The Marshall-Olkin length-biased exponential distribution and its applications

Haq, Muhammad Ahsan ul; Usman, Rana Muhammad; Hashmi, Sharqa; Al-Omeri, Amer Ibrahim

doi:10.1016/j.jksus.2017.09.006

Cited by 35 publications

(18 citation statements)

References 10 publications

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“…Marshall Olkin length biased exponential (MOLBE) distribution [27], APT inverted Weibull (APIW) distribution [14], APT Pareto (APTP) distribution [17], and inverse Lomax (IL) distribution [4]. e corresponding probability density functions of competitor models are given below: e second data set represents the marks in Mathematics for 48 students in the slow pace programme in the year 2013 [29].…”

Section: Complexitymentioning

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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Section: Complexitymentioning

confidence: 99%

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

et al. 2020

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“…The 2 nd data set is reported by Aarset (26) Dallas (1) , which corresponds to the 30 failure times of air-conditioned system of an airplane. The data are as follows: 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, and 95. We have compared BL2PFD with the alpha power transformed inverse exponential (APTIE) distribution by Dey et al (27) , Marshall Olkin length biased exponential (MOLBE) distribution by ul Haq et al (28) , APT inverted Weibull (APTIW) distribution by Ramadan and Magdy (29) , APT Pareto (APTP) distribution by Ihtisham et al (30) and Alpha Power Transformed Inverse Lomax distribution (APTIL) by ZeinEldin et al (31) . The TTT-plot is displayed in Figure 5 , which indicates that the HRF associated with the data set has a bathtub shape, since the plot shows a first concave curvature.…”

Section: Failure Times Data Of Air-conditioned Systemmentioning

confidence: 99%

Beta Lehmann-2 power function distribution with application to bladder cancer susceptibility and failure times of air-conditioned system

Zaka¹

2020

IJST

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“…Many authors have proposed distributions using MO scheme. Marshall and Olkin (1997) developed Marshall-Olkin Exponential and Weibull distributions, Marshall-Olkin extended Lomax distribution by (Rao et al 2009), Marshall-Olkin extended uniform distribution by (Jose & Krishna, 2011), Marshall-Olkin Fré chet distribution by (Krishna et al 2013), Marshall-Olkin exponential Weibull distribution by (Pogá ny et al 2015), Marshall-Olkin extended inverted Kumaraswamy distribution by (Usman & Haq, 2018), Marshall-Olkin length biased exponential distribution by (Haq et al 2017) and Marshall-Olkin logistic-exponential distribution by (Mansoor et al 2018).…”

Section:  mentioning

confidence: 99%

Marshall-Olkin Power Lomax Distribution: Properties and Estimation Based on Complete and Censored Samples

Haq¹,

Hamedani²,

Elgarhy³

et al. 2019

IJSP

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We study a new distribution called the Marshall-Olkin Power Lomax distribution. A comprehensive account of its mathematical properties including explicit expressions for the ordinary moments, moment generating function, order statistics, Renyi entropy, and probability weighted moments are derived. The model parameters are estimated by the method of maximum likelihood. Monte Carlo simulation study is carried out to estimate the parameters and the performance of the estimates is judged via the average biases and mean squared error values. The usefulness of the proposed model is illustrated via real-life data set.

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The Marshall-Olkin length-biased exponential distribution and its applications

Cited by 35 publications

References 10 publications

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

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

Beta Lehmann-2 power function distribution with application to bladder cancer susceptibility and failure times of air-conditioned system

Marshall-Olkin Power Lomax Distribution: Properties and Estimation Based on Complete and Censored Samples

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