E-Bayesian Estimation of Two-Component Mixture of Inverse Lomax Distribution Based on Type-I Censoring Scheme

Reyad, Hesham; Othman, Soha

doi:10.9734/jamcs/2018/39087

Cited by 17 publications

(16 citation statements)

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“…Here, an explicit expression for APTIL pdf is given. By using the series representation of exponential function, equation (5) can be written as 2 Complexity…”

Section: Useful Expansionsmentioning

confidence: 99%

“…Let X be an r.v. with pdf given in equation (5). For any real number a > 0, b > 0, α > 0, and r ≥ 0, the r th moments of APTIL distribution are obtained as…”

Section: Momentsmentioning

confidence: 99%

“…Singh et al [4] investigated the reliability estimators of IL distribution under Type II censoring. Bayesian estimation of mixture of the IL model under the censoring scheme was studied in [5]. Inverse power Lomax distribution was studied in [6] and Weibull IL distribution in [7].…”

Section: Introductionmentioning

confidence: 99%

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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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“…Here, an explicit expression for APTIL pdf is given. By using the series representation of exponential function, equation (5) can be written as 2 Complexity…”

Section: Useful Expansionsmentioning

confidence: 99%

“…Let X be an r.v. with pdf given in equation (5). For any real number a > 0, b > 0, α > 0, and r ≥ 0, the r th moments of APTIL distribution are obtained as…”

Section: Momentsmentioning

confidence: 99%

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

et al. 2020

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“…The practical usefulness of the related model is illustrated in Reference [ 19 ] for its application to the analyses of geophysical data and in Reference [ 20 ] for its application in economics and actuarial sciences. Also, we refer to Reference [ 21 ] for the estimation of the reliability parameter via Type II censoring samples, in Reference [ 22 ] for the estimation of the parameters based on hybrid censored samples, and in Reference [ 23 ] for the Bayesian estimation of the two-component mixture of the IL distribution under the Type I censoring scheme. Also, recent studies have proposed extensions of the IL distributions for further purposes.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Entropy for Inverse Lomax Distribution under Multiple Censored Data

Bantan

Elgarhy

Chesneau

et al. 2020

Entropy

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The inverse Lomax distribution has been widely used in many applied fields such as reliability, geophysics, economics and engineering sciences. In this paper, an unexplored practical problem involving the inverse Lomax distribution is investigated: the estimation of its entropy when multiple censored data are observed. To reach this goal, the entropy is defined through the Rényi and q-entropies, and we estimate them by combining the maximum likelihood and plugin methods. Then, numerical results are provided to show the behavior of the estimates at various sample sizes, with the determination of the mean squared errors, two-sided approximate confidence intervals and the corresponding average lengths. Our numerical investigations show that, when the sample size increases, the values of the mean squared errors and average lengths decrease. Also, when the censoring level decreases, the considered of Rényi and q-entropies estimates approach the true value. The obtained results validate the usefulness and efficiency of the method. An application to two real life data sets is given.

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“…Some details about the Inverse Lomax distribution including its applications are available in Reyad and Othman, Falgore et al, Maxwell et al, and Hassan and Mohamed. [17][18][19][20][21][22][23] The main aim of this paper is to provide an extension of the Inverse-Lomax distribution using the Weibull-G generator by Bourguignon et al 6 Therefore, we propose the Weibull-Inverse lomax (WIL) distribution by adding two extra shape parameters to the Inverse Lomax distribution.…”

Section: Introductionmentioning

confidence: 99%

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2019

BBIJ

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In this paper, we introduced a four-parameter probability model called Weibull-Inverse Lomax distribution with decreasing, increasing and bathtub hazard rate function. The WIL distribution density function is J-shaped, positively skewed, and J-shaped in reverse. Some of the mentioned distribution's statistical characteristics are provided including moments, order statistics, entropy, mean, variance, moment generating function, and quantile function. The method of maximum likelihood estimation was used to estimate the parameters of the model. The distribution's importance is proved by its implementation to the bladder cancer data set. Goodness-of-fit of this distribution by various techniques demonstrates that the WIL distribution is empirically better for lifetime application.

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E-Bayesian Estimation of Two-Component Mixture of Inverse Lomax Distribution Based on Type-I Censoring Scheme

Cited by 17 publications

References 0 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

Estimation of Entropy for Inverse Lomax Distribution under Multiple Censored Data

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