On the Mittag-Leffler distributions

DOI10.1016/S0378-3758(98)00096-2zbMath0935.60002OpenAlexW2064860158MaRDI QIDQ1298910

Gwo Dong Lin

Publication date: 4 May 2000

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0378-3758(98)00096-2

zbMATH Keywords

Laplace transformLévy measurecompletely monotonic functionsMittag-Lefflerpositive stable distribution

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Probability distributions: general theory (60E05) Laplace transform (44A10)

Related Items (24)

A PATHWAY MODEL OF MITTAG-LEFFLER DISTRIBUTIONS AND RELATED PROCESSES ⋮ On the Semi-Mittag-Leffler Distributions ⋮ Fractional absolute moments of heavy tailed distributions ⋮ Fractional calculus of generalized \(k\)-Mittag-Leffler function and its applications to statistical distribution ⋮ Fractional Relaxation Equations and Brownian Crossing Probabilities of a Random Boundary ⋮ UNIFORM CONSISTENCY FOR NONPARAMETRIC ESTIMATORS IN NULL RECURRENT TIME SERIES ⋮ Estimation of Mittag-Leffler Parameters ⋮ Mittag-Leffler process ⋮ A note on the Linnik distributions ⋮ Mittag-Leffler vector random fields with Mittag-Leffler direct and cross covariance functions ⋮ Beyond the Poisson renewal process: a tutorial survey ⋮ Competing risks driven by Mittag-Leffler distributions, under copula and time transformed exponential model ⋮ Mittag-Leffler function distribution -- a new generalization of hyper-Poisson distribution ⋮ Moment inequalities for nonnegative random variables ⋮ A bivariate infinitely divisible distribution with exponential and Mittag-Leffler marginals ⋮ NEW RESULTS ON THE DISTRIBUTION OF DISCOUNTED COMPOUND POISSON SUMS ⋮ The discrete delta and nabla Mittag-Leffler distributions ⋮ Mittag-Leffler functions and their applications ⋮ Formulas of absolute moments ⋮ On the stochastic equation \(\mathcal{L}(Z) = \mathcal{L} [V(X + Z)\) and properties of Mittag-Leffler distributions] ⋮ On the Structure and Estimation of Reflection Positive Processes ⋮ Matrix-variate statistical distributions and fractional calculus ⋮ On a fractional alternating Poisson process ⋮ Spectral properties of superpositions of Ornstein-Uhlenbeck type processes

Cites Work

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• On Mittag-Leffler functions and related distributions
• Note on a characterization of exponential distributions
• Generalized gamma convolutions and related classes of distributions and densities
• Note on a characterization of gamma distributions
• Distributions with complete monotone derivative and geometric infinite divisibility
• Some representations of stable random variables as products
• The completely monotonic character of the Mittag-Leffler function 𝐸ₐ(-𝑥)
• The representation of 𝑒^{-𝑥^{𝜆}} as a Laplace integral

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