Transmuted Linear Exponential Distribution: A New Generalization of the Linear Exponential Distribution

Tian, Yuzhu; Tian, Maozai; Zhu, Qianqian

doi:10.1080/03610918.2013.763978

Cited by 54 publications

(23 citation statements)

References 7 publications

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“…A well-known modification of LS method is the WLS, which has a lower bias than the ordinary LS. The WLS estimates of the parameters of the TWE( , Λ) distribution are obtained by minimizing (20)…”

Section: Least Squares Estimationmentioning

confidence: 99%

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A new wrapped exponential distribution

Yilmaz

Biçer

2018

Math Sci

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We introduce a new wrapped exponential distribution named transmuted wrapped exponential (TWE) distribution, for the modeling of circular datasets by using the Transmutation Rank-Map method. This method is employed for the first time for a wrapped distribution with this study. The introduced distribution is more flexible than traditional wrapped exponential distribution. The paper provides the explicit form of important distributional properties of the introduced distribution such as expectation, median, moments, characteristic function, quantile function, hazard rate function and stress-strength reliability. Rényi and Shannon entropies are also obtained. The statistical inference problem for the TWE distribution is investigated using maximum likelihood, least squares and weighted least squares and comparative numerical study results are presented. Furthermore, we present a real dataset analysis.

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Section: Least Squares Estimationmentioning

confidence: 99%

“…In 2013, Merovci applied the QRTM to the exponentiated exponential distribution and introduced the transmuted exponentiated exponential distribution as a lifetime distribution [13]. We refer the interested reader to [3,4,9,14,16,17,20] and…”

Section: Introductionmentioning

confidence: 99%

A new wrapped exponential distribution

Yilmaz

Biçer

2018

Math Sci

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“…Several distributions have been generalized by this transmuting approach in the literature. Some of them are the transmuted Weibull distribution by Aryal and Tsokos (2011), the transmuted Maxwell distribution by Iriarte and Astorga (2014), the transmuted linear exponential distribution by Tian et al (2014), the transmuted log-logistic distribution by Granzotto and Louzada (2015), the transmuted Dagum distribution by Elbatal and Aryal (2015), the transmuted Erlang-truncated exponential distribution by Okorie et al (2016), the transmuted exponentiated Weibull geometric distribution by Saboor et al (2016), the transmuted exponential Pareto distribution by Al-Babtain (2017), the transmuted two-parameter Lindley distribution by Kemaloglu and Yilmaz (2017) and the transmuted Birnbaum-Saunders distribution by Bourguignon et al (2017).…”

Section: Introductionmentioning

confidence: 99%

Stochastic Comparisons between the Extreme Claim Amounts from Two Heterogeneous Portfolios in the Case of Transmuted-G Model

Nadeb

Torabi

Dolati

2020

North American Actuarial Journal

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Let X λ1 , . . . , X λn be independent non-negative random variables belong to the transmuted-G model and let Y i = I pi X λi , i = 1, . . . , n, where I p1 , . . . , I pn are independent Bernoulli random variables independent of X λi 's, with E[I pi ] = p i , i = 1, . . . , n. In actuarial sciences, Y i corresponds to the claim amount in a portfolio of risks. In this paper we compare the smallest and the largest claim amounts of two sets of independent portfolios belonging to the transmuted-G model, in the sense of usual stochastic order, hazard rate order and dispersive order, when the variables in one set have the parameters λ 1 , ..., λ n and the variables in the other set have the parameters λ * 1 , ..., λ * n . For illustration we apply the results to the transmuted-G exponential and the transmuted-G Weibull models.

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“…For these data, we compare the fit of the BXL distribution with those of the L, transmuted linear exponential (TLE), transmuted additive Weibull (TAW), BX and exponentiated transmuted generalized Rayleigh (ETGR) models (x > 0 for all of them). The TLE density (Tian et al, [25]) given by…”

Section: Application To Cancer Patients Datamentioning

confidence: 99%