Berk and Jones (1979) introduced a goodness of fit test statistic Rn which is the supremum of pointwise likelihood ratio tests for testing H0 : F (x) = F0(x) versus H1 : F (x) = F0(x). They showed that their statistic does not always converge almost surely to a constant under alternatives F , and, in fact that there exists an alternative distribution function F such Rn →d supt>0 N(t)/t where N ...

We have investigated statistical properties of the defect turbulence in 1D CGLE wherein many body interaction is involved between local depressing wave (LDW) and local standing wave (LSW). It is shown that the counting number fluctuation of LDW is subject to the sub-Poisson statistics (SUBP). The physical origin of the SUBP can be ascribed to pair extinction of LDWs based on the master equation...

a two server queueing system with single and batch service is considered in this paper. the arrival process is assumed to be poisson and the service rate follows an exponential distribution. server-i serves the customers in both single and batch service, while server-ii serves the customers in batch service only. the laplace transform of the transient and steady state behavior of the model is c...

The negative binomial distribution has become increasingly popular as a more flexible alternative to Poisson distribution, especially when it is questionable whether the strict requirements for Poisson distribution could be satisfied. But negative binomial distribution is better for overdispersed count data that are not necessarily heavy-tailed, for heavy tailed count data the traditional stati...

We study the distribution of discounted collective risk model where the counting process is Poisson. For the model considered here, we obtain mean, variance and moment generating function (m.g.f) of the model. To do this, we use two approaches. In the first approach we use classical methods to obtain the mean and variance. In the second approach we introduce some proper martingale and then we o...

An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Nonasymptotic bounds are derived for the distance between the distribution of a sum of independent integervalued random variables and an appropriately chosen compound Poisson law. In the case where all summands have the same ...

this paper measures event risk which is introducing by the ball committee to measure the effect of sudden news. this study calculates event risk by using the data of registered firms in tehran stock market between 1993 and 1994. for computing event risk, we use daily market capitalization for 80 firms during 1993-2009, then dividing these firms to three baskets; big, medium and small. the model...

Stein’s (1972) method is a very general tool for assessing the quality of approximation of the distribution of a random element by another, often simpler, distribution. In applications of Stein’s method, one needs to establish a Stein identity for the approximating distribution, solve the Stein equation and estimate the behaviour of the solutions in terms of the metrics under study. For some St...