Alpha-Power Pareto distribution: Its properties and applications

Abstract

In Statistical theory, inclusion of an additional parameter to standard distributions is a usual practice. In this study, a new distribution referred to as Alpha-Power Pareto distribution is introduced by including an extra parameter. Several properties of the proposed distribution, including moment generating function, mode, quantiles, entropies, mean residual life function, stochastic orders and order statistics are obtained. Parameters of the proposed distribution have been estimated using maximum likelihood estimation technique. Two real datasets have been considered to examine the usefulness of the proposed distribution. It has been observed that the proposed distribution outperforms different variants of Pareto distribution on the basis of model selection criteria.

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

“…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].…”

“…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.…”

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.…”

A New Technique for Generating Distributions Based on a Combination of Two Techniques: Alpha Power Transformation and Exponentiated T-X Distributions Family

“…In the literature, several studies have applied this technique to introduce some new distributions. These include the study of [12], in which the APT technique was applied to the exponential distribution; the study of [13], which introduced the alpha power Weibull distribution; the study of [14], which introduced the alpha power transformed Lindley distribution; the study of [15], which introduced the alpha power Pareto distribution; the study of [16], which presented the alpha power transformed inverse Lindley distribution; the study of [17], which presented the alpha power Gompertz distribution, and the study of [18], which presented the alpha power transformed log-logistic distribution.…”