19 - Beta distribution - an introduction
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- Опубліковано 11 сер 2014
- This video provides an introduction to the beta distribution; giving its definition, explaining why we may use it, and the range of beliefs that can be described by this versatile distribution.
If you are interested in seeing more of the material, arranged into a playlist, please visit: • Bayesian statistics: a... Unfortunately, Ox Educ is no more. Don't fret however as a whole load of new youtube videos are coming soon, along with a book that accompanies the series: www.amazon.co.uk/gp/product/1... Alternatively, for more information on this video series and Bayesian inference in general, visit: ben-lambert.com/bayesian-lect... For more information on econometrics and Bayesian statistics, see: ben-lambert.com/
@Ox educ.I cant help but notice that the examples given on the graph are similar to the normal,exponential and uniform probability distribution graphs respectively.
Really helpful, this clarified a lot for me. Thanks!
Do I need a background in Mathematical Statistics to understand this whole playlist? If yes, then which part of Math. Stat. should I focus on? Thanks
I would say basic probability theory. You need to know what a random variable, expection, mean, PDF, and variance are.
calculate an integrate of Binomial Distribution caz binomial is discrete and beta is contionous by integrating binomial for beta limt from x to y , and here we are calculating for probability p instead of k outcome in binomial. is'nt it ?
thanks so much, it helps a lot , god bless you.
thanks, could you tell me what function would be this one f(x)=theta*x^ (theta-1) thank you
More context is needed to answer that question. Without anything else, it looks like it would create a new distribution
Can you share the Matlab code you used?
Is the mean B(a+1, b)/B(a, b)=a/(a+b)?
what software were you using to demonstrate the pdf.
I think he is using matlab.
I'm confused with the second example- where alpha is 0.5 and beta is 1. We solve to this equation: 1/(theta^.5), but what if theta is 1? Then 1^.5 is just 1. So you're left with 1/1, or 1. But the distribution shows the curve near zero when theta equals 1. What am I missing here? Thanks, much appreciated.
If theta is 1, then your probability of the event happening is always 1, meaning that it always happens. The curve is centered on 0.5, nearing 1 at theta == 0 and theta == 1 .
+mr. blank I'm equally confused. In the case a = 0.5 and b = 1; so that we have P(theata|a,b) = 1/(theta^0.5). At theta = 0 we get inf and at 1 we should get 1, which does not look like what is drawn. What is drawn looks like at theta = 1 we get 0. Also if we integrate over theta 0:1 would we not get a value greater than 1? So the total probability is greater than 1, but that can't be.
+Ian Ono Never mind I get it.
+Ian Ono
The lecture drew a curve of P(theata|a,b) = 1/(theta^0.5) / Beta(a,b). So the curve in the video is a result from the conversion by the Beta constant, which makes its area equal to 1.
The plot - where alpha is 0.5 and beta is 1- is simply wrong! And you are almost correct, except that normalization in the denominator is beta(0.5,1)=2. Thus, when theta=1, alpha =0.5 and beta=1 we will have pdf=0.5; NOT zero as it was shown in the video. In R you can use the following function: dbeta(theta, a, b) to produce plots.
The magenta plot corresponds to beta distribution with a=0.5, b~2.
One thing that has always bothered me is that the Beta distribution seems to be used out of mathematical convenience rather than because it is actually correct.
Does anyone know of an example where the Beta distribution is the correct distribution for some values of a and b?
A distribution of batting averages
Create a histogram over probability p. At each p, draw a random number of successes from the binomial distribution with parameters p and n = (a + b - 2). Add p to the histogram each time that (a - 1) successes are observed. With enough sampling, you'll see that the histogram converges to the Beta distribution because it is the correct distribution for this.
In other words, it is modeling a sum of n Bernoulli process just like the Binomial distribution, except instead of number of successes being the random/unknown variable, it is the probability of success that is random/unknown. This is why the p^k * p^(n - k) part is the same. The only difference is the normalization constant to ensure that when summing or integrating over k or p, the result is 1.
How to solve Beta Distribution (Density and Cumulative) Equations in Excel?
I'm guessing that you could think of a and b as scale and shape parameters. Thanks this video was very helpful
They are indeed responsible for the shape. If a is bigger it is skewed right. And if b is bigger it is skewed left.
@@quintijnkroesbergen5611 You mean an increase in "b" skews it to the right, skewness is indicated by the direction where the tail is the "longest" :)
@@Ha-mb4yy Yes I dont know why I answered so confidently. I thought I understood the material back then but I did not. Thank you for correcting me.
A little louder on your volume would have been much better.
Problem_A random variable x has a beta distribution of first kind with parameter a=b=3 then find out the probability of x not greater than 0.5..?plz can anybody ans this..? 🙏🙏
@Rob Kelly bro 7077568328 is my wp nu can you send the ans of this question by solving urself ..?🙏🙏
@Rob Kelly what probability range is always lies between 0 to 1.. But uhh say that ans is 5.. How.? 😑
Isn't that one of the examples he gave? (a=b=3)
You are very expert to make difficult
not explaining clearly how the graph is generated.
ben lambert is that you?
Tmrw exams anyone ??
Bullshit !