binomial distributiondistributionsself-studyuniform distribution
I read online that a uniform distribution gives to all its values the same probability to occur. In the discrete case, an example of this would be a coin flip. (as they have the same probability to occur)
Doesn't this also fall under the binomial distribution, as they are independent trials, and the probability of success stays constant? (0.5)
Sorry if this is a ridiculous question, I am just learning the distributions and having trouble making them intuitive yet.
Thank you!
Like I said above in my comments, the paper http://arxiv.org/pdf/1304.1916v1.pdf, details exactly how to generate from the discrete uniform distribution from coin flips and gives a very detailed proof and results section of why the method works.
As a proof of concept I coded up their pseudo code in R to show how fast, simple and efficient their method is.
#Function for sampling from a discrete uniform distribution
rdunif = function(n){
v = 1
c = 0
a = 0
while(a > -1){
v = 2*v
c = 2*c + rbinom(1,1,.5) #This is the dice roll part
if(v >= n){
if(c < n){
return(c)
}else{
v = v-n
c = c-n
}
}
}
}
#Running the function k times for n = 11
n = 11
k = 10000
random.samples = rep(NA,k)
for(i in 1:k){
random.samples[i] = rdunif(n)
}
counts = table(random.samples)
barplot(counts,main="Random Samples from a Discrete Uniform(0,10)")
Suppose you observe several nests at different mean daily temperatures $t$. How does the probability $\pi(t)$ of nest success depend on the temperature $t$? (If nests are independent, the number of nests with success at temperature $t$ is then binomially distributed with $n$ equal to the number of nests observed and success probability $\pi(t)$.)
Logistic regression is one approach (using the logistic function) of specifying the success probability as a function of temperature via stretching and shifting the logistic curve, with the amount of stretching and shifting required to be estimated from the data.
Best Answer
A uniform distribution on $\{0,1\}$ and a Bernoulli distribution with $p=0.5$ (or alternatively a binomial distribution with $n=1$ and $p=0.5$) are the same distribution.