SYLLABUS:-
UNIT – I
Preliminary Data Analysis: Graphical representation-line diagram or Bar Chart, Dot diagram, Histogram, Exploratory methods- stem and leaf plot, Box plot. Random events- sample space and events, the null event, Intersection and Union, Venn Diagram and Event space. Continuous Distributions- Normal Distribution, Lognormal Distribution, Bivariate Normal Distribution.
UNIT – II
Model Estimation and Testing: Properties of Estimators- Unbiasedness, Consistency, Minimum Variance, Efficiency, Sufficiency. Estimation of Confidence Intervals. Hypothesis testing- Procedure for testing, Probabilities of Type I and Type II Errors and the power function, Tests of Hypothesis involving the Variance, the F Distribution and its use. Nonparametric methods- Wilcoxon Signed- Rank Test for Association of Paired Observations.
UNIT – III
Goodness of Fit Tests: Chi-squared Goodness of Fit test, Kolmogorov- Smirnov Goodness of Fit test, Kolmogorov- Smirnov Two- sample test, Anderson- Darling Goodness of Fit test, Other methods for testing the Goodness of Fit to a Normal Distribution.
Analysis of Variance: One-Way Analysis of Variance, Two-way analysis of Variance. Probability Plotting for Normal Distribution, Probability Plotting for Type I Extreme Value Distribution.
Identification and Accomodation of Outliers: Hypothesis Tests, Test Statistics for Detection of Outliers, Dealing with Nonnormal Data.
Estimation of Probabilities of Extreme events when outliers are present. Multivariate Analysis- Principle Components Analysis, Factor Analysis, Cluster analysis.
Spatial Correlation: The Estimation problem, Spatial Correlation and the Semivariogram, some Semivariogram Models and Physical Aspects, Spatial Interpolations and Kriging.
UNIT – IV
Frequency Analysis of Extreme Events: Order Statistics- Functions of Order Statistics, Expected value and Variance of Order Statistics, Expected Value and Variance of Order Statistics. Extreme Value Distributions- Basic Concepts, Gumbel Distribution, Weibull Distribution as an Extreme Value Model, General Extreme Value Distribution. Analysis of Natural Hazards: Floods, storms and Droughts, Earthquakes and volcanic eruptions, winds, sea levels and Highest sea waves.
Simulation techniques for Design: MonteCarlo Simulation- Statistical Experiments, Probability Integral Tranform, Sample size and accuracy of Monte Carlo Experiments.
UNIT – I
Preliminary Data Analysis: Graphical representation-line diagram or Bar Chart, Dot diagram, Histogram, Exploratory methods- stem and leaf plot, Box plot. Random events- sample space and events, the null event, Intersection and Union, Venn Diagram and Event space. Continuous Distributions- Normal Distribution, Lognormal Distribution, Bivariate Normal Distribution.
UNIT – II
Model Estimation and Testing: Properties of Estimators- Unbiasedness, Consistency, Minimum Variance, Efficiency, Sufficiency. Estimation of Confidence Intervals. Hypothesis testing- Procedure for testing, Probabilities of Type I and Type II Errors and the power function, Tests of Hypothesis involving the Variance, the F Distribution and its use. Nonparametric methods- Wilcoxon Signed- Rank Test for Association of Paired Observations.
UNIT – III
Goodness of Fit Tests: Chi-squared Goodness of Fit test, Kolmogorov- Smirnov Goodness of Fit test, Kolmogorov- Smirnov Two- sample test, Anderson- Darling Goodness of Fit test, Other methods for testing the Goodness of Fit to a Normal Distribution.
Analysis of Variance: One-Way Analysis of Variance, Two-way analysis of Variance. Probability Plotting for Normal Distribution, Probability Plotting for Type I Extreme Value Distribution.
Identification and Accomodation of Outliers: Hypothesis Tests, Test Statistics for Detection of Outliers, Dealing with Nonnormal Data.
Estimation of Probabilities of Extreme events when outliers are present. Multivariate Analysis- Principle Components Analysis, Factor Analysis, Cluster analysis.
Spatial Correlation: The Estimation problem, Spatial Correlation and the Semivariogram, some Semivariogram Models and Physical Aspects, Spatial Interpolations and Kriging.
UNIT – IV
Frequency Analysis of Extreme Events: Order Statistics- Functions of Order Statistics, Expected value and Variance of Order Statistics, Expected Value and Variance of Order Statistics. Extreme Value Distributions- Basic Concepts, Gumbel Distribution, Weibull Distribution as an Extreme Value Model, General Extreme Value Distribution. Analysis of Natural Hazards: Floods, storms and Droughts, Earthquakes and volcanic eruptions, winds, sea levels and Highest sea waves.
Simulation techniques for Design: MonteCarlo Simulation- Statistical Experiments, Probability Integral Tranform, Sample size and accuracy of Monte Carlo Experiments.
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