CE 264000 Data Analysis

CE 264000 Data Analysis
. • Import the time series into a spreadsheet program of your choice (Micro$oft Office/Excel or LibreOffice/Calc). • Calculate the minimum, maximum, median and the first four moments (mean, standard deviation, skewness and kurtosis) of the time series • Calculate the 10-base logarithm of the time series and compute the same properties (minimum, maximum, and the first four moments) for the resulting new data series. Exercise 2: • Calculate and create an X-Y plot of the empirical cumulative distribution function of the discharge time series. • Plot the cumulative density function in normal and lognormal (along the x axis) coordinate spaces • Calculate and create a bar chart of the probability mass density function of the 10-base logarithmic discharge time series by discretizing (binning) into 5-10 size categories (by slicing up the value ranges defined by the minimum and maximum). Try to maximize the round numbers in the category boundaries by selecting the starting “bin” and the binning size with exact numbers (e.g. log10 X =-1.0,-0.75, 0.50,…, 2.0, 2.25, 3.0 ) Exercise 3: Fit logarithmic normal distribution to the empirical cumulative distribution function using the method of moments. In other words, estimate the normal distribution's parameters ( µ ,s ) from the time series and plot it along with the CDF derived from the data in the previous exercise in different color or line style. Calculate the probability mass function for the category bins that you used to discretize your data in the previous exercise (the difference of the CDF values at the upper and lower bounds of the bin). Plot the the fitted PMF against the empirical PMF.