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.

In this work, we analyzed the hybrid nanofluid (Ag+CuO+kerosene oil) flow past a bidirectionally extendable surface in the presence of a variable magnetic field. The hybrid nanofluid flow considered is electrically conductive and steady. For the simulation of the problem, the Cattaneo–Christov double-diffusion (CCDD) model was considered, which generalizes Fourier’s and Fick’s laws. The impact of the Hall current produced was taken into account. The physical problem was transformed into a mathematical form with the help of suitable transformations to reduce the complexity of the problem. The transformed system of coupled ordinary differential equations (ODEs) was solved with the semi-analytical method. The results are plotted in comparison with the ordinary nanofluid (CuO+kerosene oil) and hybrid nanofluid (Ag+CuO+kerosene oil). The impact of various parameters (Pr,Sc,γ0,m,M,Nb,Nt,ϵ1,ϵ2) on the state variables is described. The velocity gradient under the impact of the mass flux and magnetic parameter shows a decreasing behavior, while the Hall parameter and the stretching ratio show an increasing behavior. Moreover, the skin friction, rate of heat, and mass transfer are numerically displayed through tables. In this work, we found that the thermal and concentration relaxation coefficients showed a decreasing behavior for their increasing trends. For the validation of the implemented technique, the squared residuals are computed in Table 2, which shows that the increasing number of iterations decreases the squared residual error. The results show that Ag+CuO+kerosene oil has good performance in the reduction of the heat transfer rate.

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In this study, we propose a new flexible two-parameter continuous distribution with support on the unit interval. It can be identified as a special member of the so-called type I half-logistic-G family of distributions, defined with the Topp-Leone distribution as baseline. Among its features, the corresponding probability density function can be left skewed, right-skewed, approximately symmetric, J-shaped, as well as reverse J-shaped, making it suitable for modeling a wide variety of data sets. It thus provides an alternative to the so-called beta and Kumaraswamy distributions. The mathematical properties of the new distribution are determined, deriving the asymptotes, shapes, quantile function, skewness, kurtosis, some power series expansions, ordinary moments, incomplete moments, moment-generating function, stress strength parameter, and order statistics. Then, a statistical treatment of the related model is proposed. The estimation of the unknown parameters is performed by a simulation study exploring seven methods, all described in detail. Two practical data sets are analyzed, showing the usefulness of the new proposed model.