Asian Journal of Probability and Statistics

In this article, an extension of Inverse Lomax (IL) distribution with the Zubair-G family is considered . Various statistical properties of the new model where derived, including moment generating function, R´enyi entropy, and order statistics. A Monte Carlo simulation study was presented to evaluate the performance of the maximum likelihood estimators. The new model can be skew to the right, constant, and decreasing functions depending on the parameter values.
We discussed the estimation of the model parameters by maximum likelihood method. The application of the new model to the data sets indicates that the new model is better than the existing competitors as it has minimum value of statistics criteria.

In this paper, some basic mathematical operation for the second Zagreb indices of graph containing the join and strong product of graph operation, and the rst and second Zagreb indices of complement graph operations such as cartesian product G1 G2, composition G1 G2, disjunction G1 _ G2, symmetric dierence G1 G2, join G1 + G2, tensor product G1  G2, and strong product G1 G2 will be explained. The results are applied to molecular graph of nanotorus and titania nanotubes.

Background: Generalized Linear models are mostly fitted to data that are not correlated. However, very often data that are collected from health and epidemiological studies are correlated either as a result of the sampling methods or the randomness associated with the collection of such data. Therefore, fitting generalized linear models to such data that produce only fixed effects could lead to over dispersion in the model estimates.

Objectives: The objective of this study is to fit both generalized linear and generalized linear mixed models to a correlated data and compare the results of the two models.

Methods: Logistic regression is employed in fitting the generalized linear model since the dependent variable in the study is bivariate whilst the GLIMMIX model in SAS is used to fit the generalized linear mixed model.

Results: The generalized linear model produces over dispersion with higher errors among the parameter estimates than the generalized linear mixed model.

Conclusion: In dealing with a more correlated data, generalized linear mixed model, which can handle both fixed and random effects, is preferable to generalized linear model.

Flexible pavement design is influenced by many design parameters such as (traffic characterization, pavement depths, structure materials and environmental conditions). To study the impact of variations in design parameters on pavement performance, several attempts have been achieved to add reliability concept to the mechanistic-empirical (M-E) design of pavements. In (M-E) design of pavements, the pavement life depends on subgrade rutting and fatigue cracking, considering them as independent failure patterns. The current design methodology used in many countries such as Egypt is ignoring the impact of temperature variation (despite its importance) on the pavement design. This research aimed to predict the pavement reliability due to variation in pavement design parameters especially temperature using the first-order reliability method (FORM) considering rutting and fatigue failures. Moreover, a comparison was performed between regressions models represented from different pavement agencies to recommend the most efficient one for Egyptian temperature. The results obtained that, considering design parameters variations (without temperature); the reliability based on US Army Corps method (91.64%) was the nearest one to the current design methodology in Egypt (91.0%). After adding temperature variations, the reliability was clearly affected where the regression model of Shell Research agency was the most appropriate one for all Egyptian temperature zones as it achieved the lowest error mean (-0.03) and the lowest error standard deviation (0.0011). Moreover, the air temperature of 28ºC was considered as the inflection point for pavement reliability-temperature curve in Egypt.

The transaction cost model of Guy Barles and Halil Mete Soner is incorporated into the standard Black Scholes Equation. The resulting model is solved by a numerical method, called, the meshfree approximation using radial basis function. The errors produced by the scheme are discussed and presented in diagrams and tables.