Displaying similar documents to “On the non-convexity of the time constant in first-passage percolation.”

Some properties and applications of probability distributions based on MacDonald function

Oldřich Kropáč (1982)

Aplikace matematiky

Similarity:

In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types x n K n ( x ) , x ≥ 0 , x n K n ( x x ) , x ∈ 𝐑 and x n + 1 K n ( x ) , x ≥ 0 are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and...

Random split of the interval [0,1]

B. Kopociński (2004)

Applicationes Mathematicae

Similarity:

We define two splitting procedures of the interval [0,1], one using uniformly distributed points on the chosen piece and the other splitting a piece in half. We also define two procedures for choosing the piece to be split; one chooses a piece with a probability proportional to its length and the other chooses each piece with equal probability. We analyse the probability distribution of the lengths of the pieces arising from these procedures.

On distribution of waiting time for the first failure followed by a limited length success run

Czesław Stępniak (2013)

Applicationes Mathematicae

Similarity:

Many doctors believe that a patient will survive a heart attack unless a succeeding attack occurs in a week. Treating heart attacks as failures in Bernoulli trials we reduce the lifetime after a heart attack to the waiting time for the first failure followed by a success run shorter than a given k. In order to test the "true" critical period of the lifetime we need its distribution. The probability mass function and cumulative distribution function of the waiting time are expressed in...