Lognormal Assumption Research Articles

Dynamic reliability prediction of vehicular suspension structure with damping random uncertainties

This research is conducted such that a two degrees of freedom nonlinear stochastic vibration model of vehicular suspension structure with random bilinear damping forces and cubic nonlinear restoring forces is established. Based on extreme value theory (EVT) and Monte Carlo integration method (MCIM), a novel method of predicting the failure probabilities of the maximum amplitude responses of suspension structure is proposed. The extreme value distribution functions of amplitude responses, which are analytical expressed by underlying amplitude distribution functions, are acquired by using EVT. In order to obtain the analytical expressions of the underlying distribution functions, histograms are used to estimate their distribution forms. Under the log-normal distribution assumption, the means and standard deviations of the underlying distributions are calculated by using MCIM, and then by setting up amplitude failure levels, the extreme distribution functions and failure probabilities of amplitude responses are obtained. The Monte Carlo simulation method-based numerical analyses give enormous supports to use of the proposed prediction means.

Analytical method for evaluating (and correcting) the impact of outdoor radon concentration on the estimates of percentage of dwellings exceeding reference levels

Outdoor radon concentration contributes to indoor radon levels, generally causing a shift from lognormal distribution of measured radon concentration data distribution, and it makes more challenging the estimation of radon distribution parameters on the basis of the lognormal assumption. In particular, lognormal assumption with no correction could lead to a significantly biased estimate of the percentage of dwellings exceeding a certain level, e.g. a reference level (RL), since this is based on biased estimates of geometric mean (GM) and geometric standard deviation (GSD) of radon concentration distribution.Subtracting to each measured data a constant outdoor radon level can usually compensate data distribution departure from log-normality (except for low radon levels), if the appropriate outdoor level value is chosen by means of a lognormal fit of the data. This approach – already (but not always) used in literature – cannot be applied in cases where all the data of radon concentrations are not available (e.g., for a review study). For these cases, this work presents an analytical method to quantitatively evaluate and correct the impact of outdoor on the lognormal distribution parameter estimates and, in particular, on the percentages of dwellings exceeding radon reference levels. The proposed method is applied to a number of possible situations, with different values of outdoor radon level, GM and GSD.The results show that outdoor radon levels generally produce an underestimation of the actual GSD parameter, which increases as the outdoor level increases, and in the worse cases, could lead to an underestimation higher than 50%.Consequently, if the outdoor contribution is not properly taken into account, the percentage of dwellings exceeding a certain RL is almost always underestimated, even by 80%–90% for RL equal to 300 Bq/m3. This could have implications for the classification of areas as regards radon concentration and for the estimation of avertable lung cancers attributable to radon levels higher than some possible RLs.

It Is Time to Shift Log-Normal

The Libor market model (LMM) and other models for interest rate processes assume the instantaneous short rate is log-normal. It made sense that the rate should be bounded below by zero and that volatility in basis points be proportional to the level of the rate. But there have been some anomalous periods when the model has exhibited substantial problems, such as the 2008 financial crisis and during periods when interest rates fell into negative territory in several major economies, and the log-normal assumption was plainly violated. In this article, the authors show how the assumption that the Libor rate is log-normal can be replaced by assuming 1/(1 + Libor), that is, the price of a zero-coupon bond, is log-normal instead. Under this assumption, the forward short rate follows a shifted log-normal and the drift term in the short rate equation must be modified. With this assumption, the rate is approximately log-normal when rates are high, but it becomes closer to normal when rates are low. The performance of the modified model is illustrated for caps, swaps, and swaptions.

Seismic fragility analysis with artificial neural networks: Application to nuclear power plant equipment

The fragility curve is defined as the conditional probability of failure of a structure, or its critical components, at given values of seismic intensity measures (IMs). The conditional probability of failure is usually computed adopting a log-normal assumption to reduce the computational cost. In this paper, an artificial neural network (ANN) is constructed to improve the computational efficiency for the calculation of structural outputs. The following aspects are addressed in this paper: (a) Implementation of an efficient algorithm to select IMs as inputs of the ANN. The most relevant IMs are selected with a forward selection approach based on semi-partial correlation coefficients; (b) quantification and investigation of the ANN prediction uncertainty computed with the delta method. It consists of an aleatory component from the simplification of the seismic inputs and an epistemic model uncertainty from the limited size of the training data. The aleatory component is integrated in the computation of fragility curves, whereas the epistemic component provides the confidence intervals; (c) computation of fragility curves with Monte Carlo method and verification of the validity of the log-normal assumption. This methodology is applied to estimate the probability of failure of an electrical cabinet in a reactor building studied in the framework of the KARISMA benchmark.

Seismic fragility evaluation of arch concrete dams through nonlinear incremental analysis using smeared crack model

In the present study, a methodology for developing fragilities of arch concrete dams to assess their performance against seismic hazards is introduced. Firstly, the probability risk and fragility curves are presented, followed by implementation and representation of the way this method is used. Amirkabir arch concrete dam was subjected to non-linear dynamic analyses. A modified three dimensional rotating smeared crack model was used to take the nonlinear behavior of mass concrete into account. The proposed model considers major characteristics of mass concrete. These characteristics are pre-softening behavior, softening initiation criteria, fracture energy conservation, suitable damping mechanism and strain rate effect. In the present analysis, complete fluid-structure interaction is included to account for appropriate fluid compressibility and absorptive reservoir boundary conditions. In this study, the Amirkabir arch concrete dam is subjected to a set of 8 three-component earthquakes each scaled to 10 increasing intensity levels. Using proposed nonlinear smeared crack model, nonlinear analysis is performed where the structure is subjected to a large set of scaled and un-scaled ground motions and the maximum responses are extracted for each one and plotted. Based on the results, fragility curves were plotted according to various and possible damages indexes. Discrete damage probabilities were calculated using statistical methods for each considered performance level and incremental nonlinear analysis. Then, fragility curves were constructed based on the lognormal distribution assumption. Two damage indexes were introduced and compared to one another. The results indicate that the dam has a proper stability under earthquake conditions at MCE level. Moreover, displacement damages index is more conservative and impractical in the fragility analysis than tensional damage index.

Seismic fragility curves based on the probability density evolution method

A seismic fragility curve that shows the probability of failure of a structure in function of a seismic intensity, for example peak ground acceleration (PGA), is a powerful tool for the evaluation of the seismic vulnerability of the structures in nuclear engineering and civil engineering. The common assumption of existing approaches is that the fragility curve is a cumulative probability log-normal function. In this paper, we propose a new technique for construction of seismic fragility curves by numerical simulation using the Probability Density Evolution Method (PDEM). From the joint probability density function between structural response and random variables of a system and/or excitations, seismic fragility curves can be derived without the log-normal assumption. The validation of the proposed technique is performed on two numerical examples.

Pricing of Rainfall Derivatives Using Generalized Linear Modelling of Daily Rainfall Process

The structure of a typical rainfall insurance is complex; insurance payoffs are based on many parameters such as the rainfall volume, the rainfall distribution (the number of consecutive dry days), the number of days with excess rainfall etc. Such a complex insurance structure is essential to minimize the basis risk and to amply compensate a farmer for the loss of the crop yield due to the rainfall weather event. A rainfall derivative could always be brokered as a rainfall insurance or a traded option. To price complex rainfall insurances or to trade complex financial instrument based on the rainfall index on the capital markets, the underlying daily rainfall process needs to be modelled. The daily rainfall modelling is essential because the trading of any financial instrument based on the rainfall index requires the pricing of the instrument contingent on the daily rainfall information as it becomes available. In this work, we price a rainfall derivative by modelling the underlying daily rainfall process using generalized linear models (GLMs). The rainfall occurrence process is modelled using a binomial GLM and the rainfall intensity process is modelled using a quasi-likelihood GLM with the gamma, the Pareto and the lognormal distribution assumptions. Our models estimate the average annual monsoon rainfall correctly but overestimate the standard deviation, the skewness and the excess kurtosis of the annual monsoon rainfall distribution. The expected total derivative payoff obtained using only the models with the gamma distribution assumption is comparable to that obtained from Burn analysis. There was no significant gain from using a model with two auto-regressive rainfall intensity terms.

Seismic fragility curves for structures using non-parametric representations

Fragility curves are commonly used in civil engineering to assess the vulnerability of structures to earthquakes. The probability of failure associated with a prescribed criterion (e.g. the maximal inter-storey drift of a building exceeding a certain threshold) is represented as a function of the intensity of the earthquake ground motion (e.g. peak ground acceleration or spectral acceleration). The classical approach relies on assuming a lognormal shape of the fragility curves; it is thus parametric. In this paper, we introduce two non-parametric approaches to establish the fragility curves without employing the above assumption, namely binned Monte Carlo simulation and kernel density estimation. As an illustration, we compute the fragility curves for a three-storey steel frame using a large number of synthetic ground motions. The curves obtained with the non-parametric approaches are compared with respective curves based on the lognormal assumption. A similar comparison is presented for a case when a limited number of recorded ground motions is available. It is found that the accuracy of the lognormal curves depends on the ground motion intensity measure, the failure criterion and most importantly, on the employed method for estimating the parameters of the lognormal shape.

Initial probabilistic studies into a deflection-based design format for concrete floors exposed to fire

Abstract Performance Based Design is increasingly applied in structural fire engineering, sometimes entailing the use of deflection-based criteria to demonstrate adequate performance. Since no deflection-based design format currently exists which takes into account the many uncertainties associated with structural performance during fire, the attainment of an ‘adequate safety level’ is not necessarily ensured. Building on earlier studies, the feasibility of a deflection-based design format with a single global safety factor is explored for concrete floors exposed to fire. Considering the common assumption of lognormality for slab deflections, safety factors can be defined. The subsequent feasibility study however indicates that the assumption of a lognormal distribution is problematic in case of fire. A conceptual alternative to the global safety factor is explored, where the load on the slab is step-wise increased up to the point where a predefined deflection criterion is reached. This alternative approach seems promising, as it results in a known distribution type for the calculated maximum distributed load. Next steps for the development of this concept are identified.

Evaluations of Stochastic Fatigue Crack Growth Models through Experimental Data

The study is focused on the comparisons between a polynomial and power-law stochastic fatigue crack growth models through evaluations of experimental data. Both models were assumed that the fatigue crack growth rate equals to a deterministic function in terms of fatigue crack size multiplied by a stationary log-normal random factor. Compact-tension specimens cut from a 2024-T351 aluminum-alloy plate were used for fatigue crack growth experiments under random loads performed on twenty-five specimens. The log-normal probability papers for both models were investigated to show the validity of the log-normal assumption of the random factor . The investigations on the probability of crack exceedance and distribution of random time of the two models were also made, and the comparisons of the results for both models were made as well.

An efficient method for modelling tourists’ length of stay

Modelling tourists’ length of stay imposes relevant challenges to researchers. The log-linear ordinary least squares (OLS) regression is a simple but limited statistical technique due to its log-normal distributional assumption. Duration models allow more flexible distributional assumptions, but they create unnecessary statistical complexity. Considering these limitations, a third and most efficient alternative that joins statistical simplicity and distributional flexibility is examined in this article. Generalized linear models (GLMs) are used to explain tourists’ length of stay at each of 100 Brazilian destinations. The log-gamma distribution is shown generally to fit data better than the log-normal alternative, indicating that GLMs outperform the log-linear OLS without requiring the complexity of duration models.

Data assimilation in a coupled physical-biogeochemical model of the California Current System using an incremental lognormal 4-dimensional variational approach: Part 2—Joint physical and biological data assimilation twin experiments

Coupled physical and biological data assimilation is performed within the California Current System using model twin experiments. The initial condition of physical and biological variables is estimated using the four-dimensional variational (4DVar) method under the Gaussian and lognormal error distributions assumption, respectively. Errors are assumed to be independent, yet variables are coupled by assimilation through model dynamics. Using a nutrient-phytoplankton-zooplankton-detritus (NPZD) model coupled to an ocean circulation model (the Regional Ocean Modeling System, ROMS), the coupled data assimilation procedure is evaluated by comparing results to experiments with no assimilation and with assimilation of physical data and biological data separately. Independent assimilation of physical (biological) data reduces the root-mean-squared error (RMSE) of physical (biological) state variables by more than 56% (43%). However, the improvement in biological (physical) state variables is less than 7% (13%). In contrast, coupled data assimilation improves both physical and biological components by 57% and 49%, respectively. Coupled data assimilation shows robust performance with varied observational errors, resulting in significantly smaller RMSEs compared to the free run. It still produces the estimation of observed variables better than that from the free run even with the physical and biological model error, but leads to higher RMSEs for unobserved variables. A series of twin experiments illustrates that coupled physical and biological 4DVar assimilation is computationally efficient and practical, capable of providing the reliable estimation of the coupled system with the same and ready to be examined in a realistic configuration.

Survey on Log-Normally Distributed Market-Technical Trend Data

In this survey, a short introduction of the recent discovery of log-normally-distributed market-technical trend data will be given. The results of the statistical evaluation of typical market-technical trend variables will be presented. It will be shown that the log-normal assumption fits better to empirical trend data than to daily returns of stock prices. This enables one to mathematically evaluate trading systems depending on such variables. In this manner, a basic approach to an anti-cyclic trading system will be given as an example.

How Investors Set Valuation Ratios Using a Micro-Founded Gordon Asset Pricing Model

A Micro-Founded Gordon Asset Pricing Model (MF-GAPM) is developed that allows calculation of the current E/P of an equity using reported data. In the original Gordon Model, the discounting is done assuming constant growth and a constant discount rate, with the simple result E/P = r - g where r is the so-called required yield and g is the growth expectation. The MF-GAPM applies the standard CRRA utility methodology to the real-world problem of investors maximizing their real returns, but in contrast to common practice in academic finance where the growth is subject to stochastic fluctuations, the MF-GAPM assumes constant growth like the original Gordon Model. It is shown that the E/P that maximizes the utility of the investors lifetime return then reduces to E/P = (γ-1)*µ where µ is the growth expectation and γ is the curvature of the investors CRRA utility function. This result can be viewed as a micro-founded Gordon Model with required yield equal r = γ*µ. An Empirical Model (Empirical Model) is developed to identify the data variables that investors use to set the MF-GAPM’s assumed parameters. The Empirical Model identifies two broad classes of variables whose variation about their own stationary means explain the variation of E/P about its mean: a sentiment variable S_N and a trailing earnings growth variable EG_N. The two data variables suggest there are two types of investors: rational investors who trade on observed earnings growth and irrational investors who trade on sentiment. Noting the natural associations, the first-order expansions of the functional relationships µ = µ(EG_N) and γ = γ(S_N) provide direct links between the data variables and the parameters of the MF-GAPM. The direct links allow price forecasts to be made using only expectations for the future values of the data variables themselves – expectations about expectations are not required. The feasibility of forecasting prices considering the Model’s StdError is discussed. The lack of randomness in the observed historical earnings growth record is discussed in an Academic Addendum as the rational for abandoning the i.i.d. lognormal growth assumption. With the inclusion of both rational and irrational agents, the MF-GAPM seeks to integrate the classical and behavioral approaches to finance.

Error estimation of TEMOM for Brownian coagulation

In the present study, the error estimation of Taylor series expansion method of moment (TEMOM) for particle population balance equation due to Brownian coagulation is proposed. The app-roximation introduced by Taylor series polynomials has two parts: one is the approximation of nonlinear collision kernel, and the other is the approximation of higher and fractional particle moment. The results show that the two kinds of errors have the same order in the original TEMOM model, which is related to the third derivative of collision kernel and the first four integer order particle moments, i.e., M0, M1, M2, and M3. Based on the lognormal size distribution assumption, the system errors are obtained for different TEMOM models due to Brownian coagulation; and all the errors are small and acceptable. The results have confirmed the validity of TEMOM model.Copyright © 2016 American Association for Aerosol Research

An investigation of the impact of left-censored soil contamination data on the uncertainty of descriptive statistical parameters.

Left-censored concentration data are frequently encountered because measuring instruments cannot detect concentrations below the instrument detection limit. For statistical analysis of left-censored data, the environmental literature mainly refers to the following methods: maximum likelihood estimator, regression on order statistics using log-normal and gamma assumption (rROS and GROS, respectively), and Kaplan-Meier. A number of simulation experiments examined the performance of these methods in terms of bias and/or mean square error. However, no matter which method is adopted, some uncertainty is introduced into outcomes because all that is known about a left-censored observation is that the concentration falls between 0 and the detection limit. The data used in the present study come from analysis of soil samples collected for a site characterization in Montreal, Canada. Employing nonparametric bootstrap, the authors quantify the uncertainty and bias in the mean and standard deviation estimates obtained by the maximum likelihood estimation (under log-normal, Weibull, and gamma distributions), rROS, GROS, and Kaplan-Meier methods. First, the authors demonstrate that the highest uncertainty is associated with the maximum likelihood estimator under log-normality and Weibull assumptions, whereas a gamma assumption leads to estimates with less uncertainty. Second, the authors show that although an increase in sample size improves the uncertainty, it reduces the bias only in the rROS, GROS, and Kaplan-Meier methods. Finally, comparing percentage uncertainty in the mean of contaminant data, the authors illustrate that adopting an inappropriate estimator results in large uncertainties. Environ Toxicol Chem 2016;35:2623-2631. © 2016 SETAC.

The Use of Conditional Probability Integral Transformation Method for Testing Accelerated Failure Time Models

This paper suggests the use of the conditional probability integral transformation (CPIT) method as a goodness of fit (GOF) technique in the field of accelerated life testing (ALT), specifically for validating the underlying distributional assumption in accelerated failure time (AFT) model. The method is based on transforming the data into independent and identically distributed (i.i.d) Uniform (0, 1) random variables and then applying the modified Watson statistic to test the uniformity of the transformed random variables. This technique is used to validate each of the exponential, Weibull and lognormal distributions' assumptions in AFT model under constant stress and complete sampling. The performance of the CPIT method is investigated via a simulation study. It is concluded that this method performs well in case of exponential and lognormal distributions. Finally, a real life example is provided to illustrate the application of the proposed procedure.

The Binomial CEV Model and the Greeks

AbstractThis article compares alternative binomial approximation schemes for computing the option hedge ratios studied by Chung and Shackleton (2002), Chung, Hung, Lee, and Shih (2011), and Pelsser and Vorst (1994) under the lognormal assumption, but now considering the constant elasticity of variance (CEV) process proposed by Cox (1975) and using the continuous‐time analytical Greeks recently offered by Larguinho, Dias, and Braumann (2013) as the benchmarks. Among all the binomial models considered in this study, we conclude that an extended tree binomial CEV model with the smooth and monotonic convergence property is the most efficient method for computing Greeks under the CEV diffusion process because one can apply the two‐point extrapolation formula suggested by Chung et al. (2011). © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:90–104, 2017

Trade-Off Between Power and Bandwidth Consumption in a Reconfigurable Xhaul Network Architecture

The increasing number of wireless devices, the high required traffic bandwidth, and power consumption will lead to a revolution of mobile access networks, which is not a simple evolution of traditional ones. Cloud radio access network technologies are seen as promising solution in order to deal with the heavy requirements defined for 5G mobile networks. The introduction of the common public radio interface (CPRI) technology allows for a centralization in BaseBand unit (BBU) of some access functions with advantages in terms of power consumption saving when switching off algorithms are implemented. Unfortunately, the advantages of the CPRI technology are to be paid with an increase in required bandwidth to carry the traffic between the BBU and the radio remote unit (RRU), in which only the radio functions are implemented. For this reason, a tradeoff solution between power and bandwidth consumption is proposed and evaluated. The proposed solution consists of: 1) handling the traffic generated by the users through both RRU and traditional radio base stations (RBS) and 2) carrying the traffic generated by the RRU and RBS (CPRI and Ethernet flows) with a reconfigurable network. The proposed solution is investigated under the lognormal spatial traffic distribution assumption. After proposing resource dimensioning analytical models validated by simulation, we show how the sum of the bandwidth and power consumption may be minimized with the deployment of a given percentage of RRU. For instance we show how in 5G traffic scenarios this percentage can vary from 30% to 50% according to total traffic amount handled by a switching node of the reconfigurable network.

Multi-Human Detection Algorithm Based on an Impulse Radio Ultra-Wideband Radar System

In this paper, we propose a multi-human detection algorithm based on impulse radio ultra-wideband radar system. With our proposed algorithm, the multi-human detection can be performed by repeatedly performing clustering and detecting processes. More specifically, the system detects an effective peak of the first single cluster which is composed of peaks adjacent to each other and then repeat this process until effective peaks of clusters caused by multiple people are successfully detected sequentially. As our performance metrics, we take into account the performance analysis in terms of the error probability based on the results of the statistical analysis. More specifically, we first cross-verify that the empirical result theoretically follows the Log-normal distribution by comparing the theoretical and empirical results obtained through laboratory experiments. Then, we statistically analyze the received signals under the Log-normal distribution assumption. After that, this statistical result is adopted to the performance analysis of the error probability in terms of the total error probability. Note that the performance of our proposed algorithm is affected by the threshold value. Based on it, the optimal threshold is analyzed and we provide the sample guidelines for optimally adjusting the threshold value under given various environment factors. Finally, some selected experimental results are presented to show the validity of our proposed algorithm by comparing the performance between the proposed algorithm and the conventional algorithm.