Two-Parameter Exponential Distribution with Randomly Censored and Outlier Data

Abstract

The two-parameter exponential distribution is an important statistical distribution, widely used in medicine, engineering,
economics, demography, and longevity data. In the present work, the two-parameter exponential distribution under random censoring
with the presence of outlier data is presented, and its parameters are estimated using the moment, maximum likelihood, and Bayesian
methods. In parameter estimation, using maximum likelihood estimators, asymptotic confidence intervals are determined; while, by
considering appropriate prior distributions, Bayesian estimation under squared error and LINEX loss functions is presented for the
parameters. Next, using simulation, the estimators are compared by using statistical measures. Finally, utilizing a real data set, the
suitability of the fitness of the model is evaluated according to different estimation methods.