Question

The following data was collected from a global warming exercise regarding the time elapsed in months between major floods attributed to global warming. Time Elapsed: 1,2,2,1,1,1,2,2,3,4,3,4,3,5,3,4,3,4,6,7,8,6,7,6,8,7,6,7,6,7,6,8,9,9,10,10,11,11,11,9,9,10,12,13,14,14,14,13, 13,12,12,15,15,16,16,17,17,16,18,19,20,20,21,23,23,19,19,11,13,12,24

Using the Method of Moments (MM) for a data fit investigation to a distribution

i. Find an estimate for the Exponential distribution parameter.

ii. Find estimators for Gamma distribution parameters.

iii. Find estimators for Normal distribution parameters

iv. Write down the log-likelihood function for the normal distribution (only in terms of the summation with the correct indexes) and calculate its value in R using the maximum likelihood estimates of µ and σ

v. Assess the fit of these three distributions to the empirical distribution for the time elapsed by presenting all three fits on to a cumulative probability graph. Which model would you recommend? Why?

vi. Select the best model among the tested models via AIC.

Answer 1

i. Find an estimate for the Exponential distribution parameter.

ii. Find estimators for Gamma distribution parameters.

iii. Find estimators for Normal distribution parameters

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