Questions tagged [derived-distributions]

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Probability distribution derivation given histogram of outputs

I'm not too versed in statistics, but I am currently dealing with a problem that pertains to probability. If any assumptions are off on my part, please correct me. I have a 2D polynomial function of ...
David G.'s user avatar
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2 votes
1 answer

reverse sigmoid and its derivative

I wonder, if someone could please check/help me with this simple code: ...
cs0815's user avatar
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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 ...
zsky3333's user avatar
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2 votes
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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 ...
psyguy's user avatar
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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,...
pglpm's user avatar
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Distribution of $\frac{1}{1+Y}$ if $Y$ is Normally Distributed [duplicate]

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? ...
Jan Stuller's user avatar
6 votes
1 answer

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 $\mathbb{E}[X]=X_0$...
Jan Stuller's user avatar
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Derivation and meaning of 1 minus the cumulative distribution?

If the cumulative distribution function of a random variable is $$F(x) = P(X\leq x)$$ how can this be transformed mathematically to, and the meaning of $$1-F(x)$$
develarist's user avatar
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2 votes
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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_{...
Jxson99's user avatar
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Conditional probability of measured distribution given intrinsic distribution

I have a population whose property $X$ that is distributed according to its intrinsic distribution $P$, $ \sim P(X)$. I make a measurement of $X$ on this population and I get that $var \sim Q(X)$ ...
Lorenzo Zanisi's user avatar
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function/transformation of a random variable in the context of parametric degradation reliability

Working on a reliability project and ran across this problem of parametric degradation over time relative to a failure threshold. Need to calculate the distribution of failure times $t_{f,i}$ for a ...
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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 ...
DEVA's user avatar
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1 vote
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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 ...
kosmos's user avatar
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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.'s user avatar
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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,\...
Felipe Campelo's user avatar
3 votes
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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 ...
Amitai's user avatar
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3 votes
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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} ...
K_inverse's user avatar
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24 votes
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{...
qed's user avatar
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