<p>This paper aims to introduce a comparative study for the E-Bayesian criteria with three various Bayesian approaches; Bayesian, hierarchical Bayesian and empirical Bayesian. This study is concerned to estimate the shape parameter and the hazard function of the Gompertz distribution based on type-II censoring. All estimators are obtained under symmetric loss function [squared error loss (SELF))] and three different asymmetric loss functions [quadratic loss function (QLF), entropy loss function (ELF) and LINEX loss function (LLF)]. Comparisons among all estimators are achieved in terms of mean square error (MSE) via Monte Carlo simulation.</p>

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We introduce a new four parameter continuous model, called the Kumaraswamy compound Rayleigh (KwCR) distribution that extends the compound Rayleigh distribution. We study some mathematical properties of this distribution such as; mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and probability generating functions, reliability analysis, Lorenz, Bonferroni and Zenga curves, Rényi of entropy, order statistics and record statistics. We consider the methods of moments and maximum likelihood for estimating the model parameters.

Objectives: This study aimed to explore the correlation of central cornealthicknesses (CCT), mean keratometry (KM) and axial length (AL) to myopia degree in sphericalequivalent (SE) among Sudanese adults. Study Design: Cross sectional study. Setting:University Eye complex clinic and Makka Eye complex Omdurman. Period: April to October2015. Methods: Central Corneal Thickness (CCT), k-reading (KM), axial length and thedegree of refraction (SE) 0f 200 myopic eyes and 60 emmetropic eyes as a control groupwere measured. Results: Adult Sudanese females (57%) were found greater than males (43%)population; (χ 2 = 109.5, p = 0.000 ), most of the participants’ age was less than 25 years(χ 2 = 109.5, p = 0.000 ), and the mean myopic spherical equivalent (SE) was – 4.79 ± 2.55 D,ranging from -1.00 to -11.00 D. The mean CCT of the myopic group was 542.8 ±11.9 μm,while for the emmetropic group was 538.7 ±12.4 μm. The cornea were steeper in eyes withlonger axial length (r = 0.24, p =0.001). Eyes with higher myopic spherical equivalent hadlonger axial length (r =0.30, p <0.001). Mean keratometrys were steeper with increasing age(r= 0.24, p= 0.001). This study has shown that CCT has no correlation with degree of myopia(p= 0.46), gender (p= 0.99), and age (p= 0.07). The CCT, KM, and AL means for myopicparticipants were found significantly greater than emmetropic participants (p=0.000, 0.000,and 0.044 respectively. Conclusion: The females participants of myopia were higher rate thanmales, early adults’ age group were of higher rate myopic incident; there was no correlationbetween CCT and the degree of myopia, gender, and age. CCT, KM, and AL means for myopicwere found higher than emmetropic participant. Eyes with more myopic spherical equivalenthad longer axial length; corneal curvature mean becomes steeper with increasing age.