On Burr III Marshal Olkin family: development, properties, characterizations and applications

Bhatti, Fiaz Ahmad; Hamedani, G. G.; Korkmaz, Mustafa Ç.; Cordeiro, Gauss M.; Yousof, Haitham M.; Ahmad, Munir

doi:10.1186/s40488-019-0101-7

Cited by 14 publications

(7 citation statements)

References 22 publications

(21 reference statements)

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“…The TL-OBIII-LLoG distribution is fitted to two real data sets and compared to fits of several non-nested four parameter distributions. The TL-OBIII-LLoG distribution is compared to the new modified Weibull (NMW) distribution introduced by Doostmoradi et al [15], beta generalized exponential (BGE) distribution introduced by Barreto-Souza et al [6], beta generalized Lindley (BGL) distribution by Oluyede and Yang [29], exponentiated modified Weibull distribution by Elbatal [16], Weibull Lomax (WL) distribution by Tahir et al [34], generalized Weibull log-logistic (GWLLoG) distribution by Cordeiro et al [11] and Burr III Marshall Olkin-Lindley (BIIIMO-L) distribution by Bhatti et al [7]. The pdf's of the four parameter NMW, BGE, BGL, EMW, WL, GWLLoG, BIIIMO-L distributions are given in equations ( 20), ( 21), ( 22), ( 23), ( 24), ( 25) and ( 26) respectively, that is,…”

Section: Applicationsmentioning

confidence: 99%

“…The limitations of the well-known standard distribution in data modeling have motivated researchers to extend distributions by adding one or more shape parameters to gain flexibility in the new distribution. Some of the generated families in the literature including the odd Burr III family of distributions by Jamal et al [19], the Nadarajah Haghighi Topp-Leone-G family of distributions by Reyad et al [33], the Marshall-Olkin Odd Burr III-G family of distributions by Afify et al [2], the generalized transmuted-G family proposed by Nofal et al [28], Marshall-Olkin alpha power-G by Nassar et al [27], beta-G by Eugene et al [17], Topp Leone odd Lindley-G by Reyad et al [32], odd Lomax-G by Cordeiro et al [9], exponentiated Weibull-H by Cordeiro et al [10], the Burr III Marshal Olkin family of distributions by Bhatti et al [7]; among others. The Burr III (BIII) distribution was one of the twelve cumulative distribution functions introduced by Burr [8].…”

Section: Introductionmentioning

confidence: 99%

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The Topp-Leone Odd Burr III-G Family of Distributions: Model, Properties and Applications

Moakofi

Oluyede²,

Gabanakgosi

2022

Stat., optim. inf. comput.

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We propose and investigate a new generalized family of distributions called the Topp-Leone Odd Burr III-G (TL- OBIII-G) family of distributions. We present the sub-families of this new family of distributions. Properties of the new family of distributions includs sub-models, quantile function, moments, incomplete and probability weighted moments, distribution of the order statistics, and Renyi entropy are derived. The Maximum likelihood estimation technique is used to estimate the model parameters, and a Monte Carlo simulation study is employed to examine the performance of the model. Two real data sets are used to prove the importance of the TL-OBIII-G family of distributions.

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Section: Applicationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Topp-Leone Odd Burr III-G Family of Distributions: Model, Properties and Applications

Moakofi

Oluyede²,

Gabanakgosi

2022

Stat., optim. inf. comput.

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“…The function of density has a variety of forms that are applicable to a wide range of applications [ 32 ]. Some recent developments in Burr family of distributions are Burr X Pareto distribution [ 33 ], Weibull Burr XII distribution [ 34 ], Burr III-Marshal Olkin-G family [ 35 ], Unit generalized log Burr XII distribution [ 36 ], Unit Burr-XII distribution [ 37 ] and Burr XII-moment exponential distribution [ 38 ].…”

Section: The Hcmb−iii Distributionmentioning

confidence: 99%

Half circular modified burr−III distribution, application with different estimation methods

2022

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The data related to many medical, environmental and ecological variables are often measured in terms of angles wherein its range is defined in [0,π). This type of data is referred to as axial or half circular data. Modeling based on half circular data has not received its due share of attention in statistical literature. In this paper, we introduce a new half circular distribution based on inverse stereographic projection technique on modified Burr−III distribution, called the half circular modified Burr−III (hcMB−III) distribution. The basic properties of the proposed distribution are derived. It is common observation that while estimating the parameters of a model, one usually adopts maximum likelihood estimation method as the starting point. In this paper, we consider seven frequentist methods of estimation, besides using maximum likelihood method for estimating the parameters of the hcMB−III distribution. Monte Carlo simulations are performed for investigating the performances of the considered methods in terms of their biases and mean square errors using small, medium and large sample sizes. Finally, one data set related to posterior corneal curvature of the eyes of 23 patients, is analyzed to check potentiality of the newly proposed model.

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“…Bhatti et al [14] introduce a new family called Burr III Marshall Olkin family and present some special submodels. Some of them have a bimodality shape in their pdf.…”

Section: Introductionmentioning

confidence: 99%

Some inferences based on a mixture of power function and continuous logarithmic distribution

El-Bar

Lima

Ahsanullah

2020

Journal of Taibah University for Science

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In recent decades, many families of distributions and, consequently, new distributions are proposed in order to provide a good flexibility and fit to real data sets. However, several of these distributions have a complicated shape to express their probability density function (pdf) and cumulative distribution function (cdf). Examples of families that involve such functions are: beta-G (see Eugene et al. Beta normal distribution and its applications. Commun Stat -Theory Methods. 2006;31:497-512, for example) and gamma-G (for more details, see Nadarajah et al. The Zografos-Balakrishnan-G family of distributions: mathematical properties and application. Commun Stat -Theory Methods. 2015;44:186-215) families. In this sense, we introduce a new bounded distribution by using a mixture of power function and continuous logarithmic distribution, named as the power logarithmic (PL) distribution, that has a simple form in the expressions of its pdf and cdf. Various statistical and mathematical properties of the new model are obtained in closed form, which is a very positive aspect when we propose a new model. Based on the basic properties, two new characterizations of the new model will be given. Finally, the applicability of PL model to modelling real data is proved by two real data sets, showing the good fit of the new distribution, when compared with others already know in the literature.

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On Burr III Marshal Olkin family: development, properties, characterizations and applications

Cited by 14 publications

References 22 publications

The Topp-Leone Odd Burr III-G Family of Distributions: Model, Properties and Applications

The Topp-Leone Odd Burr III-G Family of Distributions: Model, Properties and Applications

Half circular modified burr−III distribution, application with different estimation methods

Some inferences based on a mixture of power function and continuous logarithmic distribution

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