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pro vyhledávání: '"Mane, S. A."'
Autor:
Mane, S. R.
We present new expressions for the $k$-generalized Fibonacci numbers, say $F_k(n)$. They satisfy the recurrence $F_k(n) = F_k(n-1) +\dots+F_k(n-k)$. Explicit expressions for the roots of the auxiliary (or characteristic) polynomial are presented, usi
Externí odkaz:
http://arxiv.org/abs/2410.07922
Autor:
Kandekar, S. A., Mane, S. A.
In 2013, Tapolcai demonstrated that a network with two completely independent spanning trees (CISTs) is sufficient for implementing protection routing. In a graph \( G \) with \( k \geq 2 \) spanning trees, denoted as \( T = \{T_1, T_2, \ldots, T_k\}
Externí odkaz:
http://arxiv.org/abs/2410.03379
Autor:
Mane, S. R.
The negative binomial distribution NB$(k,r)$ of Type I is the probability distribution for a sequence of independent Bernoulli trials (with success parameter $p\in(0,1)$) with $r$ nonoverlapping success runs of length $\ge k$. We present a new, more
Externí odkaz:
http://arxiv.org/abs/2401.07981
Autor:
Mane, S. R.
We derive a simple expression for the $r^{th}$ factorial moment $\mu_{(r)}$ of the geometric distribution of order $k$ with success parameter $p\in(0,1)$ (and $q=1-p$) in terms of its probability mass function $f_k(n)$. Specifically, $\mu_{(r)} = r!f
Externí odkaz:
http://arxiv.org/abs/2312.15886
Autor:
Mane, S. R.
The factorial moments of the standard Poisson distribution are well known and are simple, but the raw moments are considered to be more complicated (Touchard polynomials). The present note presents a recurrence relation and an explicit combinatorial
Externí odkaz:
http://arxiv.org/abs/2312.00704
Autor:
Mane, S. R.
This note analyzes properties of the median $\nu$ of the Poisson distribution of order $k$. Given a value for the median in the interval $\nu\in[1,k]$, an equation to calculate the corresponding value of the rate parameter $\lambda$ is derived. Numer
Externí odkaz:
http://arxiv.org/abs/2310.14537
Autor:
Mane, S. R.
Kostadinova and Minkova published an expression for the probability mass function (pmf) of the Poisson distribution of order $k$, as a combinatorial sum ($\mathit{Pliska~Stud.~Math.~Bulgar.}\ {\bf 22},\ 117-128\ (2013)$). Inspired by their elegant so
Externí odkaz:
http://arxiv.org/abs/2310.08615
Convexity and monotonicity of the probability mass function of the Poisson distribution of order $k$
Autor:
Mane, S. R.
This note focuses on the properties of two blocks of elements of the probability mass function (pmf) of the Poisson distribution of order $k\ge2$. The first block is the elements for $n\in[1,k]$ and the second block is the elements for $n\in[k+1,2k]$
Externí odkaz:
http://arxiv.org/abs/2310.05671
Autor:
Mane, S. R.
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Our main result is a proof that for sufficiently small values of the rate parameter $\lambda$, the probabil
Externí odkaz:
http://arxiv.org/abs/2310.00827
Autor:
Mane, S. R.
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Although its probability mass function (pmf) is known, what is lacking is a $visual$ interpretation, which
Externí odkaz:
http://arxiv.org/abs/2309.13493