ESTIMATION OF P(X > Y) FOR THE POSITIVE EXPONENTIAL FAMILY OF DISTRIBUTIONS

A positive exponential family of distributions is taken into consideration. Two measures of reliability are discussed. Uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES) are developed for the reliability functions. In addition to the UMVUES and MLES, we derive the method of moment estimators (MOME). The performances of two types of estimators are compared through Monte Carlo simulation

Inference on the Parameters and Reliability Characteristics of Generalized Inverted Scale Family of Distributions based on Records

A generalized inverted scale family of distributions is considered. Two measures of reliability are discussed, namely ρ(t) = P(X > t) and P = P(X > Y ). Point and interval estimation procedures are developed for the parameters, ρ(t) and P based on records. Two types of point estimators are developed - uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES). A comparative study of different methods of estimation is done through simulation studies and asymptotic confidence intervals of the parameters based on MLE and log transformed MLE are constructed. Testing procedures are also developed for the parametric functions of the distribution and a real life example has been analysed for illustrative purposes

Inference on the parameters and reliability characteristics of the generalized inverse Weibull distribution based on records.

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three parameters generalized inverse Weibull distribution with decreasing and unimodal failure rate is studied. Two measures of reliability are discussed, namely R(t) = P(X>t) and P=P(X>Y). Point and interval estimation procedures are developed for the parameters, R(t) and P based on records. Two point estimators are developed, namely uniformly minimum variance unbiased estimators (UMVUE) and maximum likelihood estimators (MLE). A comparison of different methods of estimation is done through simulations and asymptotic confidence intervals of the parameters based on MLE and log transformed MLE are constructed. Confidence intervals for the MLE and UMVUE of the parametric functions are obtained. Testing procedures are also developed for various hypotheses

On Estimation of Reliability Functions using Record values from Proportional Hazard Rate Model

Two measures of reliability functions, namely R(t)=P(X>t) and P=P(X<Y) have been studied based on record values from proportional hazard rate model (PHR) model. For estimation of P, we generalize the results of Basirat et al. (2016) when X and Y belong to different family of distributions from PHR model. Uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE) and Bayes estimator (BS) are obtained for the powers of the parameter and reliability functions. Simulation studies and a real data example have been presented for illustrative purposes. Asymptotic and exact confidence intervals of the parameters and reliability functions are constructed. Testing procedures are also developed for various hypotheses

On the Construction of Preliminary Test Estimators of the Reliability Characteristics for the Exponential Distribution Based on Records

SYNOPTIC ABSTRACT: The one-parameter exponential distribution plays an important role in reliability theory. Two measures of reliability for exponential distribution are considered, R(t) = P(X > t) and P = P(X > Y). Sometimes, due to past knowledge or experience, the experimenter may be in a position to make an initial guess on some of the parameters of interest. In such cases, we can provide an improved estimator by incorporating the prior information on the parameters. Preliminary test estimators (PTES) have been developed in the literature for the parameters of various distributions. To the best of the knowledge of the authors, PTES are not available for reliability functions R(t) and P. For record values from exponential distribution, we define PTES based on uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE), and empirical Bayes estimator (EBE) for the powers of the parameter, R(t) and P. Bias and mean square error (MSE) expressions for the proposed estimators are derived to examine their efficiency. A comparative study of different methods of estimation is done through simulations, and it is established that PTES perform better than ordinary UMVUES, MLES, and EBES

Estimation and testing procedures for the reliability functions of a family of lifetime distributions based on records

A family of lifetime distributions is considered. Two measures of reliability are considered, R(t) = P(X > t) and P = P(X > Y). Point estimation and testing procedures are developed for R(t) and P based on records. Two types of point estimators are developed—uniformly minimum variance unbiased estimators and maximum likelihood estimators. A comparative study of different methods of estimation is done through simulation studies. Testing procedures are developed for the hypothesis related to different parametric functions

Estimation and Testing Procedures for the Reliability Functions of Three Parameter Burr Distribution under Censorings

Athree parameter Burr distribution is considered. Two measures of reliability are discussed. Point and interval estimation procedures are developed for the parameters, and reliability functions under type II and type I censoring. Two types of point estimators namely- uniformly minimum variance unbiased estimators (UMVUES) and maximum likelihood estimators (MLES) are derived. Asymptotic variance-covariance matrix and confidence intervals for MLE’s are obtained. Testing procedures are also developed for various hypotheses