Analytic and Asymptotic Properties of the Generalized Student and Generalized Lomax Distributions

Analytic and asymptotic properties of the generalized Student Lomax distributions are discussed, with main focus on representation these as scale mixtures laws that appear limit in classical theorems probability theory, such normal, folded exponential, Weibull, Fréchet distributions. These representations result possibility proving some for statistics constructed from samples random sizes which laws. An overview known distribution is given, simple bounds its tail probabilities presented. analog ‘multiplication theorem’ proved, identifiability considered. The normal mixture mixing this studied. Some general inequalities proved relate tails distribution. It values parameters, infinitely divisible admits a Laplace Necessary sufficient conditions presented provide convergence sums number independent variables finite variances other to As an example, sample quantiles defined absolute value variable shown can be represented maximum minimum demonstrated Weibull or consequence, it limiting extreme size. mixed geometric considered, corresponding extension famous Rényi theorem proved. law large numbers Poisson presented, has