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Let $b(x)$ be the probability that a sum of independent Bernoulli random variables with parameters $p_1, p_2, p_3, ldots in [0,1)$ equals $x$, where $lambda := p_1 + p_2 + p_3 + cdots$ is finite. We prove two inequalities for the maximal ratio $b(x)/pi_lambda(x)$, where $pi_lambda$ is the weight function of the Poisson distribution with parameter $lambda$.
In this paper, we have developed a new class of sampling schemes for estimating parameters of binomial and Poisson distributions. Without any information of the unknown parameters, our sampling schemes rigorously guarantee prescribed levels of precision and confidence.
A generalization of the Poisson distribution based on the generalized Mittag-Leffler function $E_{alpha, beta}(lambda)$ is proposed and the raw moments are calculated algebraically in terms of Bell polynomials. It is demonstrated, that the proposed d
In this paper, we deal with the problem of calibrating thresholding rules in the setting of Poisson intensity estimation. By using sharp concentration inequalities, oracle inequalities are derived and we establish the optimality of our estimate up to
The purpose of this paper is to estimate the intensity of a Poisson process $N$ by using thresholding rules. In this paper, the intensity, defined as the derivative of the mean measure of $N$ with respect to $ndx$ where $n$ is a fixed parameter, is a
We are interested in estimating the location of what we call smooth change-point from $n$ independent observations of an inhomogeneous Poisson process. The smooth change-point is a transition of the intensity function of the process from one level to