1 citations · 1 across the 9 of their papers we have counts for
9 papers
Representation-free Densities of Ratios and Powers of Stable Variables
Nomvelo Karabo Sibisi, Sibusiso Sibisi
We derive representation-free densities of ratios of the positive stable random variable and obtain their Laplace/Stieltjes transforms. We state representation-free densities of oc…
Distributions based on Stable Mixtures and Gamma-Stable Convolutions
Nomvelo Karabo Sibisi
This paper explores mixture distributions induced by a product of the positive stable random variable and a power of another positive random variable. The paper also considers the…
Convolutions and Mixtures of Gamma, Stable and Mittag-Leffler Distributions
Nomvelo Karabo Sibisi
This paper uses convolutions of the gamma density and the one-sided stable density to construct higher level densities. The approach is applied to constructing a 4-parameter Mittag…
Stable Densities, Fractional Integrals and the Mittag-Leffler Function
Nomvelo Karabo Sibisi
This paper combines probability theory and fractional calculus to derive a novel integral representation of the three-parameter Mittag-Leffler function or Prabhakar function, where…
A Probabilistic Perspective on Feller, Pollard and the Complete Monotonicity of the Mittag-Leffler Function
Nomvelo Karabo Sibisi
The main contribution of this paper is the use of probability theory to prove that the three-parameter Mittag-Leffler function is the Laplace transform of a distribution and thus c…
On Feller, Pollard and the Complete Monotonicity of the Mittag-Leffler Function
Nomvelo Karabo Sibisi
Pollard used contour integration to show that the Mittag-Leffler function is the Laplace transform of a positive function, thereby proving that it is completely monotone. He also c…
Infinitely Divisible Distributions and Commutative Diagrams
Nomvelo Sibisi
We study infinitely divisible (ID) distributions on the nonnegative half-line . The Lévy-Khintchine representation of such distributions is well-known. Our primary co…
A Cluster Model for Growth of Random Trees
Nomvelo Sibisi
We first consider the growth of trees by probabilistic attachment of new vertices to leaves. This leads to a growth model based on vertex clusters and probabilities assigned to clu…
Growth of Random Trees by Leaf Attachment
Nomvelo Sibisi
We study the growth of a time-ordered rooted tree by probabilistic attachment of new vertices to leaves. We construct a likelihood function of the leaves based on the connectivity…