Estimating the Entropy of a Lomax Distribution under Generalized Type-I Hybrid Censoring


Mahmoud Riad Mahmoud, Badiaa S. KH. Mohamed
Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Cairo, Egypt.

Moshera A. M. Ahmad
El Gazeera High Institute For Computer & Management Information System, Egypt.


The data are said to be censored when some important information about the subject’s event time that is required to make a conclusion is not available to the practitioner. Censoring is said to be single Type-I censoring (or time censoring) when the experimental time is fixed and the number of observed failures is a random variable. In contrast, censoring is said to be single Type-II censoring (or failure censoring) when the number of observed failures is fixed and the experimental time is a random variable. A mixture of Type-I and Type-II censoring is called a single hybrid censoring scheme. The disadvantage of a hybrid censoring scheme is that there is a possibility that very few failures may occur before time. In that case, the efficiency of the estimator(s) might below. For this reason, So, Scientists proposed the generalized Type-I hybrid censoring as a modification of the hybrid censoring scheme. The reason behind the proposed modification is to fix the underlying disadvantages inherent in the hybrid censoring scheme. In information theory, entropy plays a central role which measures the uncertainty associated with the cumulative distribution function. The concept of information entropy was introduced by Claude Shannon in his 1948 paper “A Mathematical Theory of Communication”. In this paper, we obtain the entropy estimate of a two-parameter Lomax distribution based on the first type of hybrid censoring scheme (HCS). The maximum probability estimates to the unknown parameters are extracted to the entropy estimate.