Glass in building. Procedures for goodness of fit and confidence intervals for Weibull distributed glass strength data

2003 ◽  
Keyword(s):  
Confidence Intervals ◽  
Goodness Of Fit ◽  
Strength Data ◽  
Glass Strength

A numerical prediction of flexural strength probability for NBG-18 nuclear grade graphite using strength pair model

2017 ◽  
Vol 52 (3) ◽  
pp. 204-211 ◽  
Author(s):  
Manik Bansal ◽  
Indra Vir Singh ◽  
Bhanu K Mishra ◽  
Kamal Sharma ◽  
IA Khan
Keyword(s):  
Flexural Strength ◽  
Goodness Of Fit ◽  
Numerical Data ◽  
Failure Criteria ◽  
Numerical Prediction ◽  
Nuclear Grade ◽  
Goodness Of Fit Test ◽  
Strength Data ◽  
Pair Model ◽  
Proposed Model

In this work, a strength pair model has been proposed for the numerical prediction of flexural strength probability of NBG-18 nuclear grade graphite. The input to the proposed model is a random strength pair of tensile and compressive strengths whose value is based on its probability of occurrence in the experimental data. A finite element–based deterministic numerical approach has been implemented. To account for the large difference in tensile and compressive strengths, Drucker–Prager failure criteria has been implemented. The failure envelope of the Drucker–Prager failure criteria is assumed to have uniaxial fit with Mohr–Coulomb model in the principal stress space. A total of 292 simulations with random pairs of tensile and compressive strength are performed on a three-point bend specimen to obtain a set of flexural strength data. The flexural strength data obtained through numerical simulations are fitted using normal and Weibull distributions. The flexural strength probability obtained from the proposed model is found on conservative side. A goodness-of-fit test concludes that Weibull distribution fits the numerical data better than normal distribution.

scholarly journals Fitting a logistic growth model to yield traits of lettuce cultivars growing in summer

2020 ◽  
Vol 14 (1) ◽  
Author(s):  
Fernanda Carini ◽  
Alberto Cargnelutti-Filho ◽  
Jéssica Maronez De Souza ◽  
Rafael Vieira Pezzini ◽  
Cassiane Ubessi ◽  
...  
Keyword(s):  
Confidence Intervals ◽  
Growth Model ◽  
Iterative Process ◽  
Logistic Model ◽  
Goodness Of Fit ◽  
Least Squares Method ◽  
Logistic Growth ◽  
Model Parameters ◽  
Yield Traits ◽  
Logistic Growth Model

The objective of this study was to fit a logistic model to fresh and dry matters of leaves and fresh and dry matters of shoots of four lettuce cultivars to describe growth in summer. Cultivars Crocantela, Elisa, Rubinela, and Vera were evaluated in the summer of 2017 and 2018, in soil in protected environment and in soilless system. Seven days after transplantation, fresh and dry leaf matters and fresh and dry shoot matters of 8 plants were weighed every 4 days. The model parameters were estimated using the software R, using the least squares method and iterative process of Gauss-Newton. We also estimated the confidence intervals of the parameters, verified the assumptions of the models, calculated the goodness-of-fit measures and the critical points, and quantified the parametric and intrinsic nonlinearities. The logistic growth model fitted well to fresh and dry leaf and shoot matters of cultivars Crocantela, Elisa, Rubinela, and Vera and is indicated to describe the growth of lettuce.

scholarly journals Design impact and significance of non-stationarity of variance in extreme rainfall

2015 ◽  
Vol 371 ◽  
pp. 117-123 ◽  
Author(s):  
M. Al Saji ◽  
J. J. O'Sullivan ◽  
A. O'Connor
Keyword(s):  
Confidence Intervals ◽  
Goodness Of Fit ◽  
Daily Rainfall ◽  
Trend Detection ◽  
Climate Change Signal ◽  
Annual Maximum ◽  
Important Indicator ◽  
Detection Techniques ◽  
The Mean ◽  
The Impact

Abstract. Stationarity in hydro-meteorological records is often investigated through an assessment of the mean value of the tested parameter. This is arguably insufficient for capturing fully the non-stationarity signal, and parameter variance is an equally important indicator. This study applied the Mann-Kendall linear and Mann-Whitney-Wilcoxon step change trend detection techniques to investigate the changes in the mean and variance of annual maximum daily rainfalls at eight stations in Dublin, Ireland, where long and high quality daily rainfall records were available. The eight stations are located in a geographically similar and spatially compact region (< 950 km2) and their rainfalls were shown to be well correlated. Results indicate that while significant positive step changes were observed in mean annual maximum daily rainfalls (1961 and 1997) at only two of the eight stations, a significant and consistent shift in the variance was observed at all eight stations during the 1980's. This period saw a widely noted positive shift in the winter North Atlantic Oscillation that greatly influences rainfall patterns in Northern Europe. Design estimates were obtained from a frequency analysis of annual maximum daily rainfalls (AM series) using the Generalised Extreme Value distribution, identified through application of the Modified Anderson Darling Goodness of Fit criterion. To evaluate the impact of the observed non-stationarity in variance on rainfall design estimates, two sets of depth-frequency relationships at each station for return periods from 5 to 100-years were constructed. The first was constructed with bootstrapped confidence intervals based on the full AM series assuming stationarity and the second was based on a partial AM series commencing in the year that followed the observed shift in variance. Confidence intervals distinguish climate signals from natural variability. Increases in design daily rainfall estimates obtained from the depth-frequency relationship developed from the truncated AM series, as opposed to those using the full series, ranged from 5 to 16% for the 5-year event and from 20 to 41% for the 100-year event. Results indicate that the observed trends exceed the envelopes of natural climate variability and suggest that the non-stationarity in variance is associated with a climate change signal. Results also illustrate the importance of considering trends in higher order moments (e.g. variance) of hydro-meteorological variables in assessing non-stationarity influences.

Embedded Distributions: Two Numerical Examples

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Goodness Of Fit ◽  
Asymptotic Theory ◽  
Extreme Value ◽  
Confidence Bands ◽  
Fibre Strength ◽  
Data Sets ◽  
Strength Data ◽  
Log Likelihood ◽  
Embedded Model ◽  
Two Parameter

This chapter illustrates use of (i) the score statistic and (ii) a goodness-of-fit statistic to test if an embedded model provides an adequate fit, in the latter case with critical values calculated by bootstrapping. Also illustrated is (iii) calculation of parameter confidence intervals and CDF confidence bands using both asymptotic theory and bootstrapping, and (iv) use of profile log-likelihood plots to display the form of the maximized log-likelihood and scatterplots for checking convergence to normality of estimated parameter distributions. Two different data sets are analysed. In the first, the generalized extreme value (GEVMin) distribution and its embedded model the simple extreme value (EVMin) are fitted to Kevlar-fibre breaking strength data. In the second sample, the four-parameter Burr XII distribution, its three-parameter embedded models, the GEVMin, Type II generalized logistic and Pareto and two-parameter embedded models, the EVMin and shifted exponential, are fitted to carbon-fibre strength data and compared.

Factorizations of the residual likelihood criterion in discriminant analysis

1966 ◽  
Vol 62 (4) ◽  
pp. 743-752 ◽  
Author(s):  
J. Radcliffe
Keyword(s):  
Discriminant Analysis ◽  
Confidence Intervals ◽  
Goodness Of Fit ◽  
Discriminant Functions ◽  
Approximate Factorization ◽  
Analytic Proof ◽  
Independent Variables ◽  
Canonical Variables ◽  
Residual Likelihood ◽  
The Difference

Certain exact tests were developed by Williams (1952) to deal with the goodness of fit of a single hypothetical discriminant function. Bartlett (1951) generalized these results by the use of the geometric method to any number of dependent and independent variables. Bartlett's paper is divided into two parts. The first deals with an approximate factorization of the residual likelihood criterion into an effect due to the difference between the hypothetical and sample functions, and an effect due to non-collinearity. A method is given for constructing confidence intervals from the first factor. The second part of the paper gives two possible exact factorizations of the likelihood criterion, expressing the results in terms of the sample canonical variables. Kshirsagar (1964a) has expressed these results in terms of the original variables and given an analytic proof of the distribution of the factors. Williams (1955, 1961) has outlined a generalization of these results to several discriminant functions and given the result for one of the possible factorizations.

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