Censored Negative Exponential Distribution as a Mixed Distribution and Derivation of Its Moments

Abstract

Censored negative exponential distribution is treated as a mixed type distribution having two distinct types of components. These components give arise to continuous as well as discrete random variables. Moments (mean and variance) are derived for the doubly censored, right censored, and left censored negative exponential distributions (NEDs) along with separations of continuous and discrete components and their respective means and variances. Moments obtained for the censored NEDs are then compared to the corresponding values of the uncensored NEDs and the changes in the proportions of the moments due to censoring are examined and assessed. Plots of moments of the censored distributions including a three dimensional scatter plot are presented considering different hypothetical values at which censoring may occur. These distributions are widely applied in fitting and modeling failure time data in survival and reliability analyses.

Nepal Journal of Science and Technology Vol. 14, No. 1 (2013) 167-176

DOI: http://dx.doi.org/10.3126/njst.v14i1.8937