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In this study, a dataset comprising 20,328 body weight records from birth to 360 days of age was utilized to compare five growth curve models and genetic analysis of growth curve parameters in Iran-Black sheep. The data and genealogical information were collected between 1981 and 2007 from the Breeding Station of Abbasabad in the Khorasan Razavi province of northeast Iran. The performance of five statistical models including Brody, negative exponential, von Bertalanffy, Logistic, and Gompertz for describing the growth curve of the studied population was evaluated by applying the SAS software. The statistical measures used for model comparisons were Akaike's information criterion (AIC), root mean square error (RMSE), and adjusted coefficient of determination (R²adj). The Brody model, exhibiting the highest R²adj and the lowest values for both AIC and RMSE, was selected as the best model for characterizing the growth curve in this breed. Consequently, the parameters of the growth curve, including parameter A (considered as weight at maturity), B (considered as an integration constant), and K (maturation rate) were predicted by applying the Brody model. To investigate the effect of maternal components on the growth curve parameters, nine univariate animal models, including different combinations of the direct additive genetic, maternal additive genetic, maternal permanent environmental, and maternal temporary environmental effects, were fitted. Subsequently, two multivariate animal models, comprising the standard (SMM) and fully recursive (FRM) models were analyzed by using the Bayesian inference. The FRM outperformed SMM in terms of lower means square error (MSE) and higher Pearson's correlation coefficients between the actual and predicted records (r(y, y)) values, indicating better goodness of fit. The posterior means for heritability of A, B, and K parameters were low but statistically significant under SMM and FRM. It may be concluded that the growth trajectory traits of Iran-Black sheep are influenced mainly by non-additive genetic and environmental effects, emphasizing the importance of considering these effects for developing the corresponding breeding strategies. The Spearman's rank correlation coefficients between the estimated breeding values for growth curve traits under SMM and FRM indicated significant re-ranking of animals, favoring FRM for genetic evaluation in Iran-Black sheep. [ABSTRACT FROM AUTHOR]

Symmetrical as well as asymmetrical statistical models play a prominent role in describing and predicting the real-world phenomena of nature. Among other fields, these models are very useful for modeling data in the sector of civil engineering. Due to the applicability of the statistical models in civil engineering and other related sectors, this paper offers a statistical methodology to improve the distributional flexibility of traditional models. The suggested method/approach is called the extended-X family of distributions. The proposed method has the ability to generate symmetrical and asymmetrical probability distributions. Based on the extended-X family approach, an updated version of the Weibull model, namely, the extended Weibull model, is studied. The proposed model is very flexible and has the ability to capture the symmetrical and asymmetrical shapes of its density function. For the extended-X method, the estimation of parameters, a simulation study, and some mathematical properties are derived. Finally, the practical illustration/usefulness of the suggested model is shown by analyzing two data sets taken from the field of engineering. Both data sets represent the fracture toughness of alumina (Al2O3). [ABSTRACT FROM AUTHOR]

Symmetrical as well as asymmetrical statistical models play a prominent role in describing and predicting the real-world phenomena of nature. Among other fields, these models are very useful for modeling data in the sector of civil engineering. Due to the applicability of the statistical models in civil engineering and other related sectors, this paper offers a statistical methodology to improve the distributional flexibility of traditional models. The suggested method/approach is called the extended-X family of distributions. The proposed method has the ability to generate symmetrical and asymmetrical probability distributions. Based on the extended-X family approach, an updated version of the Weibull model, namely, the extended Weibull model, is studied. The proposed model is very flexible and has the ability to capture the symmetrical and asymmetrical shapes of its density function. For the extended-X method, the estimation of parameters, a simulation study, and some mathematical properties are derived. Finally, the practical illustration/usefulness of the suggested model is shown by analyzing two data sets taken from the field of engineering. Both data sets represent the fracture toughness of alumina (Al2O3).

In this paper, we introduce a new statistical methodology for updating the flexibility level of the traditional distributions. The newly developed method is called, the logarithmic-U family of distributions. For the logarithmic-U distributions, the estimation of the parameters via the maximum likelihood method is discussed. Some mathematical properties of the logarithmic-U distributions are also derived. By using the logarithmic-U method, an updated version of the Weibull model, namely, the logarithmic Weibull distribution is introduced. A simulation study for the logarithmic Weibull distribution is provided. Finally, the practical illustration of the logarithmic Weibull distribution is shown by analyzing two data sets taken from the engineering sector. The first data set represents the fracture toughness of Al2O3 material. Whereas, the second data set represents the fatigue fracture of Kelvar 373/epoxy. The practical applications show that the proposed logarithmic Weibull distribution is very competent for analyzing data sets in engineering and other related sectors.

In this paper, we introduce a new statistical methodology for updating the flexibility level of the traditional distributions. The newly developed method is called, the logarithmic- U family of distributions. For the logarithmic- U distributions, the estimation of the parameters via the maximum likelihood method is discussed. Some mathematical properties of the logarithmic- U distributions are also derived. By using the logarithmic- U method, an updated version of the Weibull model, namely, the logarithmic Weibull distribution is introduced. A simulation study for the logarithmic Weibull distribution is provided. Finally, the practical illustration of the logarithmic Weibull distribution is shown by analyzing two data sets taken from the engineering sector. The first data set represents the fracture toughness of Al 2 O 3 material. Whereas, the second data set represents the fatigue fracture of Kelvar 373/epoxy. The practical applications show that the proposed logarithmic Weibull distribution is very competent for analyzing data sets in engineering and other related sectors. [ABSTRACT FROM AUTHOR]

SEM is a very popular analytical method for quantitative studies in many disciplines. The goal of SEM is to determine the model that best fits the data. The data sets were generated from the multivariate contaminated normal distribution in this study. The aim of the study was to determine the best goodness of fit measures not affected by data structures and sample sizes. ADF, ML, and GLS estimation methods were applied under the multivariate nonnormality. According to the ADF method, AGFI, GFI, and RMSEA were not affected by sample size and correlation changes. CFI, NFI, and NNFI values were affected by both sample size and correlation changes. RMR always received values outside the acceptable fit limits in all sample sizes and correlation values. Consequently; if the data are multivariate nonnormality, the sample size should be greater than 250 units and AGFI, GFI and RMSEA fit measures should be used. [ABSTRACT FROM AUTHOR]