Linked Questions
19 questions linked to/from Relationship between Binomial and Beta distributions
4
votes
1
answer
2k
views
Relationship between Binomial distribution and the Beta distribution [duplicate]
I have been investigating the details of the Beta distribution and the Binomial distribution and have 2 questions to ask, but first a slight preamble to explain the background to my questions. In the ...
- 51
1
vote
0
answers
102
views
Show that $P(X \ge r ) = P (Y \le p)$ [duplicate]
Let $ X \sim \text{Bin}(n,p) $ and $ Y \sim \text{Beta}(r,n-r+1) $. Show , without integration by parts, that $P(X \ge r ) = P (Y \le p)$.
From which point of view I answer this question.
- 931
0
votes
0
answers
18
views
The tail distribution of a binomial distribution can be expressed in terms of an appropriate beta distribution function - Explanation [duplicate]
I was reading the paper: "Estimating Probabilities of Default for Low Default Portfolios" by Katja Pluto and Dirk Tasche and they mention the following:
The tail distribution of a binomial ...
5
votes
2
answers
5k
views
One Sigma error and 68% tolerance interval
I have first a clarifying question, and second, a question asking about how to do something, depending on the answer to the first question.
Suppose you have a set of data of some PDF which is non-...
- 153
10
votes
2
answers
199
views
A farmer is growing a magical tree
This is not homework. It's a story I came up with to explain a statistical distribution I became interested in. If this is a known distribution, I'd love to be pointed in that direction.
A farmer has ...
- 141
4
votes
2
answers
1k
views
Why is the beta distribution so flat when a, b=1?
If the beta distribution is a prior of a Bernoulli distribution (i.e. a rate of success for a binary outcome), then it is completely counterintuitive to me that the beta distribution should be ...
5
votes
2
answers
1k
views
Bayes Billiard Balls
I am reading the book Introduction to Probability by Joe Blitzstein, and I came across the following problem.
Using a story show that for any integers $k$ and $n$ with $0 \le k \le n$,
\begin{equation*...
- 1,279
1
vote
3
answers
1k
views
How to convert the parameters in a binomial distribution to those in a beta distribution?
I know that the beta distribution is the generalized continuous case of the discrete binomial distribution. Let's say I have a binomial distribution, $B(N,p)$. I would like to know the corresponding $\...
- 291
1
vote
1
answer
2k
views
Densities of Arrival Times of Poisson Process
People arrive at a store as a non-homogeneous Poisson process with rate t, where t is the time measured in hours between noon and 6pm.
If we know that precisely one person arrived in the first hour, ...
- 123
3
votes
1
answer
2k
views
Probability distribution for a proportion based on (continuous) quantities
I have a problem related with probability distributions and parameter estimation, which comes from a real case. I would be very grateful if you could help me.
Let us suppose that we have a continuous ...
- 789
4
votes
2
answers
373
views
What is the density of the $m$'th element of a sorted vector of $n$ uniformly distributed random variables
$X_1, X_2, ..., X_n$ are independent and uniformly distributed on $[0, 1]$. Sorting them yields a vector, whose first and last element have densities that are just the derivatives of products of CDFs.
...
- 347
4
votes
1
answer
764
views
PCA on count-based fractions, taking uncertainties into account
I'm looking to do a PCA analysis on count based data itself rather than averages. I'm hoping this will help for variable observation depths; for example, 3/4 reads is not really equivalent to 15/20. ...
- 628
3
votes
2
answers
163
views
What is the variance of the mean, conditional on being between two order statistics or quantiles?
Suppose I have a simple random sample drawn from a population with a known distribution on some population characteristic like height or income, with probability density function (pdf) $f(x)$. Order ...
- 3,247
2
votes
1
answer
297
views
Binomial CDF - Wikipedia vs Reality
The Binomial distribution article on Wikipedia defines the binomial CDF as
$F_{Bin(n,p)}(k) = I_{1-p}(n-k, k+1)$,
where $I$ is the regularized incomplete beta function.
There is a proof for the ...
- 23
2
votes
1
answer
147
views
Gamma PDF parameter interpretations
I'm reading about the Gamma distribution, but I'm struggling to understand what these parameters mean in a canonical sense. It was my belief that as Beta is to Binomial, Gamma is to Poisson. However, ...
- 3,520