基于Lognormal函数的脉搏波数学建模

对健康的日常监测,时间长,数据量大.为了简化数据量,分析了现有的使用2~4个高斯函数拟合脉搏波的脉搏波数学建模方法,在此基础上,提出了Lognormal函数模型的数学建模方法.使用4个Lognormal函数对脉搏波的一个周期进行拟合建模,以脉搏波的生理特性为基础调整4个Lognormal函数的起始时间点,并对其性能进行了分析对比.结果表明,与现有方法相比,Lognormal函数模型不仅有更高的拟合精确度,而且有更优的计算复杂度,更适合以日常健康监测为目的的体域网健康大数据应用.

Lognormal杂波环境中基于Hough变换的目标检测

给出了基于Hough变换的信号检测结构,推导了Lognormal分布杂波背景下基于Hough变换检测器的检测性能的解析表达式,设计了具体的仿真环境和仿真流程,对基于Hough变换检测器在非起伏目标和四种Swerling起伏环境下的目标检测性能进行了分析.

Polydispersity effects on the magnetization of diluted ferrofluids:a lognormal analysis

Based on a lognormal particle size distribution, this paper makes a model analysis on the polydispersity effects on the magnetization behaviour of diluted ferrofluids. Using a modified Langevin relationship for the lognormal dispersion, it first performs reduced calculations without material parameters. From the results, it is extrapolated that for the ferrofluid of lognormal polydispersion, in comparison with the corresponding monodispersion, the saturation magnetization is enhanced higher by the particle size distribution. It also indicates that in an equivalent magnetic field, the lognormally polydispersed ferrofluid is magnetically saturated faster than the corresponding monodispersion. Along the theoretical extrapolations, the polydispersity effects are evaluated for a typical ferrofluid of magnetite, with a dispersity of σ = 0.20. The results indicate that the lognormal polydispersity leads to a slight increase of the saturation magnetization, but a noticeable increase of the speed to reach the saturation value in an equivalent magnetic field.

Comparison of Cox proportional hazards model,Cox proportional hazards with time-varying coefficients model,and lognormal accelerated failure time model:Application in time to event analysis of melioidosis patients

Objective:To compare the prognostic factors of mortality among melioidosis patients between lognormal accelerated failure time(AFT),Cox proportional hazards(PH),and Cox PH with time-varying coefficient(TVC)models.Methods:A retrospective study was conducted from 2014 to 2019 among 453 patients who were admitted to Hospital Sultanah Bahiyah,Kedah and Hospital Tuanku Fauziah,Perlis in Northern Malaysia due to confirmed-cultured melioidosis.The prognostic factors of mortality from melioidosis were obtained from AFT survival analysis,and Cox’s models and the findings were compared by using the goodness of fit methods.The analyses were done by using Stata SE version 14.0.Results:A total of 242 patients(53.4%)survived.In this study,the median survival time of melioidosis patients was 30.0 days(95%CI 0.0-60.9).Six significant prognostic factors were identified in the Cox PH model and Cox PH-TVC model.In AFT survival analysis,a total of seven significant prognostic factors were identified.The results were found to be only a slight difference between the identified prognostic factors among the models.AFT survival showed better results compared to Cox's models,with the lowest Akaike information criteria and best fitted Cox-snell residuals.Conclusions:AFT survival analysis provides more reliable results and can be used as an alternative statistical analysis for determining the prognostic factors of mortality in melioidosis patients in certain situations.

Analysis of random laser scattering pulse signals with lognormal distribution

The statistical distribution of natural phenomena is of great significance in studying the laws of nature. In order to study the statistical characteristics of a random pulse signal, a random process model is proposed theoretically for better studying of the random law of measured results. Moreover, a simple random pulse signal generation and testing system is designed for studying the counting distributions of three typical objects including particles suspended in the air, standard particles, and background noise. Both normal and lognormal distribution fittings are used for analyzing the experimental results and testified by chi-square distribution fit test and correlation coefficient for comparison. In addition, the statistical laws of three typical objects and the relations between them are discussed in detail. The relation is also the non-integral dimension fractal relation of statistical distributions of different random laser scattering pulse signal groups.

Two Probability Plots of the Three-Parameter Lognormal Distribution

The two-parameter lognormal distribution is a variant of the normal distribution and the three-parameter lognormal distribution is an extension of the two-parameter lognormal distribution by introducing a location parameter. The Q-Q plot of the three-parameter lognormal distribution is widely used. To obtain the Q-Q plot one needs to iteratively try different values of the shape parameter and subjectively judge the linearity of the Q-Q plot. In this paper,a mathematical method was proposed to determine the value of the shape parameter so as to simplify the generation of the Q-Q plot. Then a new probability plot was proposed,which was more easily obtained and provided more accurate parameter estimates than the Q-Q plot. These are illustrated by three realworld examples.

Lognormal Process Software Reliability Modeling with Testing-Effort

We propose a software reliability growth model with testing-effort based on a continuous-state space stochastic process, such as a lognormal process, and conduct its goodness-of-fit evaluation. We also discuss a parameter estimation method of our model. Then, we derive several software reliability assessment measures by the probability distribution of its solution process, and compare our model with existing continuous-state space software reliability growth models in terms of the mean square error and the Akaike’s information criterion by using actual fault count data.

The Mean Difference for Lognormal Distribution

The calculation of the mean difference for the lognormal distribution involves several hard integrals featuring the error function. In this paper, considering two particular cases of an integral of the exponential function for the complement to one of the error functions, and using various symmetries, we have achieved the result of an extremely simple and useful formula of the mean difference for the lognormal distribution.

Species Abundance in a Forest Community in South China：A Case of Poisson Lognormal Distribution

: Case studies on Poisson lognormal distribution of species abundance have been rare, especially in forest communities. We propose a numerical method to fit the Poisson lognormal to the species abundance data at an evergreen mixed forest in the Dinghushan Biosphere Reserve, South China. Plants in the tree, shrub and herb layers in 25 quadrats of 20 m× 20 m, 5 m× 5 m, and 1 m× 1 m were surveyed. Results indicated that: (i) for each layer, the observed species abundance with a similarly small median, mode, and a variance larger than the mean was reverse J-shaped and followed well the zero-truncated Poisson lognormal; (ii) the coefficient of variation, skewness and kurtosis of abundance, and two Poisson lognormal parameters (& and μ) for shrub layer were closer to those for the herb layer than those for the tree layer; and (iii) from the tree to the shrub to the herb layer, the α and the coefficient of variation decreased, whereas diversity increased. We suggest that: (i) the species abundance distributions in the three layers reflects the overall community characteristics; (ii) the Poisson lognormal can describe the species abundance distribution in diverse communities with a few abundant species but many rare species; and (iii) 1/α should be an alternative measure of diversity.

The asymptotic distributions of sums of record values for distributions with lognormal-type tails

LetX 1,X 2,/h. be a sequence of i.i.d. random variables and letX (1) X (2),/h. be the associated record value sequence. We focus on the asymptotic distributions of sums of records, $T_n = \sum\nolimits_{k = 1}^n {X^{\left( k \right)} } $ ,forX 1 ∈LN(γ). In this case, we find that 2 is a strange point for parameter γ. When γ > 2,T n is asymptotically normal, while for 2 > γ > 1, we prove thatT n cannot converge in distribution to any non-degenerate law through common centralizing and normalizing and logT n is asymptotically normal.

Acceptance sampling plan of accelerated life testing for lognormal distribution under time-censoring

Abstract Lognormal distribution is commonly used in engineering. It is also a life distribution of important research values. For long-life products follow this distribution, it is necessary to apply accelerated testing techniques to product demonstration. This paper describes the development of accelerated life testing sampling plans （ALSPs） for lognormal distribution under time-censoring conditions. ALSPs take both producer and consumer risks into account, and they can be designed to work whether acceleration factor （AF） is known or unknown. When AF is known, lift testing is assumed to be conducted under accelerated conditions with time-censoring. The producer and con- sumer risks are satisfied, and the size of test sample and the size of acceptance number arc opti- mized. Then sensitivity analyses are conducted. When AF is unknown, two or more predetermined levels of accelerated stress are used. The sample sizes and sample proportion allo- cated to each stress level are optimized. The acceptance constant that satisfies producer and consumer risk is obtdned by minimizing the generalized asymptotic variance of the test statistics. Finally, the properties of the two ALSPs （one for known-AF conditions and one for unknown AF conditions） are investigated to show that the proposed method is corrcct and usablc through numerical examples.

Identifying the failure mechanism in accelerated life tests by two-parameter lognormal distributions

The failure mechanism stimulated by accelerated stress in the degradation may be different from that under normal conditions, which would lead to invalid accelerated life tests. To solve the problem, we study the re- lation between the Arrhenius equation and the lognormal distribution in the degradation process. Two relationships of the lognormal distribution parameters must be satisfied in the conclusion of the unaltered failure mechanism, the first is that the logarithmic standard deviations must be equivalent at different temperature levels, and the second is that the ratio of the differences between logarithmic means must be equal to the ratio of the differences between reciprocals of temperature. The logarithm of distribution lines must simultaneously have the same slope and regular interval lines. We studied the degradation of thick-film resistors in MCM by accelerated stress at four temperature levels （390, 400, 410 and 420 K）, and the result agreed well with our method.

Weighted semidefinite programming scheme for wireless positioning with lognormal shadowing

Received signal strength(RSS)based positioning schemes ignore the actual environmental feature that the volatility of RSS increases as signal propagation distance grows.Therefore,RSS over long distance generally has relatively large measurement error and degrades the positioning performance.To reduce the negative impact of these RSSs over long distances,a weighted semidefinite programming(WSDP)positioning scheme was proposed.The WSDP positioning scheme first assesses the signal propagation quality using the average variance of all RSS sets.Then appropriate weighting factors are set based on the variance of each RSS set,and a weighted semidefinite programming optimizer is formulated to estimate the positions of target nodes.Simulation results show that the WSDP positioning scheme can effectively improve the positioning performance.

The Lognormal Distribution and Quantum Monte Carlo Data

Quantum Monte Carlo data are often afflicted with distributions that resemble lognormal probability distributions and consequently their statistical analysis cannot be based on simple Gaussian assumptions.To this extent a method is introduced to estimate these distributions and thus give better estimates to errors associated with them.This method entails reconstructing the probability distribution of a set of data,with given mean and variance,that has been assumed to be lognormal prior to undergoing a blocking or renormalization transformation.In doing so,we perform a numerical evaluation of the renormalized sum of lognormal random variables.This technique is applied to a simple quantum model utilizing the single-thread Monte Carlo algorithm to estimate the ground state energy or dominant eigenvalue of a Hamiltonian matrix.

基于对偶树复小波变换的纹理特征提取及分割

对偶树复小波变换具有良好的方向选择性和平移不变性。该文在分析对偶树复小波分解后的6个高频子带所对应的模值子带直方图的基础上,提取一种新的纹理特征——Gamma分布参数与Lognormal分布参数的组合特征。基于该特征进行纹理图像分割,分割过程中使用了边缘保持平滑技术对特征进行平滑,并使用K均值聚类实现无监督分割。实验表明,文中所使用的特征提取方法新颖,分割结果的边缘准确性与区域一致性具有抗噪性,是一种有效的纹理分割方法。

基于非共性因子和定量化的滑坡危险性分级评价

滑坡致灾因子的选取和定量化研究是滑坡危险性分级评价的关键技术。滑坡危险性分级评价因子包括共性因子和非共性因子,共性因子在评价中定量化指标具有一致性,不能反映在滑坡个体评价体系中的差异。根据万州滑坡监测预警资料,选取了地层倾角、坡度、高差和滑坡长度与宽度的比值4个非共性因子作为滑坡危险性分级评价因子,运用Lognormal分布模型,建立了评价因子的定量化评价指标。根据建立的5级评价指标体系对万州滑坡资料进行了验证,中危险性以上的滑坡占滑坡总数的95.8%,其中高危险性和极高危险性占74.1%。研究结果表明,该研究方法的评价因子可靠性好,易于测量和获取,可应用于区域滑坡群策群防灾害点的危险性分级评价和滑坡危险性区划。

考虑混合SC/MRC分集的层叠分布式天线系统SER性能分析

针对Nakagam i/lognorm al复合衰落信道,研究了层叠分布式天线系统(Cascade D istributed Anten-na System-CDAS)在CDMA网络中的平均误符号率性能.推导出了采用混合SC/MRC分集接收机的层叠分布式天线系统平均误符号率性能公式.利用推导出的平均误符号率表达式,分析了多径密度函数(M ultipath IntensityProfile-M IP)衰减因子、空时分集维数、活动用户数以及阴影衰落因子对平均误符号率性能的影响.仿真表明层叠分布式天线系统可以有效对抗衰落,提高系统容量以及削弱对数正态阴影衰落的影响.

循环孔隙水压力作用对混凝土动态抗压特性的影响

为研究混凝土在经历循环孔隙水压力后的力学性能,利用 10MN大型多功能液压伺服静动力三轴仪,进行了常规三轴混凝土动静力加载试验,采用 Weibull Lognormal模型和规范推荐的模型对应力-应变全曲线进行拟合对比分析。试验结果表明:经历循环孔隙水压作用后,在准静态和低应变速率下,混凝土强度明显减少,在高应变速率下,混凝土强度增加;较高加载速率对混凝土峰值应变影响较小,随着加载速率的增加,混凝土的峰值应变有增大的趋势;与未经历循环孔隙水压力相比,经历循环孔隙水压力的混凝土弹性模量有所提高,且弹性模量随着循环孔隙水压力的增加总体呈现增大趋势;采用的 Weibull Lognormal模型和规范推荐的模型对混凝土应力-应变全曲线拟合效果较好,在下降段,Weibull Lognormal模型拟合效果比规范推荐的模型好。

Classification of tight sandstone reservoirs based on NMR logging

The traditional reservoir classification methods based on conventional well logging are inefficient for determining the properties,such as the porosity,shale volume,J function,and flow zone index,of the tight sandstone reservoirs because of their complex pore structure and large heterogeneity.Specifically,the method that is commonly used to characterize the reservoir pore structure is dependent on the nuclear magnetic resonance(NMR)transverse relaxation time(T2)distribution,which is closely related to the pore size distribution.Further,the pore structure parameters(displacement pressure,maximum pore-throat radius,and median pore-throat radius)can be determined and applied to reservoir classification based on the empirical linear or power function obtained from the NMR T2 distributions and the mercury intrusion capillary pressure ourves.However,the effective generalization of these empirical functions is difficult because they differ according to the region and are limited by the representative samples of different regions.A lognormal distribution is commonly used to describe the pore size and particle size distributions of the rock and quantitatively characterize the reservoir pore structure based on the volume,mean radius,and standard deviation of the small and large pores.In this study,we obtain six parameters(the volume,mean radius,and standard deviation of the small and large pores)that represent the characteristics of pore distribution and rock heterogeneity,calculate the total porosity via NMR logging,and classify the reservoirs via cluster analysis by adopting a bimodal lognormal distribution to fit the NMR T2 spectrum.Finally,based on the data obtained from the core tests and the NMR logs,the proposed method,which is readily applicable,can effectively classify the tight sandstone reservoirs.

SAMPLING INSPECTION OF RELIABILITY IN (LOG)NORMAL CASE WITH TYPE I CENSORING

This article proposes a statistical method for working out reliability sampling plans under Type I censored sample for items whose failure times have either normal or lognormal distributions. The quality statistic is a method of moments estimator of a monotonous function of the unreliability. An approach of choosing a truncation time is recommended. The sample size and acceptability constant are approximately determined by using the Cornish-Fisher expansion for quantiles of distribution. Simulation results show that the method given in this article is feasible.