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# SA7 - Stat 133 Fall 2009 Short assignment 7 Working with...

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Stat 133, Fall 2009 Short assignment 7: Working with non-standard distributions Due Tuesday Nov. 24 at 11 pm on bSpace The Pareto distribution is often used to model data that has a long right tail, such as incomes. Its pdf is f ( x ) = ακ α x α +1 , x > κ and its cdf is F ( x ) = 1 - κ x α , x > κ Functions for working with the Pareto distribution are not built into R , so in this assignment you’ll write your own. Write two functions, dpareto and ppareto , to calculate the pdf and cdf. Both should have arguments x , alpha , and kappa , and both should include a check that all values in x are greater than kappa , producing an error message if not. Create a sequence of x values and use it to make two plots illustrating the pdf and cdf for a specific choice of α and κ . The inverse CDF method is an algorithm for generating random samples from a distribution when its CDF F ( x ) has an inverse that’s available in closed form. To generate B samples, we 1. simulate B random samples y (1) , . . . , y ( B ) from a uniform distribution on [0 ,
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• Fall '08
• Staff
• Probability distribution, probability density function, Cumulative distribution function, Inverse transform sampling, random samples, inverse cdf method

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