Quantile Plots Research Articles

Development of Entrepreneurship Scale Towards University Students

The aim of this study is to develop a reliable and valid measurement tool to evaluate the entrepreneurship characteristics of university students. The study group is comprised of 386 students at the Faculty of Nursing, Near East University. Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA) were applied in order to assess the construct validity of entrepreneurship scale. Prior to the application of Exploratory Factor analysis, Kolmogrov Smirnov, Shapiro Wilks tests were applied in order to identify whether the data set shows normal distribution; QQ plot was analysed with regard to the distribution and the skewness and kurtosis values of distribution were checked accordingly. In consideration with the generated results, the data set was considered as showing normal distribution. Upon ensuring the normality assumption required for the Exploratory Factor analysis, Kaiser-Mayer-Olkin (KMO) coefficient and Barlett sphericity test that are used in the identification of data eligibility for the Exploratory Factor Analysis were applied respectively. The findings with regard to the reliability of scale were ensured with Cronbach Alpha (internal consistency). The findings showed that the reliability coefficient for internal consistency is sufficient. It is concluded that our study can be used in scientific researches since it was checked in terms of validity and reliability.

Communication Skills in Athletes

The aim of this study is to find out the different level of communication skills between volleyball, handball, basketball athletes. Near East University Athletes Development Club athletes’ participated in this study. The data collected from 60 athletes in the teams of volleyball (17), handball (24) and basketball (19) in 2018-2019. 38.33% of the participants were 19 years of age and 23.33% were between the ages of 20-22, 38.33% were aged 23 and over. Moreover, 51.67% were women and 48.33% were male. Frequency distribution in data analysis, t-test for comparison of two groups and ANOVA analysis of variance to determine the relationship between more than two variables, chi square, standard deviation, the fit of the data set to normal distribution, Shapiro-Wilk test, QQ plot graph and distribution-related skewness-kurtosis coefficients were examined. Levene techniques were applied for homogeneity of variances. The difference between the views of the groups was interpreted by taking into account the P <0.05 significance level. According to the results; there was no significant difference between the mean scores of the communication skills scale at the level of P <0.05 when the athletes were examined in terms of age and sports barriers, but the difference between the points they got from the behavioral sub-dimension in communication skills inventory was statistically significant. In conclusion, it has been found that sports have a positive effect on the communication skills of athletes.

Fin Shape Dependence of Electrostatics and Variability in FinFETs

The performance of advanced nanoscale devices is limited by different process variability issues, including patterning proximity effects. Most manufactured fin-shaped field-effect transistors (FinFETs) have some imperfections in the fin shape due to imperfections in lithography and deformation due to other high-temperature process steps. In this work, full three-dimensional (3D) device simulations are performed to study the effects of such variability in the fin shape on the electrostatics of trigate FinFETs. Variability due to random discrete dopants (RDDs) and metal grain granularity (MGG) is considered separately and in combination. The device threshold voltage variation due to RDDs and MGG is critically examined. Finally, we calculate the mean and standard deviation of these parameters (QQ plots) to quantify the variability. It is shown that there is a strong correlation between the drain-induced barrier lowering (DIBL) and random discrete dopant position in the channel.

Performance of bias-correction schemes for CMORPH rainfall estimates in the Zambezi River basin

Abstract. Satellite rainfall estimates (SREs) are prone to bias as they are indirect derivatives of the visible, infrared, and/or microwave cloud properties, and hence SREs need correction. We evaluate the influence of elevation and distance from large-scale open water bodies on bias for Climate Prediction Center-MORPHing (CMORPH) rainfall estimates in the Zambezi basin. The effectiveness of five linear/non-linear and time–space-variant/-invariant bias-correction schemes was evaluated for daily rainfall estimates and climatic seasonality. The schemes used are spatio-temporal bias (STB), elevation zone bias (EZ), power transform (PT), distribution transformation (DT), and quantile mapping based on an empirical distribution (QME). We used daily time series (1998–2013) from 60 gauge stations and CMORPH SREs for the Zambezi basin. To evaluate the effectiveness of the bias-correction schemes spatial and temporal cross-validation was applied based on eight stations and on the 1998–1999 CMORPH time series, respectively. For correction, STB and EZ schemes proved to be more effective in removing bias. STB improved the correlation coefficient and Nash–Sutcliffe efficiency by 50 % and 53 %, respectively, and reduced the root mean squared difference and relative bias by 25 % and 33 %, respectively. Paired t tests showed that there is no significant difference (p &lt; 0.05) in the daily means of CMORPH against gauge rainfall after bias correction. ANOVA post hoc tests revealed that the STB and EZ bias-correction schemes are preferable. Bias is highest for very light rainfall (&lt; 2.5 mm d−1), for which most effective bias reduction is shown, in particular for the wet season. Similar findings are shown through quantile–quantile (q–q) plots. The spatial cross-validation approach revealed that most bias-correction schemes removed bias by &gt; 28 %. The temporal cross-validation approach showed effectiveness of the bias-correction schemes. Taylor diagrams show that station elevation has an influence on CMORPH performance. Effects of distance &gt; 10 km from large-scale open water bodies are minimal, whereas effects at shorter distances are indicated but are not conclusive for a lack of rain gauges. Findings of this study show the importance of applying bias correction to SREs.

Application of Extreme Value Theory in Predicting Climate Change Induced Extreme Rainfall in Kenya

Climate change has brought about unprecedented new weather patterns, one of which is changes in extreme rainfall. In Kenya, heavy rains and severe flash floods have left people dead and displaced hundreds from their settlements. In order to build a resilient society and achieve sustainable development, it is paramount that adequate inference about extreme rainfall be made. To this end, this research modelled and predicted extreme rainfall events in Kenya using Extreme Value Theory for rainfall data from 1901-2016. Maximum Likelihood Estimation was used to estimate the model parameters and block maxima approach was used to fit the Generalized Extreme Value Distribution (GEVD) while the Peak Over Threshold method was used to fit the Generalized Pareto Distribution (GPD). The Gumbel distribution was found to be the optimal model from the GEVD while the Exponential distribution gave the optimal model over the threshold value. Furthermore, prediction for the return periods of 10, 20, 50 and 100 years were made using the return level estimates and their corresponding confidence intervals were presented. It was found that increase in return periods leads to a corresponding increase in return levels. However, the GPD gave higher return levels for 10 and 20 years compared to GEVD. While, for higher return periods 50 and 100 years, the GEVD gave higher return levels compared to the GPD. Model diagnostics using probability, density, quantile and return level plots indicated that the models provided were a good fit for the data.

Frequentist Parameter Estimation of Two-Parameter Exponentiated Log-logistic Distribution BB

In this paper, we have considered frequentist parameter estimation of two parameter exponentiated log-logistic distribution based on a complete sample. The parameters are estimated using a likelihood-based classical inferential procedure. This study has tried to compute MLEs along with their asymptotic confidence interval, contour plot and standard errors. The K-S test statistic, Quantile-Quantile (QQ) and Probability-Probability (PP) plots are used to check the validity of the model. All the computations are performed in R software. Areal data set is considered for illustration of the purposed inferential procedures.

A new indirect estimation of reference intervals: truncated minimum chi-square (TMC) approach.

All known direct and indirect approaches for the estimation of reference intervals (RIs) have difficulties in processing very skewed data with a high percentage of values at or below the detection limit. A new model for the indirect estimation of RIs is proposed, which can be applied even to extremely skewed data distributions with a relatively high percentage of data at or below the detection limit. Furthermore, it fits better to some simulated data files than other indirect methods. The approach starts with a quantile-quantile plot providing preliminary estimates for the parameters (λ, μ, σ) of the assumed power normal distribution. These are iteratively refined by a truncated minimum chi-square (TMC) estimation. The finally estimated parameters are used to calculate the 95% reference interval. Confidence intervals for the interval limits are calculated by the asymptotic formula for quantiles, and tolerance limits are determined via bootstrapping. If age intervals are given, the procedure is applied per age interval and a spline function describes the age dependency of the reference limits by a continuous function. The approach can be performed in the statistical package R and on the Excel platform.

Predicting the performance of the players in NBA Players by divided regression analysis

A divided regression model is built to predict the performance of the players in the National Basketball Association (NBA) from year 1997 until year 2017. The whole data set is divided into five groups of sub data sets and multiple linear regression model is employed to model each of the sub data set. In addition, the relationships among independent variables are checked by using variance inflation factor (VIF) to identify the risk of having multicollinearity in the data. Moreover, non-linearity of regression model, non-constancy of error variance and non-normality of error terms are investigated by plotting residual plots and quantile-quantile plots. Finally, a divided regression model is built by combining the results obtained from the sub data sets and the performance of the divided regression model is verified.

Stress-Induced Variability Studies in Tri-Gate FinFETs with Source/Drain Stressor at 7 nm Technology Nodes

The epitaxially grown SiGe source/drain stressor (e-SiGe) technique has emerged to be a consistent performance booster for advanced devices below the 14 nm technology node. At nanoscale, the omnipresent residual stress is now becoming an important source of variability in advanced VLSI technologies that influence the circuit performance. Also, in deeply-scaled technologies, process and environment variations become other sources of variabilities. In this paper, we study the stress-induced variability in aggressively scaled (at 7 N) Si-channel FinFETs with epitaxially grown SiGe stressors in the source and drain regions. The stress distribution analysis is performed with the help of Technology CAD mechanical stress simulations. At first, we calibrate our simulation results with available experimental data. We generate the stress maps in FinFETs with various scaled dimensions of fin length, height and width. The effects of residual strain/stress on variability due to metal gate granularity (MGG) and random discrete dopant (RDD) in strain-engineered FinFETs (with 50 configurations) have been investigated. Furthermore, the device threshold voltage variation due to RDD and MGG are critically examined. Finally, we calculate the mean and standard deviation of these parameters (QQ plots) to quantify the variability.

A non-Gaussian random field model for earthquake slip

The present study proposes a methodology to generate stochastic slip field with desired probability structure and spectral characteristics. The characterization utilizes 100 tsunamigenic and 130 non-tsunamigenic slip models available in the SRCMOD database. First, the cumulative distribution function (CDF) of marginal slip distributions is obtained. Then, it compares the estimated CDFs with nine standard distribution functions based on model fitting criteria like Akaike Information Criterion, mean squared error, correlation coefficient, and QQ plots. The analysis showed that the majority of slip distributions follow generalized Pareto or truncated exponential distribution functions. For the parameters of CDF estimated from slip fields, an empirical relation is proposed as a function of magnitude (Mw) to predict the corresponding values. As the next step, to understand the correlation structure of the slip field, semi-variograms are estimated along strike and along downdip for all rupture models considered in the study. A total of nine theoretical variogram models is compared with the semi-variogram of each slip field. From the analysis based on model fitting criteria, most of the slip field is observed to follow a stable variogram model. An empirical equation is developed to predict the sill and range of stable variogram function for a given Mw. Then, an iterative method based on translational field theory is proposed to obtain an ensemble of non-Gaussian slip fields for a given Mw and type of source. The generated sample fields from the proposed method match with the prescribed non-Gaussian distribution and variogram structure. In the sequel, the method estimates the variogram and the corresponding spectral density of the underlying Gaussian field according to translation field theory. The scaling relations and the proposed iterative methodology can be used to obtain an ensemble of possible earthquake slip fields.

GEOSTATISTICAL MODELING OF SOYBEAN YIELD AND SOIL CHEMICAL ATTRIBUTES USING SPATIAL BOOTSTRAP

ABSTRACT The goal of this study was to use the spatial bootstrap method to model the spatial dependence structure of soybean yield and soil chemical attributes in an agricultural area. The study involved developing confidence intervals in probability plots to determine the probability distributions assumed by the data; determine the empirical distributions of the semivariances and model parameters, allowing to obtain statistics and confidence intervals; and to construct maps for the variables. The quantile-quantile plots indicated that the data follows a normal distribution. The confidence intervals for the semivariances helped to model the spatial dependence structure, and the descriptive statistics of the bootstrap replicates of the model parameters allowed to test the consistency of the estimates. The soil chemical attributes (calcium, potassium, and organic matter) were at levels suitable for soybean cultivation. However, the pH was below the ideal range in most of the study area, and water stress during cultivation decreased the mean yield. Therefore, according to the results, a recommendation to the farmer is to correct the soil pH to increase the yield.

Particulate production during debonding of fixed appliances: Laboratory investigation and randomized clinical trial to assess the effect of using flash-free ceramic brackets.

The aim of this laboratory and randomized clinical trial was to investigate particulate production at debonding and enamel clean-up following the use of flash-free ceramic brackets and to compare them with non-flash-free metal and ceramic brackets. In the laboratory study, brackets were bonded to bovine teeth. After 24hours of immersion in water, the brackets were debonded, the adhesive remnant scores noted, and the enamel cleaned with the use of rotary instruments. Four bracket-adhesive combinations and 2 different enamel pretreatment regimens were tested, including metal and ceramic brackets (conventional, adhesive precoat [APC], and APC flash-free) and conventional acid etch and self-etching primer. Quantitative (mg/m3) and qualitative analysis of particulate production was made in each case. In the clinical trial, 18 patients treated with the use of fixed appliances were recruited into this 3-arm parallel-design randomized controlled trial. They were randomly allocated to 1 of 3 groups: experimental flash-free ceramic bracket or non-flash-free ceramic or metal bracket group. Eligibility criteria included patients undergoing nonextraction maxillary and mandibular fixed appliance therapy. At completion of treatment, the brackets were debonded, and the primary outcome measure was particulate concentration (mg/m3). Randomization was by means of sealed envelopes. Data were analyzed with the use of quantile plots and linear mixed models. The effect of etch, bracket, and stage of debonding of clean-up on particle composition was analyzed with the use of mixed-effects regression. In the laboratory study, the APC brackets produced the highest particulate concentration. Although statistically significantly higher than the metal and conventional ceramic brackets, it was not significantly higher than the ceramic flash-free brackets. In the clinical study, there was no statistically significant effect of bracket type on particulate concentration (P=0.29). This was despite 3 patients with APC flash-free and 1 patient with conventional Clarity (with 1 bracket) having 1 or more ceramic bracket fracture at debonding requiring removal. No adverse events reported. Particulates in the inhalable, thoracic, and respirable fractions were produced at enamel clean-up with all bracket types. Although APC and APC flash-free brackets produced the highest concentrations in the laboratory study, there was no difference between any of the brackets in the clinical trial. The trial was not registered. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Spatiotemporal assessment of the PERSIANN family of satellite precipitation data over Fars Province, Iran

High resolution and global coverage of the satellite-based precipitation data have been found useful in many climate and hydrological studies, particularly in limited and nongauged areas. Due to systematic and nonsystematic factors, there are always deviations between ground-based and satellite-based precipitation. Among many satellite-based precipitation products, the PERSIANN (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks) family products attracted more attention. In this paper, we evaluated the PERSIANN family of monthly, seasonal, and annual precipitation data over Fars Province, Iran, at four different spatial scales, namely point (station), pixel, regional, and provincial during the period of 2003–2015 using 132 rain gauge data as baseline. The performance of the products was first evaluated by calculating some statistical metrics. The result shows that in all spatial and temporal scales, the three products mirror the precipitation pattern and underestimate the precipitation in the province. The PERSIANN-CDR outperforms the other two products and is the superior product. The performance of PERSIANNN products is the best at the provincial scale followed by regional, pixel, and point scales. The performance of PERSIANN family products is also evaluated by the quantile–quantile plot from which a set of equations is proposed to accurately predict precipitation in Fars Province from the PERSIANN-CDR precipitation data. The proposed equations are verified by 2-year precipitation data that were not used in the assessment of the products. These equations provide highly accurate precipitation data from PERSIANN-CDR data particularly in nongauged sites at various spatiotemporal scales for application such as in statistical hydrology and hydroclimate-related projects.

Model Efficiency and Uncertainty in Quantile Estimation of Loss Severity Distributions

Quantiles of probability distributions play a central role in the definition of risk measures (e.g., value-at-risk, conditional tail expectation) which in turn are used to capture the riskiness of the distribution tail. Estimates of risk measures are needed in many practical situations such as in pricing of extreme events, developing reserve estimates, designing risk transfer strategies, and allocating capital. In this paper, we present the empirical nonparametric and two types of parametric estimators of quantiles at various levels. For parametric estimation, we employ the maximum likelihood and percentile-matching approaches. Asymptotic distributions of all the estimators under consideration are derived when data are left-truncated and right-censored, which is a typical loss variable modification in insurance. Then, we construct relative efficiency curves (REC) for all the parametric estimators. Specific examples of such curves are provided for exponential and single-parameter Pareto distributions for a few data truncation and censoring cases. Additionally, using simulated data we examine how wrong quantile estimates can be when one makes incorrect modeling assumptions. The numerical analysis is also supplemented with standard model diagnostics and validation (e.g., quantile-quantile plots, goodness-of-fit tests, information criteria) and presents an example of when those methods can mislead the decision maker. These findings pave the way for further work on RECs with potential for them being developed into an effective diagnostic tool in this context.

Assessment of AERMOD modeling system for application in complex terrain in Pakistan

Atmospheric dispersion models based on Gaussian plume formulation are widely used for regulatory purposes in flat terrain. In this paper, the application of an advanced Gaussian plume modeling system, AERMOD, has been investigated over complex terrain setting through a field tracer test conducted in April 2018 near Islamabad, Pakistan. The model was validated through short term (2 h) release from a point elevated non buoyant source of SF 6 . The hourly averaged concentrations were measured at 47 discrete sampling points. The mesoscale meteorological model, WRF was coupled with AERMOD to provide hourly surface and upper boundary layer meteorological parameters. The statistical evaluation of model was carried out using Fractional Bias (FB) and Normalized Mean Square Error (NMSE). The quantile-quantile (Q-Q) plot was used to assess model's ability to follow the observed concentration distribution. For this field tracer test the model over-predicted ground level concentrations at the receptors close to the source and underestimated at the receptors located in a valley and far away from the source. Moreover, AERMOD overestimated the concentration at receptors which were at the point of direct impaction of plume and ridge. Overall, the model under-predicted the ground level concentration within a factor of two (FB = 0.63) for this field tracer test. It was found that the model better simulated the higher concentrations which are of primary interest for regulatory purposes. • AERMOD modeling system was applied to a scenario involving an elevated point source in near field complex terrain. • A short term field tracer test was carried out with 47 discrete sampling points spread across an 8 km domain. • The meteorological input was provided using NWP model, WRF. • The model indicates an overall under-prediction within a factor of 2, although higher concentrations were better simulated.

Flood Frequency Analysis of Niandan River at Baro, Nigeria

The determination of appropriate probability distribution is crucial for flood – risk reduction and mitigation of flood –induced damages in flood plains. This paper investigates the selection of an appropriate probability distribution for at – site flood frequency analysis using annual maximum series of Niandan River at Baro. The model results were subjected to five goodness of fit –tests(i.e. Probability plots, Probability Plot Correlation Coefficient (PPCC), Percent bias (PBIAS), Nash- Sutcliffe efficiency(NSE) and RMSE-observations standard deviation (RSR) and performance scoring/ranking to identified the best – fit distribution.The Normal, and Weibull distributions have been identified as the top two distributions for Niandan at baro. Assessment of other of flood frequency analysis studies across Nigeria show that no single distribution has been found appropriate for whole country. Consequently, research work for the search of best – fit distribution for Nigeria will continue into the future. Keywords : Flood flow, Flood frequency analysis, PPCC, Flood quantiles, efficiency criteria, DOI : 10.7176/CER/11-4-03 Publication date :May 31 st 2019

Uncertainty analysis of the relationship between discharge and nitrate concentration in the Lower Illinois River using a copula model

Abstract The complex relationship between water quality and river discharge has long been an active area of research. This research applies bivariate statistics to river nitrate concentration and discharge, and develops a procedure for selecting the best bivariate distribution for the chosen models. Nitrate concentration (NO3) data from five stations on the Lower Illinois River, USA, collected from 1972 to 2012 were used for demonstration of this procedure. To explore the statistical relationship between discharge and nitrate concentration, three copula statistical models were applied to determine optimal bivariate distributions. The generalized Pareto (GPA), generalized extreme value (GEV), and lognormal two- (LN2) and three-parameter (LN3) distributions were used as marginal distributions, and were combined with the Clayton, Frank, and Gumbel copula models. The probability plot correlation coefficient (PPCC) test and the S n statistic were used to select the most suitable copula models. As a result, the GPA distributions for streamflow and nitrate concentration in the Frank copula model were more accurate for representing the data from the two mainstem stations, Havana (D-31) and Valley City (D-32), and those from the Oakford station along the Sangamon River (E-25). However, the Clayton copula model using NL3 for representing streamflow and GPA for representing nitrate concentration was more accurate for stations along the Spoon (DJ-08) and La Moine Rivers (DG-01). This study enabled the development of a procedure for determining an optimal copula for application in the environmental sciences and also provided a case study for applying copula models using discharge and nutrient concentration as hydrologic and water quality variables, respectively.

Data assimilation for constructing long-term gridded daily rainfall time series over Southeast Asia

The data scarcity and poor availability of observed daily rainfalls over Southeast Asia has limited the possibility to a wider range of studies in light of impacts from climate change and extreme hydro-meteorological processes such as floods, droughts, and other watershed management practices. To fill such a gap, data assimilation was carried out in this study to construct a long-term gridded daily (0.50° × 0.50°) rainfall time series (1951–2014) over Southeast Asia. In rainfall data assimilation, the available and globally accepted high resolution gridded datasets viz. Southeast Asia observed (SA-OBS) (1981–2014), APHRODITE (1951–2007), TRMM (1998–2018), PRINCETON (1951–2008) along with limited rain gauges-based rainfalls were utilized. In this study, eight gap filling methods were employed and tested at 20 selected rainfall grids to fill the long gaps presented in the SA-OBS gridded dataset. The strength of each method and associated uncertainties were evaluated in the computed rainfalls utilizing multiple functions at missing grids. The accuracy of each method, in case of extreme rainfalls, was tested by quantile–quantile (Q–Q) plots at different quantile intervals. The distance power method based on the Pearson correlation coefficient and the multiple linear regression method performed satisfactorily and produced minimum uncertainties in filling rainfall gaps. To test the accuracy and compatibility of gap-filled SA-OBS gridded dataset with other sources of datasets, the seasonality analysis and rainfall indices comparison were carried out. Results showed that the gap-filled SA-OBS dataset was better comparable to other sources of rainfalls. For the construction of the long-term rainfall time series (1951–2014), quantile mapping was adopted for bias correction and the quality of the final merged dataset was evaluated.

Spatial variability of annual rainfall in East Java Regions: application of histogram and normal QQ-Plot

This research aims to analyse the spatial variability of annual rainfall. Daily rainfall data from 936 rain-gauges in East Java regions are used as the primary input. The average annual rainfall and the maximum annual rainfall are obtained from the daily rainfall data. Research procedures consist of data pre-treatment, ESDA, interpolation, and interpretation. Histogram and QQ-Plot were used to describe the spatial variability of annual rainfall in each sub-region. Next, an IDW interpolation method was used to create a thematic map of the annual rainfall. The results showed that local spatial variability of rainfall could be visualised more detail for each sub-region using histogram and QQ-Plot. The thematic map showed that the distribution of average annual rainfall in the region range from 1000 mm/year up more than 3000 mm/year. Maximum annual rainfall range between 2,100 mm/year up to 4,500 mm/year. The result also shows the positive correlation between the altitude of the rain-gauge and local annual rainfall received.

Mapping the Young's modulus distribution of the human tympanic membrane by microindentation

The human tympanic membrane (TM, or eardrum) is composed primarily of layers of collagen fibers oriented in the radial and circumferential directions, as well as epidermal and mucosal layers at the lateral and medial surfaces. The mechanical properties of the TM depend on the microstructures of the collagen fibers, which vary with location, resulting in a spatial variation of Young's modulus. In this study, the Young's modulus of the human TM is measured using microindentation. A 10 μm diameter spherical nanoindenter tip is used to indent the TM at different locations in the lateral and medial surfaces. Through a viscoelastic contact analysis, the steady state out-of-plane (through thickness) Young's modulus at a constant strain rate for the TM is determined from the uniaxial relaxation modulus. The measured spatial distribution of Young's modulus is reported for the entire TM pars tensa on both lateral and medial surfaces. The Young's modulus, for the four TM quadrants, is analyzed statistically using a normal quantile-quantile (Q-Q) plot. The obtained S-shaped curve indicates a bi-modal Gaussian distribution in the Q-Q plot. The spatial distribution of the Young's modulus is modeled by a bivariate Gaussian function in the polar coordinates over the entire TM on both the lateral and medial surfaces. It is shown that the anterior-superior quadrant has the smallest value of Young's modulus. Differences are observed in the spatial distribution of the Young's modulus for both the lateral and medial surfaces. For the medial surface, Young's modulus varies mainly along the radial direction following a small-large-small trend, emanating from the umbo. For the lateral surface, the modulus at the anterior-superior quadrant shows the smallest modulus; the modulus decreases gradually along the radial directions. The quantitative results presented in this paper will help improve future simulation models of the middle ear by using spatial dependence of Young's modulus over the entire TM.