0
votes
2answers
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 ...
0
votes
0answers
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 ...
0
votes
1answer
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 ...
1
vote
1answer
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 ...
1
vote
2answers
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 ...
0
votes
2answers
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 ...
0
votes
1answer
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
1
vote
0answers
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 ...
0
votes
2answers
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 ...
1
vote
1answer
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 ...
2
votes
1answer
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 ...
6
votes
2answers
273 views

Beta Function — finding a lower bound based on parameters

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 ...
2
votes
2answers
723 views

Some expectation values for a Gamma distribution

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 ...