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.