30,932 research outputs found
Estimation of Stress-Strength model in the Generalized Linear Failure Rate Distribution
In this paper, we study the estimation of , also so-called the
stress-strength model, when both and are two independent random
variables with the generalized linear failure rate distributions, under
different assumptions about their parameters. We address the maximum likelihood
estimator (MLE) of and the associated asymptotic confidence interval. In
addition, we compute the MLE and the corresponding Bootstrap confidence
interval when the sample sizes are small. The Bayes estimates of and the
associated credible intervals are also investigated. An extensive computer
simulation is implemented to compare the performances of the proposed
estimators. Eventually, we briefly study the estimation of this model when the
data obtained from both distributions are progressively type-II censored. We
present the MLE and the corresponding confidence interval under three different
progressive censoring schemes. We also analysis a set of real data for
illustrative purpose.Comment: 31 pages, 2 figures, preprin
Estimation of Inverse Weibull Distribution Under Type-I Hybrid Censoring
The hybrid censoring is a mixture of Type I and Type II censoring schemes.
This paper presents the statistical inferences of the Inverse Weibull
distribution when the data are Type-I hybrid censored. First we consider the
maximum likelihood estimators of the unknown parameters. It is observed that
the maximum likelihood estimators can not be obtained in closed form. We
further obtain the Bayes estimators and the corresponding highest posterior
density credible intervals of the unknown parameters under the assumption of
independent gamma priors using the importance sampling procedure. We also
compute the approximate Bayes estimators using Lindley's approximation
technique. We have performed a simulation study and a real data analysis in
order to compare the proposed Bayes estimators with the maximum likelihood
estimators.Comment: This paper is under review in the Austrian Journal of Statistics and
will likely be published ther
Studies on properties and estimation problems for modified extension of exponential distribution
The present paper considers modified extension of the exponential
distribution with three parameters. We study the main properties of this new
distribution, with special emphasis on its median, mode and moments function
and some characteristics related to reliability studies. For Modified-
extension exponential distribution (MEXED) we have obtained the Bayes
Estimators of scale and shape parameters using Lindley's approximation
(L-approximation) under squared error loss function. But, through this
approximation technique it is not possible to compute the interval estimates of
the parameters. Therefore, we also propose Gibbs sampling method to generate
sample from the posterior distribution. On the basis of generated posterior
sample we computed the Bayes estimates of the unknown parameters and
constructed 95 % highest posterior density credible intervals. A Monte Carlo
simulation study is carried out to compare the performance of Bayes estimators
with the corresponding classical estimators in terms of their simulated risk. A
real data set has been considered for illustrative purpose of the study.Comment: 22,
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