Statistical Inference Of Generalized Exponential Distribution And Its Accerlating Life Testing

To make up the shortage of the distribution of Weibull and Gamma, the generalized exponential distribution was first proposed by Gupta and Kundu(1999), which can fit some life-data better. For the generalized exponential distribution, in the present paper we have the following results: (1) For the complete sample, the maximum likelihood estimation(MLE) and inverse moment estimation(IME) are derived and compared by Monte-Carlo simulation, and the maximum likelihood estimation of shape parameterλare proved. For the incomplete sample, the MLE and IME are derived and compared by Monte-Carlo simulation, especially for the progressively type II censored sample, the interval estimation of shape parameterλand joint confidential region are also proposed. (2) The MLE and the two-step estimation are derived for the constant-stress accelerated life testing sample of generalized exponential distribution with the constant failure mechanism, and the constant failure mechanism is tested by constructing pivotal quantity. (3) The coincidental and equivalent for the model of TFR , CE and TRV are discussed for the generalized exponential distribution, the tampered factor for models of CE and TRV are derived for the progressive stress ALT, and under the progressive stress ALT, the MLE and IME are derived for the Arrhenius model, and IME is proposed for the inverse power model. (4) The MLE and IME of parameters based on the type II step-increasing data under step stress ALT for CE model of two-parameter generalized exponential distribution are derived, and the MLE of unknown parameters using EM algorithm are obtained.