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- Zuoxiang Peng, Zhichao Weng, Saralees Nadarajah
- Mathematics and Computers in Simulation
- 2010

We derive under some regular conditions an almost sure local central limit theorem for the product of partial sums of a sequence of independent identically distributed positive random variables.

Logarithmic general error distribution, an extension of the log-normal distribution, is proposed. Some interesting properties of the logarithmic general error distribution are derived. These properties are applied to establish the asymptotic behavior of the ratio of probability densities and the ratio of the tails of the logarithmic general error and… (More)

Suppose X1,X2, . . . are independent and identically distributed (iid) random variables with common distribution function (df) F. Let Mn =max{X1, . . . ,Xn} denote the maximum of the first n random variables and let w(F) = sup{x : F(x) < 1} denote the upper end point of F. The extreme value theory seeks norming constants an > 0, bn ∈ and a nondegenerate df… (More)

Consider a triangular array of mean zero Gaussian random variables. Under some weak conditions this paper proves that the partial sums and the point processes of exceedances formed by the array are asymptotically independent. For a standardized stationary Gaussian sequence, it is shown under some mild conditions that the point process of exceedances formed… (More)

- UDC, CHENG-XIU LING, ZUOXIANG PENG, SARALEES NADARAJAH
- 2009

The moment estimator (Dekkers et al. (1989)) has been used in extreme value theory to estimate the tail index, but it is not location invariant. The location invariant Hill-type estimator (Fraga Alves (2001)) is only suitable for estimating positive indices. In this paper, a new moment-type estimator is studied, which is location invariant. This new… (More)

- Xin Liao, Zuoxiang Peng, Saralees Nadarajah
- J. Applied Probability
- 2013

We discuss tail behaviors, subexponentiality and extreme value distribution of logarithmic skew-normal random variables. With optimal normalized constants, the asymptotic expansion of the distribution of the normalized maximum of logarithmic skew-normal random variables is derived. It shows that the convergence rate of the distribution of the normalized… (More)

Let (Xn) be a sequence of independent and identically distributed random variables and let M (s) n denote the sth largest order statistic of Xk, 1 ≤ k ≤ n. In this note, the limiting distributions of M (s) Nn under power normalization are derived as the integer valued random index Nn follows the shifted negative binomial, shifted Poisson and shifted… (More)

- Zuoxiang Peng, Miaomiao Liu, Saralees Nadarajah
- Mathematics and Computers in Simulation
- 2010

- Zuoxiang Peng, Lunfeng Cao, Saralees Nadarajah
- J. Multivariate Analysis
- 2010