Questions tagged [gamma-distribution]

For problems that are related to gamma-family probability distributions.

283 questions
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hypothesis testing - gamma distribution

Let W = Y/B0 be a Random variable that has a gamma(2n,1) distribution. [Y has a gamma(2n,B) distribution and W = Y/B]. i) Suppose you want to test H0 : B ≤ B0 against H1 : B > B0 for some B0 > 0. How ...
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Probability to create $n$ screens with a probability to have a breakdown

We need five successive working stations to produce a screen and the time spent on each of the working station is distributed as an exponential random variable. The average time of each working ...
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Supply chain modelling

So I have my first probability and statistics course this year, and we're currently learning about the different distributions that can be used to model, for example, supply chains. I was wondering ...
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Gamma Distribution Moments

Show that for X ~ Gamma($\alpha$, $\beta$), for positive constant $\nu$, $E[X^\nu] = \dfrac{\beta^\nu*\Gamma(\nu + \alpha)}{\Gamma(\alpha)}$. I have the following solution: Solution However, I don'...
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Average response/waiting time for aggregated tasks with Poisson arrival

Suppose there is a specific computation task with Poisson arrival rate $\lambda$ that could be aggregated in a way that when a task arrives and triggers a computation which lasts for $D$ seconds, if ...
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Two results obtained using Poisson distribution and gamma distribution approaches do not match up

This problem is exerpted from Walpole's probability book. The number of automobiles that arrive at a certain intersection per minute has a Poisson distribution with a mean of 5. Interest centers ...
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Find a pivot for a gamma distribution

I have some issues with an exercise where I have to find an approximate pivot for a gamma distribution... Indeed, I understand how to find a pivot for a normal distribution, but I don't understand how ...
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Trying to Understand $E[X^2]$ for Gamma Distribution

I am trying to understand the following for the gamma distribution: $$E[X^2] = \frac{ \alpha(\alpha+1)}{\lambda^2}$$ I've been looking at the reasoning for $E[X]$ to make sense of what could be ...
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How we arrive to the following form of CDF after SImlification

Let $N_1, N_2, m_1, m_2$ and $N_r$ positive integer numbers. Let $X_1$ and $X_2$ two independent random variables with CDFs \begin{align}\label{} F_{X_1}(x) =&\frac{1}{\Gamma(m_1)^{N_1}} \begin{...
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Finding the distribution of $xy$ when Distribution of $x$ and $y$ is given

If $x$ follows $Beta(u,v)$ and $y$ follows $Ganma(\lambda,u+v)$ then what is the distribution of $xy$? I could only write the PDF of x and Y but not able to draw PDF of XY. I suppose that there is ...
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X~Exponential(2) and Z~Exponential(2) added is Gamma(2,2)?

Okay, so I have this problem that states $X$~$Exponential(2)$, and $Z$~$Exponential(2)$ where Z is independent from $X$. The problem that I'm trying to solve wants me to find the distribution $X+Z$ ...
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Fisher information of reparametrized Gamma Distribution

I'm trying to solve the following problem: Let $X_1,...,X_n$ be iid from $\Gamma(\alpha,\beta)$ distribution with density $f(x)=\frac{1}{\Gamma(\alpha)\beta^\alpha}x^{\alpha-1}e^{-\frac{x}{\beta}}$....
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Does the convolution property of Gamma require independence?

I understand that when α is an integer, the Gamma(α,β) distribution is the distribution of the length of time you have to wait until a total of α events have occurred, where the time between each ...
$\Gamma(\alpha+1,t)\geq (t+1)\Gamma(\alpha,t)$:Inequality related to incomplete gamma function
I am trying to prove an inequality which goes as For $\alpha\geq 1$,$\int_{t}^\infty u^{\alpha}e^{-u}du\geq (t+1) \int_{t}^\infty u^{\alpha-1}e^{-u}du$ for any $t\geq 0$. Using the notation of ...