Although the random sum distribution has been well-studied in probability theory, inference for the mean of such distribution is very limited in the literature. In this paper, two approaches are proposed to obtain inference for the mean of the Poisson-Exponential distribution. Both proposed approaches require the log-likelihood function of the Poisson-Exponential distribution, but the exact for...

We investigate the escape from a potential well of a test particle driven by fractional Gaussian noise with Hurst exponent 0<H<1. From a numerical analysis we demonstrate the exponential distribution of escape times from the well and analyze in detail the dependence of the mean escape time on the Hurst exponent H and the particle diffusivity D. We observe different behavior for the subdiffusive...

We study the dynamical states of a small-world network of recurrently coupled excitable neurons, through both numerical and analytical methods. The dynamics of this system depend mostly on both the number of long-range connections or "shortcuts", and the delay associated with neuronal interactions. We find that persistent activity emerges at low density of shortcuts, and that the system undergo...

In this article, a new censoring scheme is considered, namely, a middle part of a random sample is censored. A treatment for reconstructing the missing order statistics is investigated. The proposed procedure is studied in detail under exponential distribution which is widely used as a constant failure model in reliability. Different approaches are used to obtain point and interval reconstructo...

In this paper, we establish some recurrence relations for single and product moments of generalized order statistics from pth order exponential distribution. Further the results are deduced for the recurrence relations of record values and ordinary order statistics and using a recurrence relation for single moments we obtain characterization of pth order exponential distribution.

It is known that the nonextensive statistics was originally formulated for the systems composed of subsystems having same q. In this paper, the existence of composite system with different q subsystems is investigated by fitting the power law degree distribution of air networks with q-exponential distribution. Then a possible extension the nonextensive statistics to different q systems is provi...

This paper proposes a matrix variate generalization of the power exponential distribution family, which can be useful in generalizing statistical procedures in multivariate analysis and in designing robust alternatives to them. An example is added to show an application of the generalization.

in this paper, an extension of record models, well known as k-records, is considered. bayesian estimation as well as prediction based on k-records are presented when the underlying distribution is assumed to have a general form. the proposed procedure is applied to the exponential, weibull and pareto models in one parameter case. also, the two-parameter exponential distribution, when both param...

A novel route to the exponential trapping-time distribution within a solidlike state in water clusters is described. We propose a simple homogeneous network (SHN) model to investigate dynamics on the potential energy networks of water clusters. In this model, it is shown that the trapping-time distribution in a solidlike state follows the exponential distribution, whereas the trapping-time dist...