Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [derived-distributions]

18 questions
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6 answers

Distribution of ratio between two independent uniform random variables

Supppse $X$ and $Y$ are standard uniformly distributed in $[0, 1]$, and they are independent, what is the PDF of $Z = Y / X$? The answer from some probability theory textbook is $$ f_Z(z) = \begin{cases} 1/2, & \text{if } 0 \le z \le 1…
qed
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Distribution of $\frac{1}{1+X}$ if $X$ is Lognormal

Suppose $Z \sim \mathcal{N}(0,1)$. Suppose $X$ is a lognormally distributed random variable, defined as $X:=X_0exp^{(-0.5\sigma^2+\sigma Z)}$, in other words, $X$ is log-normal with $\mathbb{E}[X]=X_0$. Suppose we are interested in the variable of…
Jan Stuller
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3
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Distribution of percent difference of two normal variables

I have two performance measures in a given experiment that I know to be approximately normally distributed: $X_1\sim \mathcal{N}\left(\mu_1,\sigma_1^2\right)$ $X_2\sim \mathcal{N}\left(\mu_2,\sigma_2^2\right)$ I am interested in the distribution of…
Felipe Campelo
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Assessing a distribution from multiple estimates of its mean

I face a random variable whose distribution I don't know. Someone draws a sample of k observations from a population and tells me their average. He repeats the process m times. I assume m is in order of magnitude of hundreds. If 1 < k < 20, What can…
Amitai
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Derived Distribution from normal distribution

\begin{align} X_{1} \sim N(\mu_{1} , \, \sigma_{1}^2 ) \\ X_{2} \sim N(\mu_{2} , \, \sigma_{2}^2 ) \end{align} Assume $X_{1}$ and $X_{2}$ are independent, what is the distribution of $ Y = 1/X_{1} + 1/X_{2} $ ?
K_inverse
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How to derive the distribution of a random variable as the absolute value of a uniform random variable

I'm trying to derive the distribution of a random variable $Y$ given that I know the distribution of a random variable $X$ and the relationship they share. The $pdf$ of $X$ is expressed as: $ f_{X} = \begin{cases} 1/3 & \text{if -2 $<$…
Jxson99
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reverse sigmoid and its derivative

I wonder, if someone could please check/help me with this simple code: import numpy as np import matplotlib.pyplot as plt def sigmoid(x): var = -0.1 shift = 10 return np.exp(var*(x - 100)) / (1 + np.exp(var*(x - 100) )) # return 1 /…
cs0815
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Covariance between a binomial random variable and its size (number of trials) (found in the context of binomial thinning)

Assume we have a random variable $X$, and we construct another random variable $Y$ to be from a binomial distribution of size $X$ and success probability $\alpha$, i.e., $Y \sim Binom(X, \alpha)$. How can you derive the covariance of $X$ and $Y$? In…
ManuHaq
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Circular Statistics from Spherical to Cartesian Coordinates

For spherical coordinates with angles $\Theta$ (polar) following truncated normal distribution and $\Phi$ (azimuth) following circular uniform distribution, is there any closed form distribution for its cartesian coordinates ($X,Y,Z$)? Let's say…
DEVA
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When I create a distribution by summing 5 different distributions and sample data from the summed distribution will I get normal distribution?

This is a question regarding the central limit theorem. In my model, I have five sources of disturbances, each following a particular distribution. I sample the data from each and sum to determine the final disturbance. Will the distribution of the…
kosmos
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Previous knowledge to derive Student's t-distribution

I'd like to know what are the mathematical prerequisites that I would need to learn to derive the pdf of the Student's t-distribution
Adrián A.D.
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Hypothesis Testing on Derived Distributions

Suppose we have access to samples from two probability distributions $P$ and $Q$ which may be arbitrary and high dimensional but are over the same domain $\mathbb{X}$ (for example $P$ and $Q$ may be distributions over $N\times N$ images). Now…
user2757771
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Deriving quantity from two sets of data and do statistical analysis on it?

Say I have a factory that produces bottles of salt water, and there are two processes. One adds some water to a bottle and the other adds some salt. I have stats on each process. ie. a sample of how much water added to a bottle (litres), a sample of…
zsky3333
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Distribution of the mean of a Dirichlet-distributed distribution

Suppose that $(f_0,\dotsc,f_N)$, with $f_n\ge0, \sum_n f_n=1$, is a distribution (set of normalized weights or frequencies) having a Dirichlet distribution with parameters $\alpha_n$: $$\mathrm{p}(f_0,\dotsc,f_N) = \mathrm{Dir}(f_0,\dotsc,f_N \mid…
pglpm
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Distribution of $\frac{1}{1+Y}$ if $Y$ is Normally Distributed

Suppose $Y\sim N(\mu,\sigma)$ I would like to investigate the distribution of: $$\frac{1}{1+Y}$$ Does the distribution exist and is it well defined? Does it have analytically computable moments? Googling hasn't lead to any concrete results, so I…
Jan Stuller
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