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Register a new userMulticomponent stress strength reliability estimation for Pareto distribution based on upper record values
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Added by
Mohd Arshad
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
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No Arabic abstract
In this article, inferences about the multicomponent stress strength reliability are drawn under the assumption that strength and stress follow independent Pareto distribution with different shapes $(alpha_1,alpha_2)$ and common scale parameter $theta$. The maximum likelihood estimator, Bayes estimator under squared error and Linear exponential loss function, of multicomponent stress-strength reliability are constructed with corresponding highest posterior density interval for unknown $theta.$ For known $theta,$ uniformly minimum variance unbiased estimator and asymptotic distribution of multicomponent stress-strength reliability with asymptotic confidence interval is discussed. Also, various Bootstrap confidence intervals are constructed. A simulation study is conducted to numerically compare the performances of various estimators of multicomponent stress-strength reliability. Finally, a real life example is presented to show the applications of derived results in real life scenarios.
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Here in this paper, it is tried to obtain and compare the ML estimations based on upper record values and a random sample. In continue, some theorems have been proven about the behavior of these estimations asymptotically.
Here, in this paper it has been considered a sub family of exponential family. Maximum likelihood estimations (MLE) for the parameter of this family, probability density function, and cumulative density function based on a sample and based on lower record values have been obtained. It has been considered Mean Square Error (MSE) as a criterion for determining which is better in different situations. Additionally, it has been proved some theories about the relations between MLE based on lower record values and based on a random sample. Also, some interesting asymptotically properties for these estimations have been shown during some theories.
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We propose a modern method to estimate population size based on capture-recapture designs of K samples. The observed data is formulated as a sample of n i.i.d. K-dimensional vectors of binary indicators, where the k-th component of each vector indicates the subject being caught by the k-th sample, such that only subjects with nonzero capture vectors are observed. The target quantity is the unconditional probability of the vector being nonzero across both observed and unobserved subjects. We cover models assuming a single constraint (identification assumption) on the K-dimensional distribution such that the target quantity is identified and the statistical model is unrestricted. We present solutions for linear and non-linear constraints commonly assumed to identify capture-recapture models, including no K-way interaction in linear and log-linear models, independence or conditional independence. We demonstrate that the choice of constraint has a dramatic impact on the value of the estimand, showing that it is crucial that the constraint is known to hold by design. For the commonly assumed constraint of no K-way interaction in a log-linear model, the statistical target parameter is only defined when each of the $2^K - 1$ observable capture patterns is present, and therefore suffers from the curse of dimensionality. We propose a targeted MLE based on undersmoothed lasso model to smooth across the cells while targeting the fit towards the single valued target parameter of interest. For each identification assumption, we provide simulated inference and confidence intervals to assess the performance on the estimator under correct and incorrect identifying assumptions. We apply the proposed method, alongside existing estimators, to estimate prevalence of a parasitic infection using multi-source surveillance data from a region in southwestern China, under the four identification assumptions.
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