On MLEs of the parameters of a modified Weibull distribution for progressively type-2 censored samples

Lifetimes of modern mechanic or electronic units usually exhibit bathtub-shaped failure rates. An appropriate probability distribution to model such data is the modified Weibull distribution proposed by Lai et al. [15]. This distribution has both the two-parameter Weibull and type-1 extreme value distribution as special cases. It is able to model lifetime data with monotonic and bathtub-shaped failure rates, and thus attracts some interest among researchers because of this property. In this paper, the procedure of obtaining the maximum likelihood estimates (MLEs) of the parameters for progressively type-2 censored and complete samples are studied. Existence and uniqueness of the MLEs are proved.