Examples of using Statistical test in English and their translations into Serbian
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Colloquial
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Ecclesiastic
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Computer
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Cyrillic
Now, let's look at the following statistical test.
And we have a statistical tests on N bit strings.
So this is another crazy thing that the statistical test will do.
But, these statistical tests were ignorant of how the data was created.
What is the probability that the statistical test outputs one?
So statistical tests don't have to get things right. They can do whatever they like.
Let's define the statistical test B as follows.
Since statistical tests are based on probability and can be in error, they do not really prove anything.
So, let me define what a statistical test on 01 to the N is.
The statistical test basically says, if the most signifigant bit of the string you gave me is one, I'm gonna say one, meaning I think it's random.
In other words, the probability that this statistical test outputs one is exactly two-thirds.
But before we talk about actually defining security,the next thing we talk about is how do we evaluate whether a statistical test is good or not?
So in this case our statistical test B will output one with probability greater than 1/2+ epsilon.
On the other hand, let's look at what happens when we give our statistical tests a pseudo-random sequence, okay.
So now that we understand what statistical tests are, we can go ahead and define, what is a secure pseudo-random generator.
For a random string, that happens exactly half the time, andso in this case the statistical test will output one, with probability one-half.
So now we're going to run the statistical test on the output of the generator, and we ask how likely is it to output one.
But if, all of a sudden, we see a run of zeros that, say, is much bigger than ten log N,then the statistical test will say, the string is not random.
For more on why large datasets,render statistical tests problematic, see Lin, Lucas, and Shmueli(2013) and McFarland and McFarland(2015).
R and its libraries implement a wide variety of statistical and graphical techniques, including linear and nonlinear modelling,classical statistical tests, time-series analysis, classification, clustering, and others.
So all this statistical test does is it basically takes the input x that was given to it, the n bit string that was given to it, and decides whether it looks random or it doesn't look random.
We say that, as generator G is secure,if essentially no efficient, statistical tests can distinguish its output from random.
I'm gonna define these statistical tests by the letter A. And the statistical test is basically an algorithm that takes its inputs and N bit string, and simply outputs zero or one.
But basically the fact is that restricting this definition into only efficient statistical tests is actually necessary for this to be satisfiable.
What the statistical test will do is it will say, well, if the number of zero zeros is roughly N over four. In other words, the difference between the number and N over four, is, say, less than ten square root of n, then we will say that X looks random.
Because just as we did before it's very easy to build a statistical test that will distinguish the output of G from uniform.
So now that we have a definition, the next question is can we actually construct a generator and then prove that it is in fact a secure PRG. In other words,prove that no efficient statistical test can distinguish its output from random.
More precisely, what we will say is that, basically for all efficient statistical tests, a… Statistical tests, a… It so happens that if I look at the advantage.
In other words, it's very close to zero,and as a result, this, statistical test was not able to distinguish the output from random, and that has to be true for all statistical tests. .
So somehow, it was able to behave differently. Andwhat they really means is that the statistical test could basically distinguish the output of the generator from random.