I= THE NON-LINEAR FUNCTIONS OF ORDER STATISTICS AND THEIR PROPERTIES IN SELECTED PROBABILITY MODELS
 Pakistan Research Repository Home
 Title of Thesis THE NON-LINEAR FUNCTIONS OF ORDER STATISTICS AND THEIR PROPERTIES IN SELECTED PROBABILITY MODELS Author(s) EHTESHAM HUSSAIN Institute/University/Department Details Department of Statistics/ University of Karachi Session 2006 Subject Statistics Number of Pages 113 Keywords (Extracted from title, table of contents and abstract of thesis) order statistics, non-linear functions, probability models, reliability static, probabilistic model, lindley distribution, stress-strength model, maximum likelihood estimator AbstractIn this research we study the reliability (reliability static) parameterized by stress-strength model-reliability. The stress-strength model, reliability for a components (system is given by) R=P(YIn the present study we proposed "Lindley distribution" for stress-strength model, reliability. This distribution so far has not been studied for reliability assessment. The Lindley distribution is a positively skewed distribution with scale parameter e. First some properties of Lindley distribution are reviewed and estimation problem of e is considered. Then after reliability features of single component, parallel case for identical components and series case for two identical components are considered. The maximum likelihood estimators (MLEs) are obtained for these three situations. Unfortunately the formulas of MLEs rapidly become too complicated for useful result to be deduced. Nowadays numerically intensive methods are commonly used to tackle non-standard problems such as present one. We numerically investigated the properties of estimators based on parametric bootstrap (PB) methods. The comparison between true values and estimated values is made. Estimator performances Bias, Mean Squire Error (mse) Efron percentile confidence interval and its centers are assessed. Relevant computations and simulation is done by witting programs in MATHEMATICA. Our simulation studies showed performance of estimators for different combinations of parameters and sample sizes. For all sample sizes considered in this study, center of Efron percentile confidence intervals, are closed to true values of parameters of interest. The accuracy of parametric bootstrap method increases as the sample size increase.