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Open accessJournal ArticleDOI: 10.6339/JDS.201710_15(4).00008

The Transmuted Topp-Leone G Family of Distributions: Theory, Characterizations and Applications

04 Mar 2021-Journal of data science (School of Statistics, Renmin University of China)-Vol. 15, Iss: 4, pp 723-740
Abstract: Thiago G. Ramires Indranil Ghosh e and G.G. Hamedani f aDepartment of Statistics, Mathematics and Insurance, Benha University, Egypt bDepartment of Statistics, Persian Gulf University, Bushehr, Iran cFaculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran. dDepartment of mathematic, Federal University of Technology Parana, Brazil eDepartment of Mathematics and Statistics, University of North Carolina Wilmington, USA fDepartment of Mathematics, Statistics and Computer Science, Marquette University,USA

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60 results found


Open accessJournal ArticleDOI: 10.3390/SYM12010075
02 Jan 2020-Symmetry
Abstract: In this paper, we present and study a new family of continuous distributions, called the type II power Topp-Leone-G family. It provides a natural extension of the so-called type II Topp-Leone-G family, thanks to the use of an additional shape parameter. We determine the main properties of the new family, showing how they depend on the involving parameters. The following points are investigated: shapes and asymptotes of some important functions, quantile function, some mixture representations, moments and derivations, stochastic ordering, reliability and order statistics. Then, a special model of the family based on the inverse exponential distribution is introduced. It is of particular interest because the related probability functions are tractable and possess various kinds of asymmetric shapes. Specially, reverse J, left skewed, near symmetrical and right skewed shapes are observed for the corresponding probability density function. The estimation of the model parameters is performed by the use of three different methods. A complete simulation study is proposed to illustrate their numerical efficiency. The considered model is also applied to analyze two different kinds of data sets. We show that it outperforms other well-known models defined with the same baseline distribution, proving its high level of adaptability in the context of data analysis.

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Topics: Quantile function (59%), Order statistic (57%), Shape parameter (57%) ... show more

13 Citations


Journal ArticleDOI: 10.1080/09720510.2019.1685228
Abstract: A new class of models called the transmuted odd log-logistic-G family IS proposed and studied. The method of maximum likelihood is used to estimate the unknown parameters. The performance of the ma...

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Topics: Order statistic (54%), Generating function (51%)

12 Citations


Open accessJournal ArticleDOI: 10.18187/PJSOR.V15I1.2824
Abstract: In this article, we introduce a new three-parameter lifetime model called the Burr X exponentiated Weibull model. The major justification for the practicality of the new lifetime model is based on the wider use of the exponentiated Weibull and Weibull models. We are motivated to propose this new lifetime model because it exhibits increasing, decreasing, bathtub, J shaped and constant hazard rates. The new lifetime model can be viewed as a mixture of the exponentiated Weibull distribution. It can also be viewed as a suitable model for fitting the right skewed, symmetric, left skewed and unimodal data. We provide a comprehensive account of some of its statistical properties. Some useful characterization results are presented. The maximum likelihood method is used to estimate the model parameters. We prove empirically the importance and flexibility of the new model in modeling two types of lifetime data. The proposed model is a better fit than the Poisson Topp Leone-Weibull, the Marshall Olkin extended-Weibull, gamma-Weibull , Kumaraswamy-Weibull , Weibull-Frechet, beta-Weibull, transmuted modified-Weibull, Kumaraswamy transmuted- Weibull, modified beta-Weibull, Mcdonald-Weibull and transmuted exponentiated generalized-Weibull models so it is a good alternative to these models in modeling aircraft windshield data as well as the new lifetime model is much better than the Weibull-Weibull, odd Weibull-Weibull, Weibull Log-Weibull, the gamma exponentiated-exponential and exponential exponential-geometric models so it is a good alternative to these models in modeling the survival times of Guinea pigs. We hope that the new distribution will attract wider applications in reliability, engineering and other areas of research.

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12 Citations


Journal ArticleDOI: 10.6339/JDS.201910_17(4).0001
Abstract: The Topp-Leone distribution is an attractive model for life testing and reliability studies as it acquires a bathtub shaped hazard function. In this paper, we introduce a new family of distributions, depending on Topp– Leone random variable as a generator, called the Type II generalized Topp– Leone–G (TIIGTL-G) family. Its density function can be unimodel, leftskewed, right-skewed, and reversed-J shaped, and has increasing, decreasing, upside-down, J and reversed-J hazard rates. Some special models are presented. Some of its statistical properties are studied. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Rényi entropy and order statistics are derived. The method of maximum likelihood is used to estimate the model parameters. The importance of one special model; namely; the Type II generalized Topp–Leone exponential is illustrated through two real data sets.

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12 Citations


Open accessJournal ArticleDOI: 10.35378/GUJS.537832
Abstract: This article proposed a Weibull-Alpha Power Inverted Exponential (WAPIE) distribution for lifetime processes. Statistical properties of this distribution such as survival, hazard, reversed hazard, cumulative, odd functions, kurtosis, quantiles, skewness, order statistics and the entropies were derived. Parameters of this family of distribution were also obtained by maximum likelihood method. The behaviour of the estimators was studied through simulation. The behavior of the new developed distribution was further examined through real life data. The WAPIE distribution competes favourably well with other distributions.

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Topics: Kurtosis (67%), Weibull distribution (64%), Exponential distribution (64%) ... show more

11 Citations


References
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39 results found


Journal ArticleDOI: 10.1115/1.4010337
Waloddi Weibull1Institutions (1)
Abstract: This paper discusses the applicability of statistics to a wide field of problems. Examples of simple and complex distributions are given.

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8,228 Citations


Journal ArticleDOI: 10.1109/24.229504
G.S. Mudholkar1, D.K. Srivastava1Institutions (1)
Abstract: A simple generalization of the Weibull distribution is presented. The distribution is well suited for modeling bathtub failure rate lifetime data and for testing goodness-of-fit of the Weibull and negative exponential models as subhypotheses. >

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Topics: Exponentiated Weibull distribution (79%), Bathtub curve (67%), Weibull fading (65%) ... show more

910 Citations


Journal ArticleDOI: 10.1081/STA-120003130
Nicholas Eugene1, Carl Lee1, Felix Famoye1Institutions (1)
Abstract: This paper introduces a general class of distributions generated from the logit of the beta random variable. A special case of this family is the beta-normal distribution. The shape properties of the beta-normal distribution are discussed. Estimation of parameters of the beta-normal distribution by the maximum likelihood method is also discussed. The beta-normal distribution provides great flexibility in modeling not only symmetric heavy-tailed distributions, but also skewed and bimodal distributions. The flexibility of this distribution is illustrated by applying it to two empirical data sets and comparing the results to previously used methods.

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Topics: Inverse distribution (70%), Univariate distribution (69%), Heavy-tailed distribution (69%) ... show more

886 Citations


Journal ArticleDOI: 10.1093/BIOMET/84.3.641
Albert W. Marshall, Ingram Olkin1Institutions (1)
01 Sep 1997-Biometrika
Abstract: SUMMARY A new way of introducing a parameter to expand a family of distributions is introduced and applied to yield a new two-parameter extension of the exponential distribution which may serve as a competitor to such commonly-used two-parameter families of life distributions as the Weibull, gamma and lognormal distributions. In addition, the general method is applied to yield a new three-parameter Weibull distribution. Families expanded using the method introduced here have the property that the minimum of a geometric number of independent random variables with common distribution in the family has a distribution again in the family. Bivariate versions are also considered.

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856 Citations


Journal ArticleDOI: 10.2307/3212003
Abstract: : A new two parameter family of life length distributions is presented which is derived from a model for fatigue. This derivation follows from considerations of renewal theory for the number of cycles needed to force a fatigue crack extension to exceed a critical value. Some closure properties of this family are given and some comparisons made with other families such as the lognormal which have been previously used in fatigue studies.

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Topics: Life length (56%), Renewal theory (50%)

671 Citations


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