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What is the distribution of the maximum of a set of N uniform random variables when they are NOT independent - its a beta distribution if they are IID?
Wiki User
∙ 14y ago
I'm still working through this one. Yes, given N IID r.v., the maximum statistic is described by the beta distribution. Actually it is F(x) that is beta distributed. Remember that the argument of the beta distribution goes from 0 to 1. In fact, the beta distribution is the sampling distribution that describes any order statistic (k = 1 to n) taken from any distribution. Maximum and minimum become special cases. In all cases, the sample cdf of the maximum is G(x) = F(x)n. For the uniform, F(x) =(x-A)/(B-A) for a Uniform(A,B) continuous distribution. Now, if I'm using the beta cdf, B(x), for order statistics (k=1 is the minimum, k=n is the maximum), in the form, B(x|alpha, beta), then alpha = k and beta = n-k+1 and x = F(x) so the sampling distribution is: G(x) = B(F(x)|k,n-k+1) for any rank order statistic X(k), and for the maximum, B(F(x),n,1). The inverse of G(x) is interesting, G-1(p)=F-1(B-1(p))=x, where p is a probability of being equal or less than x. OK, this might not be so clear, and I try to post a bit more on this later. Your second question is difficult. Your sample is not taken independently. Each selection bears some relation to the prior selection. I don't see that even a large sample would be representative of the population, but I need to think on this some more. I thought a partial answer now is better than none at all.
Wiki User
∙ 14y ago
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What is a model in which each outcome has an equal probability of occurring?
A uniform distribution.A uniform distribution.A uniform distribution.A uniform distribution.
Is uniform distribution normal distribution?
No, they are two very different distributions.
Is uniform distribution symmetric?
yes it is
What is the variance for the uniform random variable?
the variance of the uniform distribution is (a+b)/12
What is of discrete uniform distribution?
A discrete uniform distribution assigns the same probability to two or more possible events. For example, there is a discrete uniform distribution associated with flipping a coin: 'heads' is assigned a probability of 1/2 as is the event 'tails'. (Note that the probabilities are equal or 'uniform'.) There is also a discrete uniform distribution associated with tossing a die in that there is a 1/6 probability for seeing each possible side of the die.
What has the author T V Arak written?
T. V. Arak has written: 'Uniform limit theorems for sums of independent random variables' -- subject(s): Distribution (Probability theory), Limit theorems (Probability theory), Random variables, Sequences (Mathematics)
What is a model in which each outcome has an equal probability of occurring?
A uniform distribution.A uniform distribution.A uniform distribution.A uniform distribution.
Why is population distribution not uniform all over Nepal?
In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The support is defined by the two parameters, a and b, which are its minimum and maximum values. The distribution is often abbreviated U(a,b). It is the maximum entropy probability distribution for a random variate X under no constraint other than that it is contained in the distribution's support
Which distribution is the rarest found in communities?
Uniform distribution
Is the uniform probability distribution is symmetric about the mode?
Yes, the uniform probability distribution is symmetric about the mode. Draw the sketch of the uniform probability distribution. If we say that the distribution is uniform, then we obtain the same constant for the continuous variable. * * * * * The uniform probability distribution is one in which the probability is the same throughout its domain, as stated above. By definition, then, there can be no value (or sub-domain) for which the probability is greater than elsewhere. In other words, a uniform probability distribution has no mode. The mode does not exist. The distribution cannot, therefore, be symmetric about something that does not exist.
In an ecosystem which distribution pattern spreads out evenly?
Uniform.
What distribution indicates intraspecific competition of the resources?
Uniform distribution
Are all symmetric distribution are normal?
No. The binomial distribution (discrete) or uniform distribution (discrete or continuous) are symmetrical but they are not normal. There are others.
Is uniform distribution symmetric?
yes it is
Is the uniform probability distribution's standard deviation proportional to the distribution's range?
no
Is uniform distribution normal distribution?
No, they are two very different distributions.
In an uniform distribution is the mean and median the same?
Yes, they are. A uniform distribution is one in which the probability of each outcome is the same and, as a result, the mean and median are the same. A uniform distribution should not be confused with a set of random variables, all with the same distributions - much less the same values!For example, the median of a Poisson distribution is not the same as its mean. So if you have a number of random variables (RVs), each with the same Poisson distribution, their mean and median will be different. This is true of any set of RVs whose distributions are asymmetric.And it is very easy to see that the mode need not be the same. The outcome of a single roll of a regular die is the uniform distribution over the numbers {1, 2, 3, 4, 5, 6}. The mean and median are 3.5 but the mode cannot be 3.5 since that is not a value that can ever be observed.
