Results 41 to 50 of about 94,783 (262)

Some Probabilistic Generalizations of the Cheney–Sharma and Bernstein Approximation Operators

Axioms, 2022
The objective of this paper is to give some probabilistic derivations of the Cheney, Sharma, and Bernstein approximation operators. Motivated by these probabilistic derivations, generalizations of the Cheney, Sharma, and Bernstein operators are defined ...
Seng Huat Ong, Choung Min Ng, Hong Keat Yap, Hari Mohan Srivastava   +3 more
doaj   +1 more source

Factors of alternating convolution of the Gessel numbers [PDF]

Notes on Number Theory and Discrete Mathematics
The Gessel number P(n,r) is the number of lattice paths in the plane with (1,0) and (0,1) steps from (0,0) to (n+r, n+r-1) that never touch any of the points from the set {(x,x)∈ℤ²:x≥r}. We show that there is a close relationship between Gessel numbers P(
Jovan Mikić
doaj   +1 more source

Alternative to the Binomial Series or Binomial Theorem

, 2022
This paper presents an alternative to the existing binomial series or binomial theorem. This alternative binomial theorem uses the binomial coefficients of combinatorial geometric series for constructing the new binomial series. These ideas can enable the scientific researchers to solve the real life problems.
openaire   +1 more source

A rapidly convergent method for solving third-order polynomials

AIP Advances, 2022
We present a rapidly convergent method for solving cubic polynomial equations with real coefficients. The method is based on a power series expansion of a simplified form of Cardano’s formula using Newton’s generalized binomial theorem.
Ramón A. Fernández Molina, Leonardo Di G. Sigalotti, Otto Rendón, Antonio J. Mejias   +3 more
doaj   +1 more source

Stochastic Ordering of Exponential Family Distributions and Their Mixtures

, 2009
We investigate stochastic comparisons between exponential family distributions and their mixtures with respect to the usual stochastic order, the hazard rate order, the reversed hazard rate order, and the likelihood ratio order.
Hardy, Khaledi, Marshall, Shaked, Shaked, Yaming Yu, Yu   +6 more
core   +1 more source

Sharp Estimates for Proximity of Geometric and Related Sums Distributions to Limit Laws

Mathematics, 2022
The convergence rate in the famous Rényi theorem is studied by means of the Stein method refinement. Namely, it is demonstrated that the new estimate of the convergence rate of the normalized geometric sums to exponential law involving the ideal ...
Alexander Bulinski, Nikolay Slepov
doaj   +1 more source

A q-rious positivity

, 2010
The $q$-binomial coefficients $\qbinom{n}{m}=\prod_{i=1}^m(1-q^{n-m+i})/(1-q^i)$, for integers $0\le m\le n$, are known to be polynomials with non-negative integer coefficients.
Warnaar, S. Ole, Zudilin, Wadim
core   +1 more source

Markov branching processes with disasters: extinction, survival and duality to p-jump processes

, 2019
A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval.
Hermann, F., Pfaffelhuber, P.
core   +1 more source

Lucas' theorem: its generalizations, extensions and applications (1878--2014) [PDF]

, 2014
In 1878 \'E. Lucas proved a remarkable result which provides a simple way to compute the binomial coefficient ${n\choose m}$ modulo a prime $p$ in terms of the binomial coefficients of the base-$p$ digits of $n$ and $m$: {\it If $p$ is a prime, $n=n_0 ...
Meštrović, Romeo
core  

Restricted Tweedie stochastic block models

Canadian Journal of Statistics, EarlyView.
Abstract The stochastic block model (SBM) is a widely used framework for community detection in networks, where the network structure is typically represented by an adjacency matrix. However, conventional SBMs are not directly applicable to an adjacency matrix that consists of nonnegative zero‐inflated continuous edge weights.
Jie Jian, Mu Zhu, Peijun Sang
wiley   +1 more source