HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 560

The corresponding (cumulative) distribution function (cdf) would be given by an integral that has no closed-form solution. The exponential distribution The exponential distribution is the gamma distribution with a = 1. Its pdf is given by f (x) = 1 ⋅ exp(− x ), for x > 0, β > 0 , β β while its cdf is given by F(x) = 1 - exp(-x/β), for x>0, β >0. The beta distribution The pdf for the gamma distribution is given by f (x xα −1 ⋅ (1 − x) β −1, for 0 < x < 1,α > 0, β > 0 As in the case of the gamma distribution, the corresponding cdf for the beta distribution is also given by an integral with no closed-form solution. The Weibull distribution The pdf for the Weibull distribution is given by f (x x β −1 ⋅ exp(−α ⋅ x β ), for x > 0,α > 0, β > 0 While the corresponding cdf is given by F (x) = 1 − exp(−α ⋅ x β ), for x > 0,α > 0, β > 0 Functions for continuous distributions To define a collection of functions corresponding to the gamma, exponential, beta, and Weibull distributions, first create a sub-directory called CFUN Page 17-7