Maximum likelihood estimation of the generalised Gompertz distribution under progressively first-failure censored sampling

Abstract

In this paper, the maximum likelihood estimators of the unknown parameters, as well as some lifetime parameters survival and hazard rate functions, of a three-parameter generalised Gompertz lifetime model based on progressively first-failure censored sampling are obtained. Approximate confidence intervals for the unknown parameters and the reliability characteristics are constructed based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators. Although the proposed estimators cannot be expressed in explicit forms, these can be easily obtained through the use of appropriate numerical techniques. Finally, a real data set has been analysed for illustrative purposes.