Supp returns the survival function at x for the discrete power law with exponent (1.0 / xi1 + 1.0), for values greater than or equal to u.
Supp(x, u, xi1, log = FALSE)A numeric vector of the same length as x
Vector of positive integers
Scalar, non-negative integer threshold
Scalar, a positive real number representing the shape parameter
Boolean (default 'FALSE'), whether the survival function should be returned on the log scale.
The survival function used is S(x) = Pr(X >= x), where X is a random variable following the discrete power law. The inclusion of x in the sum means S(x) may not necessarily equal to Pr(X > x) as the distribution is discrete. In the case of discrete power law, it can be shown that S(x) = hzeta(alpha, x)/hzeta(alpha, u), where hzeta is the Hurwitz zeta function i.e. hzeta(y, z) = z^(-y) + (z+1)^(-y) + (z+2)^(-y) + ... and alpha = 1.0 / xi1 + 1.0. That xi1 is used instead of alpha is for alignment with the parametrisation in dmix, Smix and mcmc_mix.
dupp for the corresponding probability mass function, Smix for the survival function of the discrete extreme value mixture distribution.
Supp(c(10,20,30,40,50), 12, 2.0)
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