-In this paper, the k-μ random variable will be considered and closed form expressions for probability density function (PDF), cumulative distribution function (CDF) and moments for this distribution will be derived. Also, product, ratio, maximum and minimum of two k-μ random variables will be studied and PDFs of these functions calculated in the closed forms. Then, obtained statistical functio...

In this paper we study the steady state availability of main k-out-of-n: F and secondary subsystems having general repair time distribution. When more than k units of main subsystem fail, then the main subsystem shuts off the secondary subsystem. The life time distributions of the main units and that of secondary subsystem are exponentially distributed. A repair facility having single repairman...

The degree distribution P (k) in complex networks has been obtained by maximizing the nonextensive information entropy with the three constraints: < 1 >= 1, < k >= μ and < k >= ρ, where <> denotes the average over P (k). The distribution P (k) is expressed by a generalized Gaussian (referred to as Q-Gaussian) which has a maximum at k = μ with a width proportional to √ ρ− μ2, in contrast to a co...

By using the independence structure of points following a determinantal point process, we study the radii of the spherical ensemble, the truncation of the circular unitary ensemble and the product ensemble with parameter n and k. The limiting distributions of the three radii are obtained. They are not the Tracy-Widom distribution. In particular, for the product ensemble, we show that the limiti...

The standard interpretation of importance-weighted autoencoders is that they maximize a tighter lower bound on the marginal likelihood than the standard evidence lower bound. We give an alternate interpretation of this procedure: that it optimizes the standard variational lower bound, but using a more complex distribution. We formally derive this result, present a tighter lower bound, and visua...

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and DeltaLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(DeltaLk, K), is related to two conditional distributions: P(DeltaLk|K), the distribution of DeltaLk for a particular K, and P(K|DeltaLk) and also to two simple distributions: P(De...

Leaf properties vary significantly within plant canopies, due to the strong gradient in light availability through the canopy, and the need for plants to use resources efficiently. At high light, photosynthesis is maximized when leaves have a high nitrogen content and water supply, whereas at low light leaves have a lower requirement for both nitrogen and water. Studies of the distribution of l...