Descriptive statistics of the ultimate strength of the plate calculated by nonlinear FEM.

Description
Consider the sample in the excel file "sample.xls" of 100 values of the ultimate strength (?u) [in MPa] of a steel square plate with initial imperfections subjected to in-plane longitudinal displacement evaluated by non-linear FE analysis.

The work to be performed should include the following:

1) Descriptive statistics of the ultimate strength of the plate calculated by nonlinear FEM.

2) Probability distribution model fitting. Fit at least 2 probability distributions to the sample using the Least Squares Fit of Transformed Data method (Probability Plot) and the Maximum Likelihood Method.

3) Test the validity of the assumed distributions using the Chi-square and the Kolomogorov- Smirnov tests.

4) Compare the two probability distributions using the Akaike Information Criterion (AIC).

5) Assume that the ultimate strength (?u ) of the plate is described by a lognormal distribution and that the uncertainty in its mean value is described by a normal distribution (prior distribution) with mean estimated by the Maximum Likelihood Method and coefficient of variation of 0.2.

Assume that the following 5 new observations of the ultimate strength of the plate were obtained { 285, 289, 278, 272, 299}.