As an application of the improved Cauchy-Schwartz inequality due toWalker (2017), we obtain an improved version of the Cramer-Rao inequality for Randomly censored data derived by Abdushukurov and Kim (1987, pp. 2171-2185). We derive a lower bound of Bhattacharya type for the mean square error of a parametric function based on Randomly censored data.

In this article, we use a measure of expected true evidence for determine the required sample size in type-II censored experiments for obtaining statistical evidence in favor of one hypothesis about the exponential mean against another.

Introduction: In survival analysis, determination of sufficient sample size to achieve suitable statistical power is important .In both parametric and non-parametric methods of classic statistics, randomn selection of samples is a basic condition. practically, in most clinical trials and health surveys randomn allocation is impossible. Fixed - effect multiple linear regression analysis covers this need and this feature could be extended to survival regression analysis. This paper is the result of sample size determination in non-randomnized surval analysis with censored and non -censored data.Methods: In non-randomnized survival studies, linear regression with fixed -effect variable could be used. In fact such a regression is conditional expectation of dependent variable, conditioned on independent variable. Likelihood fuction with exponential hazard constructed by considering binary variable for allocation of each subject to one of two comparing groups, stating the variance of coefficient of fixed - effect independent variable by determination coefficient , sample size determination formulas are obtained with both censored and non-cencored data. So estimation of sample size is not based on the relation of a single independent variable but it could be attain the required power for a test adjusted for effect of the other explanatory covariates. Since the asymptotic distribution of the likelihood estimator of parameter is normal, we obtained the variance of the regression coefficient estimator formula then by stating the variance of regression coefficient of fixed-effect variable, by determination coefficient we derived formulas for determination of sample size in both censored and non-censored data.Results: In no-randomnized survival analysis ,to compare hazard rates of two groups without censored data, we obtained an estimation of determination coefficient ,risk ratio and proportion of membership to each group and their variances from likelihood function, when data has censored cases an estimate of the probability of censorship should be considered, after obtaining the varince of maximum likelihood estimator and considering its asymptotic normal distribution and by using coefficient of determination, formulas have been derived. The derived sample size formulas could attain the required power for a test adjuasted for effect of other explanatory covariates.Discussion: application of regression model in non-randomnized survival analysis helps to derive suitable formulas to determin sample size in both randomized and non-randomnized studies in a error level, to attain necessary statistical power. In Coxs semiparametric proportional hazard model ,since the varince of the parameter can not be stated in a simple form ,a simulation model can be used. When the coefficient of determination is partialy large the power bassed on log-rank test overestimates the true value of power, but when coefficient of determination is near to difference between powers decreases zero. By increasing of regression coefficient of determination, the difference between the log-rank test and adjusted coefficient of determination of this paper increases.

means to facilitate regression analysis of high-dimensional data. When the response is censored, most existing estimators cannot be applied, or require some restrictive conditions. In this article modification of sliced inverse, regression-II have proposed for dimension reduction for non-linear censored regression data. The proposed method requires no model specification, it retains full regression information, and it provides a usually small set of composite variables upon which subsequent model formulation and prediction can be based. Finally, the performance of the method is compared based on the simulation studies and some real data set include primary biliary cirrhosis data. We also compare with the sliced inverse regression-I estimator.

The mixture of Type I and Type II censoring schemes, called the hybrid censoring. This article presents the statistical inferences on lognormal parameters when the data are hybrid censored. We obtain the maximum likelihood estimators (MLEs) and the approximate maximum likelihood estimators (AMLEs) of the unknown parameters. Asymptotic distributions of the maximum likelihood estimators are used to construct approximate confidence intervals. Monte Carlo simulations are performed to compare the performances of the different methods and one data set is analyzed for illustrative purposes.

The purpose of this paper is to investigate the determinant of educational cost in micro level (I. e. household). These determinants are categorized in four levels: household characteristics, child characteristics, head characteristics and mother characteristics. The effect of each one is estimated thorough a censored Tobit model for 2016 Iran household survey. The reason of model selection is for reporting zero cost in some cases. The result shows that urban residency and having girl child (versus boy) are context factors that increase expenditure on education. Sexuality of household head is the other important can increase income of family and so the educational costs. And finally, analyzing mother and head of the family shows that transition of financial capital to child is take place dominantly thorough head (greater effect of head income than mother income) and versus the transition of human capital to child is take place dominantly thorough head (greater effect of mother literacy than head literacy).

Background and Aim: Interval censored data occur in repeated data in medical studies. There are common methods to analysis this type of data. The purpose of this study is to examine the random imputation technique in the analysis of interval censored data. Materials and Methods: Using the Monte Carlo simulation technique, we evaluate the power of Random Imputation method, and finally we assess its performance using the actual data set. Actual dataset is related to dental information in Urmia, which contains 207 children. All calculations are done using R 3. 2. 3 software. Findings: The simulation results show that the power of random imputation technique is good and acceptable. The p-value in real data shows that there is no difference using the random imputation technique. Conclusion: Random imputation technique can be used as an alternative method in comparison with other conventional methods.

Manufacturers need to evaluate the reliability of their products in order to increase the customer satisfaction. Proper analysis of reliability also requires an effective study of the failure process of a product, especially its failure time. So, the Failure Process Modeling (FPM) plays a key role in the reliability analysis of the system that has been less focused on. This paper introduces a framework defining an approach for the failure process modeling with censored data in Constant Stress Accelerated Life Tests (CSALTs). For the first time, various types of censoring schemes are considered in this study. Usually, in data analysis, it is impossible to get closed form of estimates of the unknown parameter due to complex and nonlinear likelihood equations. As a new approach, a mathematical programming problem is formed and the Maximum Likelihood Estimation (MLE) of parameters is obtained to maximize the likelihood function. A case study in red Light- Emitting Diode (LED) lamps is also presented. The MLE of parameters is obtained using genetic algorithm (GA). Furthermore, the Fisher information matrix is obtained for constructing the asymptotic variances and the approximate confidence intervals of estimates of the parameters.