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Eighteen cattle (six Bonsmara males, seven Simmanteler x Beefmaster males and five Simmanteler x Beefmaster females) were assigned to three diets containing 0% (Control), 10% and 20% Macadamia oil cake to evaluate the effects of different levels of Macadamia oilcake (MOC) on feed intake, growth performance and carcass characteristics of feedlot cattle. Differences in average feed intake were not significant (P > 0.05). Average daily gains on the 0% and 20% MOC diets were not significantly different (P < 0.05) but were significantly higher than the average gain on 10% MOC (P < 0.05). The inclusion of 20% MOC increased feed conversion ratio significantly (P < 0.05) compared with the other two treatments. The control group had significantly heavier warm carcasses than the 10% and 20% MOC groups and the 20% MOC group had significantly heavier carcasses than the 10% MOC group. The inclusion of MOC did not significantly affect the dressing percentage and conformation scores of the animals (P > 0.05). There were no condemned livers, suggesting that either there were no toxic factors in the feed or, even if present, were probably inactive in the liver.

We develop the new Kumaraswamy Log-Logistic Weibull (KLLoGW) distribution by combining the Kumaraswamy and Log-logistic Weibull distributions. This new model is flexible for modelling lifetime data. Some statistical properties including quantile function, hazard rate function, moments and conditional moments are presented. Model parameters are estimated via the method of maximum likelihood and a Monte Carlo simulation study conducted to assess the accuracy of the estimates. Finally, the model is applied to a real dataset.

In this paper, we study the robustness of Hotelling's T when sampling from a mixture of two multivariate normal distributions. First we investigate the robustness of the T 2 statistic s test of the hypothesis HQ: μ = 0 when the underlying distribution is the mixture of two normal populations. The effect on the actual significance level when the T test is used s a test of HQ: μ\ -0 in the presence of exactly r outliers from N p ( μ^, Σ) in a sample of size N is also considered. INTRODUCTIONGiven a random sample ΧΙ,.,.,ΧΜ from a normal N p ( μ,Σ;#) distribution, Hotelling's T 2 is used for testing the hypothesis HQ: E x\ = μ\ -0 against various alternatives, for calculating critical values and for evaluating power. The distribution of T 2 has been investigated under the mixture model [Srivastava and Awan (1982), Srivastava (1984)] 2^· χ) 0 < ί< < l, t = 1,2,; ii + <5 2 = l-(1-1) Amey and Gupta (2000) derived the exact (doubly non-central) distributions of T 2 when sampling from a mixtue of two normal distributions. In this paper, we use the results obtained to study the robustness of the T 2 test. First, we investigate the robustness of the T 2 -test s a test of the hypothesis HQ : μι = 0 when the underlying distribution is the mixture of two normal populations instead of the usual normality assumption. The effect on the actual significance level when the T 2 test is used s a test of HQ : μι = 0 in the presence of exactly r outliers from N p ( μ 2) Σ) in a sample of size N is also considered. 2. THE DISTRIBUTION OF T 2 UNDER THE MIXTURE MODEL 2.1 The density of T 2 under the mixture model From Amey and Gupta (2000) we have the following result: Brought to you by | University of Michigan Authenticated Download Date | 6/15/15 10:39 AM

Summary The robustness of Mauchly's sphericity test criterion when sampling from a mixture of two multivariate normal distributions is studied. The distribution of the sphericity test criterion when the sample covariance matrix has a non‐central Wishart density of rank one is derived in terms of Meijer's G‐functions; its distribution under the mixture model is then deduced. The robustness is studied by computing actual significance levels of the test under the mixture model using the critical values under the usual normal model.