This paper reports the use of a numerical solution of nanofluid flow. The boundary layer flow over a stretching sheet in combination of two nanofluids models is studied. The partial differential equation that governs this model was transformed into a nonlinear ordinary differential equation by using similarity variables, and the numerical results were obtained by applying the shooting technique. Copper (Cu) nanoparticles (water-based fluid) were used in this study. This paper presents and discusses all numerical results, including those for the local Sherwood number and the local Nusselt number. Additionally, the effects of the nanoparticle volume fraction, Brownian motion Nb, and thermophoresis Nt on the performance of heat transfer are discussed. The results show that the stretching sheet has a unique solution: as the nanoparticle volume fraction φ (φ = 0), Nt (Nt = 0.1), and Nb decrease, the rate of heat transfer increases. Furthermore, as φ (φ = 0) and Nb decrease, the rate of mass transfer increases. The data of the Nusselt and Sherwood numbers were tested using different statistical distributions, and it is found that both datasets fit the Weibull distribution for different values of Nt and rotating φ.

The purpose of this paper is to develop a latent variable model with nonlinear covariates and latent variables. Mixed ordered categorical and dichotomous variables and covariates with two different types of thresholds (with equal and unequal spaces) are used in Bayesian multi-sample nonlinear latent variable models and the Gibbs sampling method is applied for estimation and model comparison. Hidden continuous normal distribution (censored normal distribution) and (truncated normal distribution with known parameters) are used to handle the problem of mixed ordered categorical and dichotomous data. Hidden continuous normal distribution (truncated normal distribution with known parameters) is used to handle the problem of mixed ordered categorical and dichotomous data in covariates. Statistical analysis, which involves the estimation of parameters, standard deviations and their highest posterior density, are discussed. The proposed procedure is illustrated using psychological data with the results obtained from the OpenBUGS program.

In this paper, our main objective is to use a latent variable model and to propose a suitable model with features such as a nonlinear fixed covariates and latent variables based on different models that could be described both based on mathematical as well as structural model. We also used dichotomous (Binary) variables in Non-Linear latent variables model for two populations by using Bayesian approach as well as the Gibbs sampling method to find the comparison, differences and similarities based on different data points and estimate them accordingly. We have also included Hidden continuous normal distribution that can be both censored and truncated based on the type and need of the moment using which we can screen the different aspects involved in analysing the data and further Gibbs sampling method can also be used in the same filtering. It is often used in a view to solve the problem related to dichotomous data and accordingly relate it to different variables as a continuous normal distribution. We can also make use of various inferences derived based on the statistical results that include all the perspectives considering the scope of standard errors, most common methods, simplified approaches, and highest posterior density problem for testing and so on. All the theories are substantiated using real data and the results obtained from them using the OpenBugs program. It’s obvious from the results of DIS that the results of interval censored normal distribution was the best, then, the results of interval truncated normal distribution and, finally, the results of continuous normal distribution.

This study aims to estimate the parameters of confirmatory factor analysis with non-normal variables using a Bayesian approach. In this study, the estimation method is (Markov chain Monte Carlo)" MCMC" simulation, and the ordinal variables have defined cut points (Gibbs sampling). To handle non-normal outcomes, censoring techniques with distinct cut-points are used. Additional methods are interpreted, including the (Bayesian estimator), (standard deviations) "SD", and (highest posterior density) "HPD". )Quality of life( "QOL" data and observations from the OpenBUGS program are used to explain the established process.