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This paper deals with the estimation of P[Y < X] when X and Y are two independent generalized exponential distributions with different shape parameters but having the same scale parameters. The maximum likelihood estimator and its asymptotic distribution is obtained. The asymptotic distribution is used to construct an asymptotic confidence interval of P[Y < X]. Assuming that the common scale...
Generalized linear and nonlinear mixed-effects models are used extensively in biomedical, social, and agricultural sciences. The statistical analysis of these models is based on the asymptotic properties of the maximum likelihood estimator. However, it is usually assumed that the maximum likelihood estimator is consistent, without providing a proof. A rigorous proof of the consistency by verifying...
Let X1, X2, ..., Xn be a random sample from a normal distribution with unknown mean μ and known variance σ2. In many practical situations, μ is known a priori to be restricted to a bounded interval, say [−m, m] for some m > 0. The sample mean $$\bar{X}$$ , then, becomes an inadmissible estimator for μ. It is also not minimax with respect to the squared error loss function. Minimax and...
This article considers statistical inference for a Poisson autoregressive model. A condition for ergodicity and a necessary and sufficient condition for the existence of moments are given. Asymptotics for maximum likelihood estimator and weighted least squares estimators with estimated weights or known weights of the parameters are established. Testing conditional heteroscedasticity and testing the...
The progressive Type-II hybrid censoring scheme introduced by Kundu and Joarder (Comput Stat Data Anal 50:2509–2528, 2006), has received some attention in the last few years. One major drawback of this censoring scheme is that very few observations (even no observation at all) may be observed at the end of the experiment. To overcome this problem, Cho et al. (Stat Methodol 23:18–34, 2015) recently...
In this paper, we propose two moment-type estimation methods for the parameters of the generalized bivariate Birnbaum–Saunders distribution by taking advantage of some properties of the distribution. The proposed moment-type estimators are easy to compute and always exist uniquely. We derive the asymptotic distributions of these estimators and carry out a simulation study to evaluate the performance...
Due to its flexibility, gamma distribution is commonly used for lifetime data analysis in reliability and survival studies, and especially in one-shot device testing data. In the study of such data, inducing more failures by accelerated life tests is a common practice, to obtain more lifetime information within a relatively short period of time. In this paper, we develop weighted minimum density power...
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