# Likelihood Inference for Discrete Weibull Data with Left Truncation and Right Censoring

## Authors

• Chaobing He School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China

## Keywords:

Maximum likelihood estimate, EM algorithm;Lifetime data, Missing information principle, Asymptotic variance-covariance matrix, ECM algorithm, Newton-Raphson method, Asymptotic confidence interval

## Abstract

The discrete Weibull distribution is a very popular distribution for modeling discrete lifetime data, and it is obtained by discretizing Weibull distribution. Left truncation and right censoring are often observed in lifetime data. Here, the EM algorithm is applied to estimate the model parameters of the discrete Weibull distribution fitted to data containing left truncation and right censoring. The maximization part of the EM algorithm is carried out using the ECM algorithm. The discrete Weibull distribution is also fitted using the Newton-Raphson(NR) method. The asymptotic variance-covariance matrix of the MLEs under the EM framework is obtained through the missing information principle, and asymptotic confidence intervals for the parameters are then constructed.

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2021-12-15

## How to Cite

He, C. (2021). Likelihood Inference for Discrete Weibull Data with Left Truncation and Right Censoring. EPH - International Journal of Mathematics and Statistics, 7(12), 01–11. https://doi.org/10.53555/ephms.v7i12.1847

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