Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk

Index

α-Stable

LDA models, 333

ν-Stable family, 332

Tail properties, 332

Additive Exponential Dispersion Models, 312

Ali-Mikhail-Haq copula, 397

alpha-Stable distribution

asymptotic density expansion, 196

asymptotic tail behaviour, 220

Characterization 1, 149

Characterization 2, 149

Characterization 3, 153

Characterization 4, 156

density approximation FFT and Bergstrom, 189

density approximation polynomial series, 196

density approximation quadrature, 187

density approximation reparameterization, 198

density Scale Mixture of Normals (SMiN), 206

distribution approximation quadrature, 208

distribution approximation series, 209

domain of attraction, 152, 155

Fractional Lower Order Moments, 223

Levy distribution, 151

Levy LePage series, 205

Nolan's S0 and S1-Type Parameterization, 178

parameter estimation, 215

quantile function, 210

simulation, 214

Zolotarev's A-Type parameterization, 167, 172

Zolotarev's B-Type density, 185

Zolotarev's B-Type parameterization, 175

Zolotarev's C and E-Type parameterizations, 176

Zolotarev's W-Type parameterization, 176

alpha-Stable distribution spectral measure, 162

Archimedean copula, 397

Asymmetric Laplace distribution, 327

Maximum-Likelihood estimation, 329

Asymmetric Power distribution, 446

Asymptotic equivalence in distribution, 110

asymptotically locally constant distribution, 120

Benktander II distribution, 68

Bergstrom series expansion, 196

Beta distribution, 592

Binomial-Levy LDA Model, 345

bounds

aggregate tail distributions, 111

probabilities ...