selecting a random element from vector and ... in matlab

I have 3 problem in matlab:

1. selecting a random element from vector with probability proportional to the occurrence frequency of this element in the vector?
2. selecting the most popular element from vector(the most occurrence frequency of this element in the vector)?
3. converting a vector into a probability distribution of elements.If the probability of seeing a particular element is less than a given threshold r=0.5, this element is deleted from vector.

Thanks a lot.

Answer 1

[Walter Roberson]

For the first one see http://www.mathworks.com/help/stats/randsample.html . Just submit the vector as the population, and since the population will be chosen from uniformly randomly, the probability that any particular value will be chosen will depend upon how frequently it occurs relative to the other values.

For the second one, see http://www.mathworks.com/help/matlab/ref/mode.html

For the third one:

[uniquepop, ~, popidx] = unique(ThePopulation);
counts = histc(popidx, 1:length(uniquepop));
selected_elements = uniquepop( find(counts ./ length(ThePopulation) >= r ) );

Note: with r = 0.5, selected_elements may have 0, 1, or 2 entries.

[Jack Ie]

Thanks a lot Walter. for the first problem when vector has one element, result of randsample is not correct. it return random number from 1 to that element. for example: n=[3]; x = randsample(n,1); x=1 or x=2 or x=3 but I want x=3

[Walter Roberson]

In the case that you have a population that has only one element, then use two copies of the element.

n = [3 3];
x = randsample(n, 1);