Tagged Questions

27 views

Gamma and Exponential distribution question?

The working time of one bank has an exponential distribution with a parameter λ=0.1 (in minutes). You came in the bank, but there were already 35 people before you. What's the probability that all of ...
25 views

Relationship between gamma and inverse gamma distributions under some algebraic operations

I have a question about the relationship between gamma and inverse gamma distributions. I have an equation that takes $L/(c*X)$ Where $X$ is a Gamma distribution and $c$ and $L$ are constants I'd ...
50 views

How to derive the Dirichlet-multinomial?

Common knowledge The multinomial: $$p(z|\theta) = \frac{n!}{\prod_i z_i!} \prod_i \theta_i^{z_i}$$ And the Dirichlet: $$p(\theta|\alpha) = \frac{1}{B(\alpha)}\prod_i \theta_i^{\alpha_i-1}$$ with ...
62 views

Multiplying two Gamma distributions over the same variable

I am looking at a software library where there is a function that multiplies two Gamma distributions defined over the same random variable. So, it is basically multiplying two Gamma densities with ...
148 views

pdf for non-central gamma distribution

I have a given gamma distribution as: $f(x;k,\theta) = \frac{1}{\Gamma(k)\theta^{k}}x^{k-1}e^{\frac{-x}{\theta}}$ and a non-centrality parameter $\delta$. Now, I need to find the pdf of this ...
217 views

Finding expected perimeter and area of rectangle using random distribution

Hi i have a question: A random rectangle is formed in the following way- Base X is generated from Gamma(1, λ) distribution and after generating the base, the height Y is chosen uniformly on the ...
175 views

expectation of Gamma distribution help

If x∼Gamma(1,λ) how would i find the expected value E(e^bx) where b=aλ I'm kinda stuck as to how to approach the question. Some help will be greatly appreciated Thank you in advance
207 views

exponential and gamma distribution, survival functions

I have a homework problem, that I believe I can solve correctly, using the exponential distribution survival function. But, I think, I should also be able to solve it more easily using a gamma ...
70 views

probability normal distribution

A model for the movement of a stock supposes that if the present price of the stock is s, then after one time period it will be either (1.012)s with probability 0.52, or (0.99)s with probability ...
316 views

How to sample from a Gamma distribution with shape not integer

I'm looking for an effective method to sample from a Gamma distribution that has the shape parameter not integer. However, I found everywhere the method to sample from a Gamma with an integer shape ...
1k views

How to efficiently estimate quantile function of Gamma distribution

I have an application that analyzes datasets comprised mostly of samples from a Gamma distribution. Mixed in with the data are an unknown number ($>= 0$) of outlier samples (which are actually taken ...
I would like to show that $$1-\frac{1}{c}Beta\left(c+1,\frac{1}{c}\right) \geq \frac{1}{c+1}.$$ for all $c \geq 2$. I have plotted it out for $c$ up through 200, and it seems to hold. Does anyone ...
Assuming I have a Gamma distributed random Variable $x \sim Gamma( \alpha, \beta )$. Now I like to have the following two expectation values (integrals): $E \left[ x \ln x \right]$ \$E \left[ \ln ...