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

Abstract

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 Based on New Pareto-Type Records With Applications to Precipitation and Covid-19 Data

“…For more details, see Arnold et al [6]. For some recent works on statistical inference using record data, see for example Asgharzadeh et al [8,9], Aldallal [4], Chaturvedi and Malhotra [13], Bagheri et al [10], Basiri et al [11], Sing et al [25], Qazi et al [19], Raqab et al [20] and Aly et al [5].…”