We introduce two new variance estimation procedures by using non-overlapping and overlapping blocks, respectively. The non-overlapping block (NOB) estimator can be viewed as the limit of the thinned block bootstrap (TBB) estimator recently proposed in Guan and Loh (2007), by letting the number of thinned processes and bootstrap samples therein both increase to infinity. Compared to the latter, ...

Intrinsic noise and random synaptic inputs generate a fluctuating current across neuron membranes. We determine the statistics of the output spike train of a biophysical model neuron as a function of the mean and variance of the fluctuating current, when the current is white noise, or when it derives from Poisson trains of excitatory and inhibitory postsynaptic conductances. In the first case, ...

In this paper we analyze asset returns models with diffusion part and jumps in returns with stochastic volatility either from diffusion or pure jump part. We consider different specifications for the pure jump part including compound Poisson, Variance Gamma and Levy α-stable jumps. Monte Carlo Markov chain algorithm is constructed to estimate models with latent Variance Gamma and Levy α−stable ...

We study the valuation of the variance swaps under stochastic volatility with delay and jumps. In our model, the volatility of the underlying stock price process not only incorporates jumps, which are found to be active empirically, but also exhibits past dependence: the behavior of a stock price right after a given time t depends not only on the situation at t but also on the whole past histor...

In modelling risk management strategies (i.e., within-lot batch testing, statistical process control), two basic assumptions have been normally made: that the true concentration of microorganisms are log-normally distributed within a batch, and that the variance of the samples is the same for a little or highly contaminated lot. These assumptions were evaluated by characterising the between-bat...

Properties of heterogeneous network traffic have been investigated from different aspects, resulting in different understanding. Specifically, one recent work discovers that the variance of network traffic exhibits a linear relationship with respect to the mean. Such a linear relation suggests that the traffic is “Poisson-like”, and thus “smooth”. On the other hand, prior work has shown that th...

We introduce a plane, which we call the delta-sigma plane, that is indexed by the norm of the estimator bias gradient and the variance of the estimator. The norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space. Using a uniform Cramer-Rao (CR) bound on estimator variance, a delta-sigma tradeoff curve is specified that...

In a family of random variables, Taylor’s law or power fluctuation scaling is variance function that gives the $$\sigma ^{2}>0$$ variable (rv) X with expectation $$\mu >0$$ as $$ : ^{2}=A\mu ^{b}$$ for finite real $$A>0,\ b$$ are same all rvs in family. Equivalently, TL holds when $$\log \sigma ^{2}=a+b\log \mu ,\ a=\log A$$ , some set. Here we analyze possible values exponent b five families i...

The main purpose of this article is to present a new class bivariate mixed Poisson regression models with varying dispersion that offers sufficient flexibility for accommodating overdispersion and accounting the positive correlation between number claims from third-party liability bodily injury property damage. Maximum likelihood estimation family achieved through an expectation-maximization al...

A M/M/1 queue with catastrophes is a modified model for which, according to the times of Poisson process, occur leaving system empty. In this work, we study fractional catastrophes, which formulated by considering derivatives in Kolmogorov’s Forward Equations original Markov process. For resulting obtain state probabilities, mean and variance number customers at any time. addition, discuss esti...