Abstract
The Marshall-Olkin family of probability distributions has been the inspiration of numerous research publications in the field of probability distributions. In this paper, we present several new properties of this family. In particular, we focus on stochastic orders, stress-strength reliability, Lorenz and the Leimkhuler curves, compounding, and integrated tail distribution. Two applications related to Lorenz curves and ruin theory are finally presented.
Acknowledgement
The authors would like to thank the anonymous referees for valuable comments and suggestions which improved the presentation of this paper.
EGD was partially funded by grant PID2021-127989OB-I00 (Ministerio de Economía y Competitividad, Spain) and by grant TUR-RETOS2022-075 (Ministerio de Industria, Comercio y Turismo).
Communicated by Gejza Wimmer
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© 2024 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- 10.1515/ms-2024-frontmatter4
- Intervals of posets of a zero-divisor graph
- Coalgebraic methods for Ramsey degrees of unary algebras
- On nonexistence of D(n)-quadruples
- Rees short exact sequences and preenvelopes
- Generalized discrete Grüss and related results with applications
- Radius problem associated with certain ratios and linear combinations of analytic functions
- Existence results for a fourth order problem with functional perturbed clamped beam boundary conditions
- Oscillatory and asymptotic behavior of even-order nonlinear differential equations with mixed neutral terms
- On a solvable four-dimensional system of difference equations
- Euclidean operator radius inequalities of d-tuple operators and operator matrices
- Equable parallelograms on the Eisenstein lattice
- On certain star versions of the Hurewicz property using ideals
- Relative versions of star-Menger property
- The Maxwell-Boltzmann-Exponential distribution with regression model
- New results for the Marshall-Olkin family of distributions
- A new family of copulas based on probability generating functions
- Induced mappings on the hyperspace of totally disconnected sets
Articles in the same Issue
- 10.1515/ms-2024-frontmatter4
- Intervals of posets of a zero-divisor graph
- Coalgebraic methods for Ramsey degrees of unary algebras
- On nonexistence of D(n)-quadruples
- Rees short exact sequences and preenvelopes
- Generalized discrete Grüss and related results with applications
- Radius problem associated with certain ratios and linear combinations of analytic functions
- Existence results for a fourth order problem with functional perturbed clamped beam boundary conditions
- Oscillatory and asymptotic behavior of even-order nonlinear differential equations with mixed neutral terms
- On a solvable four-dimensional system of difference equations
- Euclidean operator radius inequalities of d-tuple operators and operator matrices
- Equable parallelograms on the Eisenstein lattice
- On certain star versions of the Hurewicz property using ideals
- Relative versions of star-Menger property
- The Maxwell-Boltzmann-Exponential distribution with regression model
- New results for the Marshall-Olkin family of distributions
- A new family of copulas based on probability generating functions
- Induced mappings on the hyperspace of totally disconnected sets