General results for the Marshall and Olkin's family of distributions

Barreto‐Souza, Wagner; Lemonte, Artur J.; Cordeiro, Gauss M.

doi:10.1590/s0001-37652013000100002

Cited by 45 publications

(16 citation statements)

References 24 publications

(24 reference statements)

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“…Alexander et al (2012), Marciano et al (2012), Lemonte (2012, 2014), Cordeiro et al (2012aCordeiro et al ( , b, 2013dCordeiro et al ( , 2014b, Lemonte and Cordeiro (2013) The Mc G family of distributions reduces to the beta G family of distribution for c = 1 and to the Kw G family of distribution for a = c. Further, the Mc G family of distributions for G(x) = x contains as particular cases the beta type 1 distribution (c = 1) and the Kumaraswamy distribution (a = c).…”

Section: Muhammad H Tahir and Saralees Nadarajah R(t) = G(t)g(t)mentioning

confidence: 99%

Parameter induction in continuous univariate distributions: Well-established G families

Tahir

Nadarajah

2015

An. Acad. Bras. Ciênc.

103

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The art of parameter(s) induction to the baseline distribution has received a great deal of attention in recent years. The induction of one or more additional shape parameter(s) to the baseline distribution makes the distribution more flexible especially for studying the tail properties. This parameter(s) induction also proved helpful in improving the goodness-of-fit of the proposed generalized family of distributions. There exist many generalized (or generated) G families of continuous univariate distributions since 1985. In this paper, the well-established and widely-accepted G families of distributions like the exponentiated family, Marshall-Olkin extended family, beta-generated family, McDonald-generalized family, Kumaraswamygeneralized family and exponentiated generalized family are discussed. We provide lists of contributed literature on these well-established G families of distributions. Some extended forms of the Marshall-Olkin extended family and Kumaraswamy-generalized family of distributions are proposed.

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Section: Muhammad H Tahir and Saralees Nadarajah R(t) = G(t)g(t)mentioning

confidence: 99%

Parameter induction in continuous univariate distributions: Well-established G families

Tahir

Nadarajah

2015

An. Acad. Bras. Ciênc.

103

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“…where f G E(α( j+1),λ) (x) denotes the pdf of a random variable with generalized exponential distribution with parameters α( j + 1) and λ, see also [3]. Note that the density g(x; α, λ, θ ) can be represented in the generalized mixture form of beta generalized exponential probability density functions, Barreto-Souza et al [4], as g(…”

Section: The Probability Density Functionmentioning

confidence: 99%

Marshall-Olkin generalized exponential distribution

Ristić

Kundu

2015

METRON

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Marshall and Olkin (Biometrika 641-652, 1997) introduced a new way of incorporating a parameter to expand a family of distributions. In this paper we adopt the MarshallOlkin approach to introduce an extra shape parameter to the two-parameter generalized exponential distribution. It is observed that the new three-parameter distribution is very flexible. The probability density functions can be either a decreasing or an unimodal function. The hazard function of the proposed model, can have all the four major shapes, namely increasing, decreasing, bathtub or inverted bathtub types. Different properties of the proposed distribution have been established. The new family of distributions is analytically quite tractable, and it can be used quite effectively, to analyze censored data also. Maximum likelihood method is used to compute the estimators of the unknown parameters. Two data sets have been analyzed, and the results are quite satisfactory.

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“…In addition, Santos-Neto et al [16] introduced the MOE Weibull family of distributions and studied some of its mathematical properties. Barreto-Souza et al [2] and Cordeiro and Lemonte [5] provided general results of the Marshall and Olkin's family of distributions. This article introduces the Marshall-Olkin extended Burr III (MOEBIII) distribution and study its performance and flexibility using a simulation study and real data.…”

Section: Introductionmentioning

confidence: 95%

Marshall-Olkin extended Burr III distribution

Al-Saiari¹,

Mousa²,

Baharith³

2016

imf

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In this paper, a new extended Burr III distribution using Marshall and Olkin method is introduced. Some characteristics and properties of the new distribution are studied. Maximum likelihood and Bayesian methods are used to estimate model parameters. Also, the asymptotic distributions of the maximum likelihood is used to obtain confidence intervals for the parameters. Monte Carlo simulations are carried out to investigate the performance of the new distribution. Finally, a real data set is analyzed to illustrate the results.

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General results for the Marshall and Olkin's family of distributions

Cited by 45 publications

References 24 publications

Parameter induction in continuous univariate distributions: Well-established G families

Parameter induction in continuous univariate distributions: Well-established G families

Marshall-Olkin generalized exponential distribution

Marshall-Olkin extended Burr III distribution

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