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A new generalized Lindley-Weibull class of distributions: Theory, properties and applications

  • Boikanyo Makubate , Thatayaone Moakofi EMAIL logo and Broderick Oluyede
Published/Copyright: January 29, 2021
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 71 Issue 1

Abstract

We propose a new generalized class of distributions called Lindley-Weibull Power Series (LWPS) distributions and their special case called Lindley-Weibull logarithmic (LWL) distributions. Structural properties of the LWPS class of distributions and its sub-model LWL distribution including moments, order statistics, Rényi entropy, mean and median deviations, Bonferroni and Lorenz curves, and maximum likelihood estimates are derived. A simulation study to examine the bias and mean square error of the maximum likelihood estimators for each parameter is presented. Finally, real data examples are presented to illustrate the applicability and usefulness of the proposed class of distributions.

MSC 2010: 60E05; 62F10
Keywords: Lindley Distribution; Weibull Distribution; Power Series Distribution; Logarithmic Distribution; Maximum Likelihood Estimation

  1. (Communicated by Gejza Wimmer )

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Appendix A

The elements of the score vector are given by

∂ℓ∂β=−α∑i=1nxiβlnxi+∑i=1nα(1+λ+λxi)xiβ−1(1+βlnxi)λ2(1+xi)+(1+λ+λxi)αβxiβ−1+∑i=1nC″θ1−1+λ+λxi1+λe−λxi−αxiβC′θ1−1+λ+λxi1+λe−λxi−αxiβθ1+λ+λxi1+λe−λxi−αxiβαxiβlnxi,∂ℓ∂θ=nθ−nC′(θ)C(θ)+∑i=1nC″θ1−1+λ+λxi1+λe−λxi−αxiβC′θ1−1+λ+λxi1+λe−λxi−αxiβ×1−1+λ+λxi1+λe−λxi−αxiβ,∂ℓ∂α=−∑i=1nxiβ+∑i=1n(1+λ+λxi)(βxiβ−1)λ2(1+xi)+(1+λ+λxi)αβxiβ−1+∑i=1nC″θ1−1+λ+λxi1+λe−λxi−αxiβC′θ1−1+λ+λxi1+λe−λxi−αxiβθ1+λ+λxi1+λe−λxi−αxiβxiβ,

and

∂ℓ∂λ=−nxi+∑i=1n2λ(1+xi)+(1+xi)αβxiβ−1λ2(1+xi)+(1+λ+λxi)αβxiβ−1+(∑i=1nC″θ1−1+λ+λxi1+λe−λxi−αxiβC′θ1−1+λ+λxi1+λe−λxi−αxiβ×θe−λxi−αxiβxi1+λ+λxi1+λ−(1+λ)(1+xi)−(1+λ+λxi)(1+λ)2).
Received: 2019-12-12
Accepted: 2020-06-01
Published Online: 2021-01-29
Published in Print: 2021-02-23

© 2021 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Regular papers
  2. Prof. RNDr. Ing. Lubomír Kubáček, DrSc., Dr.h.c. –Nonagenarian
  3. Doc. RNDr. Roman Frič, DrSc. passed away
  4. Outer and inner approximations in quantum spaces
  5. Linear derivations on Banach *-algebras
  6. New fractional order discrete Grüss type inequality
  7. Exponential trigonometric convex functions and Hermite-Hadamard type inequalities
  8. Generalized Minkowski type inequality for pseudo-integral
  9. Study of the Q-spiral-like functions of complex order
  10. Radius of starlikeness of certain analytic functions
  11. Successive approximations for a differential equation in a Banach space via Constantin condition
  12. Approximation of the multi-m-Jensen-quadratic mappings and a fixed point approach
  13. Oscillation and asymptotic behavior of a higher-order neutral delay difference equation with variable delays under Δm
  14. Sequence selection properties in Cp(X) with the double ideals
  15. On the paranormed Nörlund difference sequence space of fractional order and geometric properties
  16. On certain Diophantine equations concerning the area of right triangles
  17. Weighted projective Ricci curvature in Finsler geometry
  18. Euler classes of vector bundles over manifolds
  19. A new generalized Lindley-Weibull class of distributions: Theory, properties and applications
  20. Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments
  21. The (α, β)-ramification invariants of a number field
https://doi.org/10.1515/ms-2017-0462
Keywords for this article
Lindley Distribution; Weibull Distribution; Power Series Distribution; Logarithmic Distribution; Maximum Likelihood Estimation

Articles in the same Issue

  1. Regular papers
  2. Prof. RNDr. Ing. Lubomír Kubáček, DrSc., Dr.h.c. –Nonagenarian
  3. Doc. RNDr. Roman Frič, DrSc. passed away
  4. Outer and inner approximations in quantum spaces
  5. Linear derivations on Banach *-algebras
  6. New fractional order discrete Grüss type inequality
  7. Exponential trigonometric convex functions and Hermite-Hadamard type inequalities
  8. Generalized Minkowski type inequality for pseudo-integral
  9. Study of the Q-spiral-like functions of complex order
  10. Radius of starlikeness of certain analytic functions
  11. Successive approximations for a differential equation in a Banach space via Constantin condition
  12. Approximation of the multi-m-Jensen-quadratic mappings and a fixed point approach
  13. Oscillation and asymptotic behavior of a higher-order neutral delay difference equation with variable delays under Δm
  14. Sequence selection properties in Cp(X) with the double ideals
  15. On the paranormed Nörlund difference sequence space of fractional order and geometric properties
  16. On certain Diophantine equations concerning the area of right triangles
  17. Weighted projective Ricci curvature in Finsler geometry
  18. Euler classes of vector bundles over manifolds
  19. A new generalized Lindley-Weibull class of distributions: Theory, properties and applications
  20. Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments
  21. The (α, β)-ramification invariants of a number field
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