The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance |
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asymptotically normal Bessel function bivariate ch.f characteristic function characterization classical Laplace distribution classical Laplace r.v. converges in distribution corresponding Cov(Y covariance matrix denote derived deviation distribution function distribution with density distribution with mean entropy equal estimator Exercise exponential distribution finite variance gamma distribution Gaussian geometric stable laws given hyperbolic distributions i.i.d. standard independent infinitely divisible integral interval Kotz Kozubowski Laplace density Laplace distribution CL(0 Laplace laws Laplace motion Let X1 likelihood function limit linear Linnik distribution location parameter mean 1/p mean zero MLE's normal distribution Note obtain order statistics probability Proof properties Proposition quantile r.v. with mean random sample relation Remark sample median scale parameter Section Show skewness standard classical Laplace standard Laplace standard normal symmetric Laplace distribution Theorem unimodal univariate W₁ Y₁ zero and variance