Abstract
Statistician always tries to find an easy method that gives a suitable fit. However, proposing a new distribution always solves many statistical problems. In this paper, we introduce a new extension of the Lindley distribution. We made a statistical inference under complete and Type-II censored sample on a new extension of the Lindley distribution. We have deduced its PDF and CDF using a cubic transmuted family that is because the new equations are very easy in computation. We called the new form the cubic transmuted Lindley distribution. The probability distribution function and the cumulative distribution function were also written as a closed form along with some mathematical properties. The classical method, which is the maximum likelihood estimation technique and maximum product of spacing technique, was used to find the estimators of the unknown model parameters. At last, to prove the superiority and applicability of the model, three real data sets are implemented and compared using the proposed method. We made a comparison with some of its baseline distributions and some other extensions, and our model outperforms the published ones.