Abstract
In this paper, a new three-parameter lifetime distribution, alpha power transformed inverse Lomax (APTIL) distribution, is proposed. The 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. The 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.
Highlights
Introduction e inverseLomax (IL) is originally developed as a lifetime distribution. e inverse Lomax is member of family of generalized beta distribution
We utilized three data sets to show that alpha power transformed inverse Lomax (APTIL) can be a better life testing distribution compared with some known probability distributions such as alpha power transformation (APT) Weibull (APW) distribution [9], alpha power transformed inverse exponential (APTIE) distribution [10], Complexity
We can use the likelihood ratio (LR) test to compare the fit of the ALTIL distribution with other models for given data sets. e form of the test is suggested its name
Summary
Erefore, depending on our study, we can consider the ML estimation method is the best for APTIL distribution
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