In this paper, an asymptotic distribution of the estimator for variance function a compound periodic Poisson process with power trend is discussed. The component intensity not assumed to have certain parametric form, except it known period. slope be positive, but its value unknown. objectives research are modify existing and determine distribution. This begins by modifying formulation estimator...

Background and Purpose—We studied temporal trends in major stroke outcomes in Perth, Western Australia (WA), comparing 3 12-month periods, roughly 5 years apart, between 1989 and 2001. Methods—The Perth Community Stroke Study (PCSS) used uniform definitions and procedures in a representative segment (approximately 143 000 people in the year 2000) of Perth, WA. Crude and age-standardized inciden...

Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis. Banyumas Regency one of the districts with quite high cases in Central Java. This study aims to analyze factors that affect number tuberculosis using regression analysis count data. Poisson simplest data model has assumption equidispersion, is, mean value equal variance. However, its application, these often not fulfill...

We consider a stochastic volatility model with jumps where the underlying asset price is driven by a process sum of a 2-dimensional Brownian motion and 2-dimensional compensated Poisson process. The market is incomplete, there is an infinity of Equivalent Martingale Measures (E.M.M) and an infinity of hedging strategies. We characterize the set of E.M.M, and we hedge by minimizing the variance ...

Given a sample from a discretely observed compound Poisson process we consider estimation of the density of the jump sizes. We propose a kernel type nonparametric density estimator and study its asymptotic properties. Asymptotic expansions of the bias and variance of the estimator are given and pointwise weak consistency and asymptotic normality are established. We also derive the minimax conve...

We show that the variance of the number of edges in the random sphere of innuence graph built on n i.i.d. sites which are uniformly distributed over the unit cube in R d , grows linearly with n. This is then used to establish a central limit theorem for the number of edges in the random sphere of innuence graph built on a Poisson number of sites. Some related proximity graphs are discussed as w...

In the statistical analysis of spatial point patterns, it is often important to investigate whether the point pattern depends on spatial covariates. This paper describes nonparametric (kernel and local likelihood) methods for estimating the effect of spatial covariates on the point process intensity. Variance estimates and confidence intervals are provided in the case of a Poisson point process...

The reliability of detecting source variability in sparsely and irregularly sampled X-ray light curves is investigated. This motivated by the unprecedented survey capabilities eROSITA on board Spektrum-Roentgen-Gamma observatory, providing for many thousand sources its final-depth equatorial deep-field survey. Four methods are evaluated: excess variance, amplitude maximum deviations, Bayesian b...

The statistics of outbreaks in a model for the propagation of meningococcal disease is analyzed, taking into account the possibility that the population is fragmented into weakly connected patches. It is shown that, depending on the size of the sample studied, the ration between the variance and the average of infected cases can vary from unity (Poisson statistics) to epsilon(-1), where epsilon...

In particular, the location of S in R d is immaterial (stationarity) and E(N(S)) = λμ =Var(N(S)) (equality of mean and variance). An alternative characterization of the Poisson process involves the limit of the uniform distribution on expanding cubes C ⊆ R . Let ν denote the volume of C. Given m independent uniformly distributed particles in C and a measurable set S ⊆ C of volume μ, the probabi...