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We describe the integrand in the martingale (or stochastic integral) representation of a square integrable functional F of a Lévy process in terms of (a derivative or difference operator acting on) a map ßF introduced in Rajeev and Fitzsimmons (Stochastics81, 467–476, 2009). The kernels in the chaos expansion of F are also described in terms of the iterated derivative and difference operators.
In this paper, we study the empirical Byes (EB) test problem in the continuous one-parameter exponential family under associated samples and strong mixing samples. Under mild regularity conditions, it is shown that the convergence rates of proposed EB test rules under associated or strong mixing samples are the same as that of EB test rules under independent observations.
Asadi and Zohrevand (2007). On the dynamic cumulative residual entropy. J. Statist. Plann. Inference, 137, 1931–1941] define the decreasing dynamic cumulative residual entropy (DDCRE) class of life distributions, some properties of the DDCRE class are studied. Navarro et al. (2010). Some new results on the cumulative residual entropy. J. Statist. Plann. Inference, 140, 310–322] further investigate...
This paper presents a result that provides a positive answer to the question of existence of regularities of the so called random in a broad sense mass phenomena (Kolmogorov, 1986). The theorem of existence of statistical regularities of mass phenomena in the form of closed in weak-* topology families of finitely-additive probability distributions, and their significance to decision theory, constitute...
Rank-based sampling methods have a wide range of applications in environmental and ecological studies as well as medical research and they have been shown to perform better than simple random sampling (SRS) for estimating several parameters in finite populations. In this paper, we obtain nonparametric confidence intervals for quantiles based on randomized nomination sampling (RNS) from continuous...
Using fractions of gamma and exponentially titled stable random variables this article develops a stick-breaking representation of a truncated normalized generalized gamma process. Sampling from the posterior of this process requires sampling from gamma titled stable random variables and we develop an algorithm to do so that is readily implemented in the open source software R. A Blocked Gibbs sampling...
In this article we study stochastic monotone properties of the deficit at ruin in terms of the increasing convex (concave) order. Also, we conduct comparisons on the extended deficit at ruin in the sense of the usual stochastic order and expectation. Additionally, the increasing convex (concave) order between the deficit at ruin and the amount of every drop in surplus is presented as well.
Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical techniques based on maximum likelihood and related methods. Recently Ghosh et al. (2013b) proposed a general class of divergence measures, namely the S-Divergence Family and discussed its usefulness in robust parametric estimation through some numerical illustrations. In this...
A classical result states that the sample variance of a standard Gaussian sample has the chi-square distribution. In this note, a partial reverse of this result is proved for independent infinitely divisible random variables X1,…,Xn,n≥2. If n≥3, E X 1 = ⋯ = E X n and the random variable n S n 2 = ( X 1 − X ¯...
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