Let X = (Xk)k=0,1,... denote the jump chain of the block counting process of the Λ-coalescent with Λ = β(2 − α, α) being the beta distribution with parameter α ∈ (0, 2). A solution for the hitting probability h(n,m) that the chain X ever visits the state m, conditional that it starts in the state X0 = n, is obtained via an analytic method based on generating functions. For α ∈ (1, 2) the result...

In this present paper, the main aim of the authors are to present extended k-gamma, k-beta functions and extended k-beta distribution where k > 0. These newly defined functions are the generalized forms of the extended gamma, beta functions and extended beta distribution. Also, we further generalize the said functions and some of their properties.

introduction:the use of beta emitters is one of the effective methods for palliation of bone metastasis. the risk of normal tissue toxicity should be evaluated in the bone pain palliation treatment. methods: in this study, the monte carlo simulation code mcnpx was used for simulation a bone phantom model consisted of bone marrow, bone and soft tissue. specific absorbed fractions were calculated...

The confluent hypergeometric beta distribution due to Gordy has been known since the 1990s, but not much of is in terms its mathematical properties. In this paper, we provide a comprehensive treatment properties distribution. We derive shape probability density function and expressions for cumulative function, hazard rate reversed moment generating characteristic moments, conditional entropies,...