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

Abstract

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.

Statistical Inference of Odd Fréchet Inverse Lomax Distribution with Applications

“…By inserting equations (1) and (2) in equation (14), the pdf of the OFIL distribution can be written as a linear combination of the IL distribution as…”

“…(iv) Alpha-power transformed IL (APTIL) distribution [14]: 10 Complexity (v) Weibull IL (WIL) distribution [12]:…”

“…Maxwell et al [13] proposed and studied Marshall-Olkin IL distribution and compared this new model with other competitive models using real data applications. ZeinEldin et al [14] proposed and alpha-power transformed IL distribution.…”

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

“…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.…”

Estimation of Entropy for Inverse Lomax Distribution under Multiple Censored Data

“…Also, recent studies have proposed extensions of the IL distributions for further purposes. In this regard, let us cite Reference [ 24 ] for the inverse power Lomax (or power IL) distribution, Reference [ 25 ] for the Weibull IL distribution, Reference [ 26 ] for the alpha power transformed IL distribution, Reference [ 27 ] for the Marshall-Olkin IL distribution and Reference [ 28 ] for the odd generalized exponentiated IL distribution.…”