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Likelihood inference for lognormal data with left truncation and right censoring with an illustration. (English) Zbl 1221.62038
Summary: The lognormal distribution is quite commonly used as a life-time distribution. Data arising from life-testing and reliability studies are often left truncated and right censored. Here, the EM algorithm is used to estimate the parameters of the lognormal model based on left truncated and right censored data. The maximization step of the algorithm is carried out by two alternative methods, with one involving approximation using Taylor series expansion (leading to approximate maximum likelihood estimate) and the other based on the EM gradient algorithm [K. Lange, J. R. Stat. Soc., Ser. B 57, No. 2, 425–437 (1995; Zbl 0813.62021)]. These two methods are compared based on Monte Carlo simulations. The Fisher scoring method for obtaining the maximum likelihood estimates shows a problem of convergence under this setup, except when the truncation percentage is small. The asymptotic variance-covariance matrix of the MLEs is derived by using the missing information principle [T. A. Louis, ibid., Ser. B 44, 226–233 (1982; Zbl 0488.62018)], and then the asymptotic confidence intervals for scale and shape parameters are obtained and compared with corresponding bootstrap confidence intervals. Finally, some numerical examples are given to illustrate all the methods of inference developed here.

MSC:
62F10 Point estimation
62N01 Censored data models
62N05 Reliability and life testing
62F25 Parametric tolerance and confidence regions
65C05 Monte Carlo methods
Software:
SPLIDA
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References:
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