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Math 524: Excel Assignment 2

Due Saturday, 17 February, at midnight

For Data Set “Continuous X,” perform the following in Excel:

1. Compute the maximum likelihood estimates for three distributions: (1) Lognormal(µ, σ), (2) Exponential(θ), and (3) Gamma(α, θ).

2. Perform the Kolmogorov-Smirnov test for each of the three distributions, all at the α = 0.05 level of significance.

3. Choose a distribution based on the Schwarz-Bayesian criterion. How does that choice fit with the results of the Kolmogorov-Smirnov tests?

4. Perform the chi-square goodness-of-fit test for the distribution you chose; use the α = 0.05 level of significance. Use ten groups of size Ej = 10.

For Data Set “Discrete N,” perform the following in Excel:

1. Compute the maximum likelihood estimates for three distributions: (1) P oisson(λ), (2) Binomial(m, q), and (3) NegativeBinomial(r, β). For the Binomial, you’ll have to create a likelihood profile. For the Negative Binomial, do not use Excel’s built-in pmf because r is restricted to be a positive integer in Excel.

2. Perform two likelihood rate tests at the α = 0.05 level of significance. (1) Compare the Binomial (H1) with the Poisson (H0), and (2) compare the Negative Binomial (H1) with the Poisson (H0).

3. Choose a model based on the two likelihood ratio tests, and perform a chi-square goodness-of-fit test on that model at the α = 0.05 level of significance. Use six groups of roughly equal numbers of Oj .