Related papers: On the Confidence Interval for the parameter of Po…
In this paper, we develop a computational approach for estimating the mean value of a quantity in the presence of uncertainty. We demonstrate that, under some mild assumptions, the upper and lower bounds of the mean value are efficiently…
It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals.…
We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…
It is proved, that for a certain kind of input distribution, the strongly binomially attenuated photon number distribution can well be approximated by a Poisson distribution. This explains why we can adopt poissonian distribution as the…
In this paper introduces a new family of continuous distributions namely the Poison transmuted-G family of distribution is proposed by inducing two addition parameter on the base line G distribution. Some of its mathematical properties…
We consider the problem of estimating the parameters of a supercritical controlled branching process consistently from a single observed trajectory of population size counts. Our goal is to establish which parameters can and cannot be…
A validated simulation model primarily requires performing an appropriate input analysis mainly by determining the behavior of real-world processes using probability distributions. In many practical cases, probability distributions of the…
Practical or scientific considerations often lead to selecting a subset of parameters as ``important.'' Inferences about those parameters often are based on the same data used to select them in the first place. That can make the reported…
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…
The classical Binary Symmetric Channel has a fixed transition probability. We discuss the Binary Symmetric Channel with a variable transition probability that depends on a Poisson distribution. The error rate for this channel is determined…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
Matrix-form Poisson probability distributions were recently introduced as one matrix generalization of Panjer distributions. We show in this paper that under the constraint that their representation is to be nonnegative, they have a…
We introduce and study interval partition diffusions with Poisson--Dirichlet$(\alpha,\theta)$ stationary distribution for parameters $\alpha\in(0,1)$ and $\theta\ge 0$. This extends previous work on the cases $(\alpha,0)$ and…
In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order $n^{-1}$, where $n$ is the sample size.…
We prove that the size of the e-core of a partition taken under the Poissonised Plancherel measure converges in distribution to, as the Poisson parameter goes to infinity and after a suitable renormalisation, a sum of e-1 mutually…
On the basis of integral representations of Poisson and binomial distribution functions via complete and incomplete Euler \Gamma- and B-functions, we introduce and discuss continuous counterparts of the Poisson and binomial distributions.…
We consider a general regression model, without a scale parameter. Our aim is to construct a confidence interval for a scalar parameter of interest $\theta$ that utilizes the uncertain prior information that a distinct scalar parameter…
A random variable is equi-dispersed if its mean equals its variance. A Poisson distribution is a classical example of this phenomenon. However, a less well-known fact is that the class of normal densities that are equi-dispersed constitutes…