named distribution does it have? I am confused what method to use here. A beta does not converge to a ...
0
votes
0answers
12 views

stabilizing variance

Let $X_n$ be a Markov sequence such that $X_n=(1+X_{n-1})Y_n$ with $X_0=0$ and $Y_n$ - iid and independent of $X_n$'s. Suppose $\mathbb{E}[Y_1]=1$ and $\mathbb{E}[Y_1^2]=\varkappa$ with ...
0
votes
0answers
26 views

Derivation of F distribution

Prove that the PDF of Snecdor's F distribution, given by: $$F=\frac{U/n_1}{V/n_2}$$ Where $U=\chi^2(n_1)$ and $V=\chi^2(n_2)$, is given by: ...
0
votes
1answer
78 views

Question on transformations

Two efficiency experts take independent measurements Y1 and Y2 on the length of time workers take to complete a certain task. Each measurement is assumed to have the density function given by f(y) = ...
0
votes
1answer
44 views

Transformations

The length of time that a machine operates without failure is denoted by X and the length of time to repair a failure is denoted by Y. After a repair is made, the machine is assumed to operate like a ...
1
vote
1answer
37 views

Transformations problem

$$ \mbox{Let}\ x\ \mbox{have pdf}\quad {\rm f}\left(x\right) = {n \choose x}p^{x}\left(1 - p\right)^{n-x} $$ for $x = 0,1,2,\ldots,n$ where $n$ is positive integer constant and $0 < p < 1$ is ...
1
vote
1answer
54 views

How do i determine the charasteristic function of X^2?

I'm wondering how I kind show that the charasteristic function of $X^2$ given that $X\in N(0,1)$ is $\varphi_{X^2}(t)=\frac{1}{\sqrt{1-2it}}$. I have tried using the change of variables such that ...
1
vote
0answers
29 views

Relation with $F$ distribution and $t$ distribution

If $X\sim F_{n,n}$ , then show that $$\frac{\sqrt n(\sqrt X-\frac{1}{\sqrt X})}{2}\sim t_n$$
0
votes
0answers
23 views

$t$ distribution

Let $X$ and $Y$ be iid random variables with $t$ distribution with $n$ degrees of freedom ,$t_n$. Show that , $$\frac{\sqrt n(Y-X)}{2\sqrt{XY}}$$ also follows $t_n$ distribution
0
votes
0answers
94 views

check the independence of transformed variable of two independent Gamma random variables

Let $X$ and $Y$ are two independent random variables following Gamma Distribution $X\sim \Gamma(\alpha,0,1)$ and $Y\sim \Gamma(\beta,0,1)$ Show that the ...
2
votes
0answers
55 views

Stabilize Variance for Statistics (Transformation)

Problem: When $Y (> 0)$ has mean and variance equal to $\mu$ and $\mu/n$ respectively, it is shown in the textbook that the appropriate transformation of Y to stabilize variance is the square root ...
2
votes
3answers
53 views

X has pdf $f(x) = \frac{x^{2}}{18}$ for -3<x<3, what is the pdf of $X^{2}$

So this was my solution: Say, $Z = X^{2}$, then $X=\pm \sqrt{Z}$ and, $$P(Z=z)=P(X = \sqrt{z}) + P(X = -\sqrt{z}) = \frac{z}{18} + \frac{z}{18} = \frac{z}{9}$$ for $$0<z<9$$ However: ...
0
votes
1answer
207 views

How to deal with non random data in statistical analysis?

I have a set of monthly water quality data, and I want to use them in a few statistical analysis (such as finding distribution or using in copula models) which require random variables as input. I ...
3
votes
2answers
451 views

Kernel density estimation for heavy-tailed distributions using the champernowne transformation

I am trying to follow this paper to estimate the density for a heavy-tailed distributions using the champernowne transformation. Alternative link to the paper Another alternative link to the paper ...
0
votes
1answer
485 views

Justification for transforming explanatory variables

I am using linear and generalised linear models, and have transformed my explanatory variables using $log10(\bullet)$ and $sqrt(\bullet)$ transformations, and my response variable using an arcsine ...
0
votes
1answer
5k views

Arcsine squareroot transformation for data ranging from -$1$ to $1$

According to the Handbook of Biological Statistics, the arcsine squareroot transformation is used for proportional data, constrained at $-1$ and $1$. However, when I use ...