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In this paper, we derive several results related to total path length and Sackin index in two classes of random recursive trees. A limiting distribution of the normalized version of the Sackin index is given by the contraction method in random recursive trees. Also, we show the normalized total path length converges in L2 and almost surely to a limiting random variable in plane-oriented recursive trees via martingales.

This study seeks to present a sophisticated artificial intelligence (AI) framework to model the compressive strength (fc′) of concrete containing waste foundry sand (WFS), with the aim of minimizing the need for time‐consuming laboratory tests and skilled technicians. For this purpose, artificial neural network (ANN) is hybridized with two metaheuristic algorithms—particle swarm optimization (PSO) and ant colony optimization (ACO) to predict the fc′ of 340 samples containing WFS collected from the literature. Results indicated that the ACO + ANN model showed the best performance with the Pearson coefficient of 0.9971, mean absolute error of 0.0221 MPa, and root mean squared error of 0.7473 MPa. The values of prediction errors exhibited that more than 90% of them in the ACO + ANN model fall within the range of (−1.5 MPa, 1.5 MPa), while this range for the PSO + ANN and traditional ANN models was obtained as (−3 MPa, 3 MPa) and (−4 MPa, 4 MPa), respectively. Furthermore, the proposed ACO + ANN model predicted the fc′ in the range of 5.24–54.48 MPa. Besides, the results indicated that the water‐to‐cement ratio, cement strength class, and cement content had the most significant impact on the fc′ of WFS‐containing concrete. Finally, a comparison was made between the proposed ACO + ANN model and four other AI models recently proposed in the literature, in which the performance criteria demonstrated that the proposed ACO + ANN model outperformed the models in the literature. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the modified F-indices (modified first Zagreb index and modified forgotten topological index) of random m-oriented recursive trees (RMORTs). First, through two recurrence equations, we compute the mean and the variance of these indices in our random tree model. Second, we show four convergence in probability based on these indices. Third, the asymptotic normalities, through the martingale central limit theorem, are given. [ABSTRACT FROM AUTHOR]

In this paper, under the Type-II progressive censored scheme, we obtain the point and interval estimates of stress-strength parameter (R), when stress and strength are two independent Weibull-standard normal variables. We study the problem in three cases. First, assuming that stress and strength have the different scale parameters and the common shape parameter, we obtain maximum likelihood estimation, approximation maximum likelihood estimation and two Bayesian approximation estimates due to the lack of explicit forms. Also, we construct the asymptotic and highest posterior density intervals for R. Second, assuming that common shape parameter is known, we derive the maximum likelihood estimation and Bayes estimate and uniformly minimum variance unbiased estimate of R. Third, assuming that all parameters are unknown and different, we achieve the statistical inference of R, namely maximum likelihood estimation, approximation maximum likelihood estimation and Bayesian inference of R. Furthermore, we use the Monte Carlo simulations to compare of the performance of different methods. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a novel learning approach to solve the heat transfer problem from convecting-radiating fin model. This model is a nonlinear differential equation in which different boundary conditions cause different profile shapes including rectangular, triangular, trapezoidal and concave parabolic. We consider one-dimensional, steady conduction in the fin and neglect radiative exchange between adjacent fins and between the fin and its primary surface. Our method is based on using the quasilinearization method to linearize the nonlinear models and applying shifted Gegenbauer polynomials as new kernel in least squares support vector machines method. The results of fin efficiency and heat transfer rate of the problems which compared with available previous results indicate better efficiency and accuracy of the proposed approach. [ABSTRACT FROM AUTHOR]

To introduce a flexible stress-strength model, statistical inference of the stress-strength parameter R = P(X < Y ), when stress X and strength Y are two independent two-parameter new Weibull-Fréchet variables, is considered under Type II progressive censored samples. The MLE, AMLE, asymptotic confidence intervals, Bayes estimate and HPD intervals of R are achieved in three different cases. Also, to compare the performance of three different methods, we apply the Monte Carlo simulations and also analyze a data set for illustrative aims. [ABSTRACT FROM AUTHOR]

Generalized weighted exponential (GWE) distributions are a natural generalization of weighted exponential distributions. This paper attempts to revisit the GWE distribution in order to address the main inferential aspects of this distribution, such as the maximum likelihood estimators of the unknown parameters and their corresponding asymptotic confidence intervals, that vanished in previous works. Also, it develops some new distributional results about the GWE distribution and provides more interesting closed form expressions for previously presented results. A simulation study and a real world application are also worked out to assess the maximum likelihood estimators and to illustrate the theory. [ABSTRACT FROM AUTHOR]

For any fixed integer d ≥ 2, the d-ary increasing tree is a rooted, ordered, labeled tree where the out-degree is bounded by d, and the labels along each path beginning at the root increase. Total path length, or search cost, for a rooted tree is defined as the sum of all root-to-node distances and the Sackin index is defined as the sum of the depths of its leaves. We study these quantities in random d-ary increasing trees. [ABSTRACT FROM AUTHOR]

The Hosoya index, also known as the Z index, of a graph is the total number of matchings in it. In this paper, we study the Hosoya index of the tree structures. Our aim is to give some results on Z in terms of Fibonacci numbers in such structures. Also, the asymptotic normality of this index is given. [ABSTRACT FROM AUTHOR]

Abrams' law is used to predict the compressive strength of cementitious materials based on water/cement ratio (W/C). While compressive strength does not only depend on W/C, but also there are many factors that influence the strength of mortar, such as cement strength class and sand/cement ratio (S/C). Novelty of this study, the effect of three types of cement strength classes in 54 cement mortar mix designs on generalization of modified Abrams' law and Bolomey's formula are investigated. Modified equations base on cement strength class and S/C were proposed for the compressive and flexural strength of cement mortar in the range between a very low W/C and a very high W/C. The results showed that the modified equations additional to W/C are strongly influenced by the cement strength class and S/C. Moreover, to show sensitivity of above parameters microstructural characteristics were also studied by the scanning electron microscope (SEM) and an energy dispersive spectrometer analysis (EDS). [ABSTRACT FROM AUTHOR]

In actuary, the derivation of loss distributions from insurance data is of great interest. Fitting an adequate distribution to real insurance data is not an easy task, mainly due to the nature of the data, which shows several features to be accounted for. Although, because of its stochastic and numerical simplicity, it is often assumed that the involved financial risk factors are normally distributed, but empirical studies indicate that most of financial risk factors have distributions with high peaks and heavy tails. Thus, it is important in the actuarial science to model insurance risks with skewed distributions. Claims size data in non-life insurance policies are very skewed and exhibit high kurtosis and extreme tails. Skew distributions are reasonable models for describing claims in property-liability insurance. We fit several well-known skew distributions (skew-normal, skew-Laplace, generalized logistic, generalized hyperbolic, variance gamma, normal inverse Gaussian, Marshal-Olkin Log-Logistic and Kumaraswamy Marshal-Olkin Log-Logistic distributions) to the amount of automobile accident claims for property damage to a third party. The data are from financial records of a state-owned major general insurance company in Iran. The fitted models are compared using AIC (Akaike information criterion), BIC (Bayesian information criterion) and Kolmogorov-Smirnov goodness-of-fit test statistics. We find that the Kumarasamy Marshal-Olkin Log-Logistic distribution is better than other considered distributions in describing the features of the observed data. This distribution is a very perfect distribution to describe the skew data. The value at risk and conditional tail expectation, as most common risk measures in insurance, are estimated for the data under consideration. [ABSTRACT FROM AUTHOR]

The Gutman index and degree distance of a connected graph G are defined as Gut(G)= Σ{u,v}⊆V(G) d(u)d(v)dG(u,v), DD(G)=Σ{u,v}⊆V(G) d(u)+ d(v)dG(u,v), respectively, where d(u) is the degree of vertex u and dG(u; v) is the distance between vertices u and v. In this paper, through a recurrence equation for the Wiener index, we study the first two moments of the Gutman index and degree distance of increasing trees. [ABSTRACT FROM AUTHOR]

Skew distributions are reasonable models for describing claims in property-liability insurance. We consider two well-known datasets from actuarial science and fit skew-normal and skew-logistic distributions to these dataset. We find that the skew-logistic distribution is reasonably competitive compared to skew-normal in the literature when describing insurance data. The value at risk and tail value at risk are estimated for the dataset under consideration. Also, we compare the skew distributions via Kolmogorov-Smirnov goodness-of-fit test, log-likelihood criteria and AIC. [ABSTRACT FROM AUTHOR]

In this paper we study the first Zagreb index in bucket recursive trees containing buckets with variable capacities. This model introduced by Kazemi in 2012. We obtain the mean and variance of the first Zagreb index and introduce a martingale based on this quantity. [ABSTRACT FROM AUTHOR]