Alpha-Power Transformed Lindley Distribution: Properties and Associated Inference with Application to Earthquake Data

Dey, Sanku; Ghosh, İndranil; Kumar, Devendra

doi:10.1007/s40745-018-0163-2

Cited by 46 publications

(35 citation statements)

References 40 publications

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“…Figure 6: ABs of β for ML, CV and PR estimates. 6. As it seems from Figure 6, the ABs of the ML of β take the smallest values corresponding to the other estimates of all methods for the same sample size.…”

Section: Simulation Studymentioning

confidence: 69%

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Alpha power transformed extended exponential distribution: properties and applications

Hassan¹,

Mohamd²,

Elgarhy³

et al. 2018

J. Nonlinear Sci. Appl.

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In this paper, a three-parameter lifetime model motivated by alpha power transformation is considered. We call the proposed distribution as; the alpha power transformed extended exponential (APTEE). The APTEE model contains new recent models as; alpha power transformed exponential and alpha power transformed Lindley distributions. At the same time, it contains classical models as exponential, gamma, and Lindley distributions. The properties of the APTEE distribution are derived. Parameter estimation is accomplished using maximum likelihood, percentiles, and Cramer-von Mises methods. Simulation issues and applications to real data are emphasized.

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Section: Simulation Studymentioning

confidence: 69%

“…In view of the APT, we explore the APTEE model from the EE distribution. The APTEE distribution contains special recent models, namely; APT exponential (Mahdavi and Kundu [15]) and APT Lindley (Dey et al [6]). At the same time, it contains special classical distributions which are exponential, Lindley and gamma.…”

Section: Introductionmentioning

confidence: 99%

Alpha power transformed extended exponential distribution: properties and applications

Hassan¹,

Mohamd²,

Elgarhy³

et al. 2018

J. Nonlinear Sci. Appl.

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“…The first data consists of a sample of 30 failure times of air-conditioned system of an airplane. The data are 23, 261, 87, 7,120,14,62,47,225,71,246,21,42,20,5,12,120,11,3,14,71,11,14,11,16,90,1,16,52, 95. The ML estimates, SEs of the model parameters, and analytical measures are provided in Table 5.…”

Section: Linhart and Zucchini Datamentioning

confidence: 99%

“…Mahdavi and Kundu [13] applied the APT method to the exponential distribution and they studied various properties of the alpha power exponential distribution. Based on APT method, some new distributions are considered like APT Weibull [14], APT generalized exponential [15], APT Lindley [16], APT extended exponential [17], and APT inverse Lindley [18]. Following the similar idea of Mahdavi and Kundu [13], we introduce a new three-parameter distribution, the so-called APTPL distribution.…”

Section: Introductionmentioning

confidence: 99%

On the Alpha Power Transformed Power Lindley Distribution

Hassan

Elgarhy

Mohamd

et al. 2019

Journal of Probability and Statistics

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In this paper, we introduce a new generalization of the power Lindley distribution referred to as the alpha power transformed power Lindley (APTPL). The APTPL model provides a better fit than the power Lindley distribution. It includes the alpha power transformed Lindley, power Lindley, Lindley, and gamma as special submodels. Various properties of the APTPL distribution including moments, incomplete moments, quantiles, entropy, and stochastic ordering are obtained. Maximum likelihood, maximum products of spacings, and ordinary and weighted least squares methods of estimation are utilized to obtain the estimators of the population parameters. Extensive numerical simulation is performed to examine and compare the performance of different estimates. Two important data sets are employed to show how the proposed model works in practice.

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“…In the literature, many probability distributions are generalized using this approach; for example, alpha power transformed Weibull (APTW) distribution in [9], APT generalized exponential distribution in [10], APT Lindley distribution in [11], APT extended exponential distribution in [12], alpha power inverted exponential distribution in [13], alpha power Inverse-Weibull distribution in [14], APT inverse-Lindley distribution in [15], APT power Lindley studied in [16], and APT Pareto distribution proposed in [17]. e main goal of this research article is to introduce a simpler and more flexible model called APT inverse Lomax (APTIL) distribution.…”

Section: Introductionmentioning

confidence: 99%

Alpha Power Transformed Inverse Lomax Distribution with Different Methods of Estimation and Applications

et al. 2020

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In this paper, a new three-parameter lifetime distribution, alpha power transformed inverse Lomax (APTIL) distribution, is proposed. e APTIL distribution is more flexible than inverse Lomax distribution. We derived some mathematical properties including moments, moment generating function, quantile function, mode, stress strength reliability, and order statistics. Characterization related to hazard rate function is also derived. e model parameters are estimated using eight estimation methods including maximum likelihood, least squares, weighted least squares, percentile, Cramer-von Mises, maximum product of spacing, Anderson-Darling, and right-tail Anderson-Darling. Numerical results are calculated to compare the performance of these estimation methods. Finally, we used three real-life datasets to show the flexibility of the APTIL distribution. − α , x, a, b > 0.(2)Mahdavi and Kundu [8] introduced the alpha power transformation (APT) method to add an additional parameter to a family of distributions to increase flexibility in given family. e cdf and pdf of APT-G family are Hindawi Complexity Volume 2020, Article ID 1860813, 15 pages https://doi.

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Alpha-Power Transformed Lindley Distribution: Properties and Associated Inference with Application to Earthquake Data

Cited by 46 publications

References 40 publications

Alpha power transformed extended exponential distribution: properties and applications

Alpha power transformed extended exponential distribution: properties and applications

On the Alpha Power Transformed Power Lindley Distribution

Alpha Power Transformed Inverse Lomax Distribution with Different Methods of Estimation and Applications

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