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.
In this paper, we present and study a new four-parameter lifetime distribution obtained by the combination of the so-called type II Topp–Leone-G and transmuted-G families and the inverted Kumaraswamy distribution. By construction, the new distribution enjoys nice flexible properties and covers some well-known distributions which have already proven themselves in statistical applications, including some extensions of the Bur XII distribution. We first present the main functions related to the new distribution, with discussions on their shapes. In particular, we show that the related probability density function is left, right skewed, near symmetrical and reverse J shaped, with a notable difference regarding the right tailed, illustrating the flexibility of the distribution. Then, the related model is displayed, with the estimation of the parameters by the maximum likelihood method and the consideration of two practical data sets. We show that the proposed model is the best one in terms of standard model selection criteria, including Akaike information and Bayesian information criteria, and goodness of fit tests against three well-established competitors. Then, for the new model, the theoretical background on the maximum likelihood method is given, with numerical guaranties of the efficiency of the estimates obtained via a simulation study. Finally, the main mathematical properties of the new distribution are discussed, including asymptotic results, quantile function, Bowley skewness and Moors kurtosis, mixture representations for the probability density and cumulative density functions, ordinary moments, incomplete moments, probability weighted moments, stress-strength reliability and order statistics.
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.
In this paper, we introduce and study a new three-parameter lifetime distribution constructed from the so-called type I half-logistic-G family and the inverted Kumaraswamy distribution, naturally called the type I half-logistic inverted Kumaraswamy distribution. The main feature of this new distribution is to add a new tuning parameter to the inverted Kumaraswamy (according to the type I half-logistic structure), with the aim to increase the flexibility of the related inverted Kumaraswamy model and thus offering more precise diagnostics in data analyses. The new distribution is discussed in detail, exhibiting various mathematical and statistical properties, with related graphics and numerical results. An exhaustive simulation was conducted to investigate the estimation of the model parameters via several well-established methods, including the method of maximum likelihood estimation, methods of least squares and weighted least squares estimation, and method of Cramer-von Mises minimum distance estimation, showing their numerical efficiency. Finally, by considering the method of maximum likelihood estimation, we apply the new model to fit two practical data sets. In this regards, it is proved to be better than recent models, also derived to the inverted Kumaraswamy distribution.
In this article, we propose and study a new three-parameter distribution, called the odd Fréchet inverse Lomax (OFIL) distribution, derived by combining the odd Fréchet-G family and the inverse Lomax distribution. Since Fréchet is a continuous distribution with wide applicability in extreme value theory, the new model contains these properties as well as the characteristics of the inverse Lomax distribution which make it more flexible and provide a good alternative for some well-known lifetime distributions. We initially present a linear representation of its functions and discussion on density and hazard rate function. Then, we study its various mathematical properties. Different estimation methods are used to estimate parameters of OFIL. The Monte Carlo simulation study is carried out to compare the efficiencies of different methods of estimation. The maximum likelihood estimation (MLE) method is used to estimate the OFIL parameters by considering three practical data applications. We show that the related model is the best in comparisons based on Akaike information criterion (AIC), Bayesian information criterion (BIC), and other goodness-of-fit measures.
In this paper, a cooperative Continuous static game (F-CCSG) with fuzzy parameters in the cost function of the player is presented. Through the use of the α-level sets of fuzzy numbers, the F-CCSG is converted to the corresponding α-CCSG and an extended Pareto optimality concept called the α-Pareto optimality is introduced. An algorithm for solving the α-CCSG is suggested. The algorithm is based mainly on the reference attainable point (ARP) method introduced by Wang et al., [20] and reference direction (RD) method introduced by Narula et al., [7]. One of the major improvement is the reduction of the number of iterations and hence the computational effort required to obtain the final solution. The stability of the first kind without differentiability corresponding to the final solution is determined. To clarify this approach, a numerical example is given for illustration..
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