Higher-order expansions of powered extremes of logarithmic general error distribution

In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).

Distributional expansion of maximum from logarithmic general error distribution

Logarithmic general error distribution is an extension of lognormal distribution. In this paper, with optimal norming constants the higher-order expansion of distribution of partial maximum of logarithmic general error distribution is derived.

Constant-Step Stress Accelerated Life Test of VFD under Logarithmic Normal Distribution Case

In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature increased. Statistical analysis was done by applying logarithmic normal distribution for describing the life, and least square method (LSM) for estimating logarithmic normal parameters. Self-designed special software was used to predict the VFD life. It is verified by numerical results that the VFD life follows logarithmic normal distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. The accurate calculation of the key parameters enables the rapid estimation of VFD life.

LOGARITHMIC GAUSS NORMAL DISTRIBUTION OF MICROLATEX PARTICLE OF EMULSION EXPLOSIVES

Microlatex particles of emulsion explosives determined by microphotography were studied with the law of logarithmic Gauss normal distribution, and results obtained showed that the microlatex particle just possessed the law of logarithmic Gauss normal distribution. The particle diameter in statistical average value, such as DNL, DNS, DLS, DSV and DVM was calculated through the diagram of logarithmic Gauss normal distribution of microlatex particles of emulsion explosives, so was SW.

An approach to determine coeffi cients of logarithmic velocity vertical profile in the bottom boundary layer

Velocity vertical profiles in the bottom boundary layer are important to understand the oceanic circulation.The logarithmic vertical profile,u=A ln z+B,is the universal profile for the horizontal velocity in the boundary layer,in which two coefficients(A and B)need to be determined.The two coefficients are the functions of the friction velocity(u_(*))and the roughness length(z_(0)),and they are calculated using u_(*)and z_(0).However,the measurement of u_(*)and z_(0) is a challenge.In the present study,an approach is developed to estimate the two coefficients(A and B)by using a series of fl ume laboratory experiments with fl at boundary and regularly distributed cylinders as the rough boundaries.An acoustic doppler velocimeter(ADV)is used to measure the velocity vertical profiles of the steady flow.Using the measured velocity data,the regressed logarithmic profiles are obtained.Based on the series of the A and B values,the mathematical formula for A and B are statistically established as the function of the cylinder height,inflow velocity,and the water depth,which avoids the measurement of the friction velocity and the roughness length.

Minimax Estimation of the Function of Parameters in Normal Distribution

The estimation of the functionθ=exp{αμ+bσ2} of parameters (μ,σ2) in normal distribution N(μ,σ2) is discussed. And when the prior distributions ofμandσ2 are independent, under the loss function L(θ,δ)=(θ-1×δ-1)2, the Bayesian estimation and the existence and computing method on minimax estimation are deeply discussed.

Study on the Scope of Small Amplitude of Cloud-to-ground Lightning in Lightning Weather Monitoring

Based on lightning location data in Chongqing region during 1999-2008,the frequency of lightning in various amplitude ranges and its annual variations were analyzed firstly.Afterwards,with the aid of matlab mathematical software,the distribution of the lightning location data was fitted using logarithmic normal distribution function.The results showed that after data of cloud-to-ground lightning with current amplitude from-5 to5 kA were deleted from lightning location data,the statistical characteristics of cloud-to-ground lightning could be reflected well.Meanwhile,lightning with current amplitude from-5 to 5 kA accounted for 1.05%（less than 2%）,which accorded with the detection principle of lightning position indicator（there existed error detection）.Therefore,cloud-to-ground lightning with current amplitude of-5-5 kA in lightning location data of Chongqing region was defined as small amplitude of cloud-to-ground lightning,which could provide scientific references for the processing of lightning location data in Chongqing region as well as analysis and quality control of lightning location data in other regions.

Error Correction of Lightning Location Data

[ Objective] The study aimed to correct error of lightning location data with small amplitude. [ Method] Using the curve fitting toolbox of matlab mathematical software, the distribution of lightning location data in Chongqing during 1999 -2008 was fitted based on logarithmic normal distribution function, and the specific characters of lightning data with current amplitude from -10 to 10 kA were analyzed. [ Result] During 1999 - 2008, the frequency of lightning with current amplitude from -10 to 10 kA in Chongqing City accounted for 4.93% of total frequency, while the fre- quency of lightning with current amplitude from -5 to 5 kA accounted for only 1.27%, lower than 2%, according with the conventional deletion proportion in China. Lightning data with current amplitude from -5 to 5 kA caused a great disturbance to the fitting effect, so the fitting effect was the best after these lightning data was deleted. After the lightning location system of Chongqing City was upgraded in 2005, the frequency of lightning with current amplitude from -10 to 10 kA decreased, and there were obvious changes in the frequency of lightning with current amplitude from -10 to -5 kA and from 5 to 10 kA, while the frequency of lightning with current amplitude from -5 to 5 kA was small and stable, so these data could be deleted. [Conclusion] The research could provide theoretical references for error correction of lightning location data with small amplitude in Chongqing City.