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.

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.

复合Weibull-Lognormal衰落下的能量检测性能分析

信道模型选择过于简单将导致性能评估结果不准确或误导.为了克服这一缺陷,在更准确完备且贴合实际的复合Weibull-Lognormal(WL)衰落信道模型下研究能量检测性能.针对复合WL衰落下接收机输出信噪比概率密度函数(PDF)难以给出精确表达式的问题,利用Holtzman逼近给出了WL分布的PDF的近似表达.在此基础上,给出了复合WL的衰落量(AF),同时给出了复合WL衰落下的近似平均检测概率和近似平均AUC.数值仿真结果表明:阴影衰落和多径衰落均对检测性能造成影响,多径衰落参数越小,衰落越严重,检测性能越差;阴影参数越大,衰落越严重,检测性能下降.同时得出时间带宽积u对检测性能影响较小.

Rice Lognormal衰落信道中不同译码度量特性的比较

本文推导出了ＲｉｃｅＬｏｇｎｏｒｍａｌ 衰落信道中没有信道状态信息和具有信道状态信息两种情况下的最大似然译码度量，并同传统欧氏距离度量的成对错误概率进行了比较．数值计算结果表明：对于ＴＣＭＰＳＫ 方案，信道衰落特征（ｆＤＴ）对度量特性的影响几乎可以忽略．最后，讨论了ＲｉｃｅＬｏｇｎｏｒｍａｌ

高周疲劳损伤的演化和Lognormal性统计的统一理论

建立了高周疲劳损伤的演化和Ｌｏｇｎｏｒｍａｌ性统计的统一理论，给出了循环次数变量和损伤变量的联合概率密度的Ｆｏｃｋ－Ｐｌａｎｃｋ方程，获得了该方程系数的高阶修正表示，解得了该方程的解析解，讨论了不同条件下概率密度的分布性质，得到其损伤值取失效临界值时寿命的分布满足Ｌｏｇｎｏｒｍａｌ性分布。

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.

A three-parameter single-step time integration method for structural dynamic analysis

The existing three-parameter single-step time integration methods, such as the Generalized-a method, improve numerical dissipation by modifying equilibrium equation at time points, which cause them to lose accuracy due to the interpolation of load vectors. Moreover, these three-parameter methods do not present an available formulation applied to a general secondorder non linear differential equatio n. To solve these problems, this paper proposes an innovative three-parameter single-step method by introducing an additional variable into update equations. Although the present method is spectrally identical to the Generalized-cx method for undamped systems, it possesses higher accuracy since it strictly satisfies the equilibrium equation at time points, and can be readily used to solve nonlinear equations. By the analysis of accuracy, stability, numerical dissipation and dispersion, the optimal second-order implicit and explicit schemes are generated, which can maximize low-frequency accuracy when high-frequency dissipation is specified. To check the performance of the proposed method, several numerical experiments are conducted and the proposed method is compared with a few up-to-date methods.

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.

Selection Method of Evaluation Indicators with Three-Parameter Interval Grey Number

The evaluation problem with three-parameter interval grey number (T-PIGN) widely exists in real world. To select effective evaluation indicators of the problem, this paper puts forward evaluation index system selection principle of T-PIGN based on distance entropy model, and gives out evaluation index system selection judgment criterion of T-PIGN. Furthermore, for the redundancy of evaluation index system with T-PIGN, a selection method of evaluation index system with T-PIGN is proposed. Finally, the applicability of the proposed method is verified by concrete examples.

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.

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.

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.

An Optimal Policy with Quadratic Demand, Three-Parameter Weibull Distribution Deterioration Rate, Shortages and Salvage Value

The present paper focuses an optimal policy of an inventory model for deteriorating items with generalized demand rate and deterioration rate. Shortages are allowed and partially backlogged. The salvage value is included into deteriorated units. The main objective of the model is to minimize the total cost by optimizing the value of the shortage point, cycle length and order quantity. A numerical example is carried out to illustrate the model and sensitivity analyses of major parameters are discussed.

Study on Prediction Method of Structural Three-parameter Power Function P-S-N Curve

This paper applies weighted least square method to estimate the three-parameter power function equation of the fatigue life curve, and uses comprehensive fatigue life coefficient to correct the equation, and at the same time combines probability statistics method to bring out the prediction method of structure＇s three- parameter power function P-S-N curve, finally applies the prediction method to a ship＇s frame-type elevate, based on the fatigue test data of it＇s material-SA06 aluminium alloy, to obtain it＇s structure＇s three-parameter power function P-S-N curve. Compared with the conventional least square method, the presented method can give

考虑地质条件的场地V_(S30)经验估计模型的选用——以新疆地区为例

新疆地区地震频发且强度较大,震害较为严重,因此对该区进行地震危险性分析很有必要。场地效应是影响危险性分析结果的重要因素之一,不同场地条件对地震动的放大作用不同;常用的表征场地条件的重要参数有V_(S30),但在实际工程中通常由于经济等原因,钻孔深度无法达到30m,不能直接获取真实的V_(S30)值,因此选用合理的V_(S30)经验估计模型成为研究人员关注的热点问题。为了得到更准确的V_(S30)估计值,本文共收集了新疆地区1 307个工程钻孔数据,针对目前常用的5种经验模型,基于地质图信息将钻孔场地划分为6类年代单元,采用相关系数检验法分析回归模型的系数,采用对数正态分布检验方法分析钻孔的分布特征,选取各类单元最适用的模型。结果表明,相关系数检验法在最适用模型评价方面是失效的,而通过比较对数正态分布检验下的峰度系数和偏度系数可选取出各类地质单元最适用模型。最后根据模型选取结果,计算得到全部工程钻孔的V_(S30)值,并利用克里金插值方法得出新疆地区V_(S30)值的分布结果,研究结果可为新疆地区V_(S30)的潜在使用者提供有价值的辅助信息,此分析方法也可为我国其他地区V_(S30)经验估计模型的选用提供技术思路。

应力-强度干涉模型下的滚动轴承可靠性评估与设计方法

针对滚动轴承可靠性低、缺乏设计依据等问题,提出一种应力-强度干涉模型下的滚动轴承可靠性评估与设计方法。考虑滚动轴承实际承载当量动载荷和规定当量动载荷的随机特性,假设两者为服从对数正态分布的随机变量,建立滚动轴承可靠性评估与设计模型。其次,对多型号多工况下的深沟球轴承和角接触球轴承进行仿真验证,结果表明:本文提出的滚动轴承可靠性评估与设计方法,通过分析当量动载荷的许用范围,结合轴承设计公式可以使优化后的轴承满足在该工况下的目标可靠性寿命,准确有效的实现滚动轴承的可靠性评估与设计。

纵向题目作答时间模型:对潜在加工速度的变化追踪

本研究提出四个纵向题目作答时间(RT)模型以追踪潜在加工速度的变化。四者的测量模型一致,差异主要体现于描述潜在加工速度随时间变化的结构模型。实证研究结果表明四者均有实践应用性且数据分析结果具有较高一致性。模拟研究表明四者在不同模拟条件下的参数估计返真性均良好。总之,本文提出的四个纵向RT模型具有可应用性且心理计量学性能良好;不仅丰富了纵向RT数据的分析方法,还拓展了纵向潜变量模型的应用范围。

基于GPS数据的高速公路行程时间估计与可靠性分析

准确地进行高速公路行程时间估计与可靠性分析对交通规划与缓解交通拥堵具有重要意义。针对目前行程时间估计准确性不高、可靠性分析不够全面的问题,提出基于BP神经网络的高速公路行程时间估计模型,并利用该模型计算的行程时间分析高速公路上车辆行驶的行程时间可靠性。以广州机场高速公路GPS浮动车数据为例进行实例验证,结果表明,与速度-时间积分法和位置-时间内插法相比,本文提出的模型提高了行程时间估计的准确度,同时能多方面地分析车辆行程时间的可靠性。

110kV及以上变电站地震易损性研究

本文提出了根据变电站内高压电气设备和房屋建筑的地震破坏状态计算变电站震害指数的方法,统计了2008年汶川8.0级大地震中成都、绵阳、德阳、广元、阿坝地区国家电网的121座110kV及以上变电站的震害情况,通过震害指数进行了震害等级评价。采用对数正态分布的累积函数,拟合了变电站基于峰值加速度的地震易损性曲线。计算结果表明:当地震烈度在Ⅶ度及以下时,变电站和输电线路只有基本完好和轻微破坏状态,不发生中等及以上等级的破坏;当地震烈度为Ⅷ度时,有变电站开始出现严重破坏状态;当烈度达到Ⅸ度时,有少量变电站发生严重破坏,多数为中等破坏;当烈度为X度及以上时,多数变电站达到严重破坏和毁坏。