We provide an analysis of the records process associated with a marked, general mixed Poisson process. In particular, we obtain a new representation of the intensity of the records process. This in turn allows a new probabilistic characterization of the exponential distribution as being the only mixing distribution for which the records process is exactly a Poisson process. As a corollary, we o...

This paper discusses the shape of the stock return distribution using the all shares index of Helsinki Stock Exchange. Non-parametric kernel density estimation and power exponential family of distributions are used to model the shape of the return distribution. The parameters of power exponential distribution are estimated with Bayesian approach. The findings suggest that the shape of the distr...

Long-running applications are often subject to failures. Once failures occur, it will lead to unacceptable system overheads. The checkpoint technology is used to reduce the losses in the event of a failure. For the two-level checkpoint recovery scheme used in the long-running tasks, it is unavoidable for the system to periodically transfer huge memory context to a remote stable storage. Therefo...

In modeling evolutionary genetics, it is often assumed that mutational effects are assigned according to a continuous probability distribution, and multiple distributions have been used with varying degrees of justification. For mutations with beneficial effects, the distribution currently favored is the exponential distribution, in part because it can be justified in terms of extreme value the...

In this paper, we propose the SPR (sparse phase retrieval) method, which is a new phase retrieval method for coherent x-ray diffraction imaging (CXDI). Conventional phase retrieval methods effectively solve the problem for high signal-to-noise ratio measurements, but would not be sufficient for single biomolecular imaging which is expected to be realized with femto-second x-ray free electron la...

BACKGROUND Organisms, at scales ranging from unicellular to mammals, have been known to exhibit foraging behavior described by random walks whose segments confirm to Lévy or exponential distributions. For the first time, we present evidence that single cells (mammary epithelial cells) that exist in multi-cellular organisms (humans) follow a bimodal correlated random walk (BCRW). METHODOLOGY/P...

The responses to single photon absorptions (quantum bumps) vary randomly in size in Limulus photoreceptors. This variability is a natural consequence of simple chemical reactions involving a small number of molecules. The measured size distributions differ significantly from the exponential distribution predicted by the simplest transduction cascade models, one feature of which is that light-ac...

Grand canonical Monte Carlo simulations of a simple model semiflexible equilibrium polymer system, consisting of hard sphere monomers reversibly self-assembling into chains of arbitrary length, have been performed using a novel sampling method to add or remove multiple monomers during a single MC move. Systems with two different persistence lengths and a range of bond association constants have...

This paper introduces Chain sampling plan for generalized exponential distribution when the life-test is truncated at a prespecified time are provided in this manuscript. It is assumed that the shape parameter of the generalized exponential distribution is known. The design parameters such as the minimum sample size and the acceptance number are obtained by satisfying the producer’s and consume...

In this paper we propose the model of the inhomogeneous Poisson for call frequency and inhomogeneous exponential distribution for call durations to detect events based on mobile phone call detail records. The maximum likelihood method is used to estimate the rate of frequency and call duration. This work is useful for enhancing homeland security, detecting unwanted calls (e.g., spam) and commer...